1 00:00:00,070 --> 00:00:01,780 The following content is provided 2 00:00:01,780 --> 00:00:04,030 under a Creative Commons license. 3 00:00:04,030 --> 00:00:06,880 Your support will help MIT OpenCourseWare continue 4 00:00:06,880 --> 00:00:10,740 to offer high quality educational resources for free. 5 00:00:10,740 --> 00:00:13,350 To make a donation or view additional materials 6 00:00:13,350 --> 00:00:17,260 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,260 --> 00:00:17,885 at ocw.mit.edu. 8 00:00:21,250 --> 00:00:27,650 PROFESSOR: So this first lecture is a spirited but lighthearted 9 00:00:27,650 --> 00:00:30,860 introduction into the course. 10 00:00:30,860 --> 00:00:33,320 I usually never talk about technicalities first. 11 00:00:33,320 --> 00:00:36,520 I want to talk about the excitement of the field first. 12 00:00:36,520 --> 00:00:39,420 So I will talk about technicalities a little bit 13 00:00:39,420 --> 00:00:40,460 later. 14 00:00:40,460 --> 00:00:44,190 So when you take a course in AMO physics, 15 00:00:44,190 --> 00:00:47,450 the obvious question is, what is AMO physics? 16 00:00:49,970 --> 00:00:54,870 What defines our field? 17 00:00:54,870 --> 00:00:59,800 Actually, by far the best definition 18 00:00:59,800 --> 00:01:07,650 of what AMO physics is-- it is what AMO physicists do, 19 00:01:07,650 --> 00:01:15,420 which is defined by a community of AMO researchers. 20 00:01:15,420 --> 00:01:18,460 And this is really characteristic for our field. 21 00:01:18,460 --> 00:01:20,660 I will tell you in the next 10 minutes 22 00:01:20,660 --> 00:01:24,150 or so about these enormous dynamics of the field, how 23 00:01:24,150 --> 00:01:28,500 AMO physics has changed in a fraction of my lifetime. 24 00:01:28,500 --> 00:01:33,174 And what happened is, I felt, whatever I was doing-- 25 00:01:33,174 --> 00:01:35,090 and it turned out to be very different of what 26 00:01:35,090 --> 00:01:37,460 I did 10 and 15 and 20 years ago-- has 27 00:01:37,460 --> 00:01:39,880 stayed in the center of AMO physics. 28 00:01:39,880 --> 00:01:41,990 So myself and the whole community, 29 00:01:41,990 --> 00:01:45,040 we're moving, and took the field along. 30 00:01:45,040 --> 00:01:49,740 So therefore AMO physics is what gets AMO researchers excited. 31 00:01:49,740 --> 00:01:50,460 It's not a joke. 32 00:01:50,460 --> 00:01:53,240 It's the way it sort of happened. 33 00:01:53,240 --> 00:01:56,610 Well, a little bit more mechanically, 34 00:01:56,610 --> 00:01:59,060 we can define AMO physics. 35 00:01:59,060 --> 00:02:02,360 AMO physics is what is made out of the building 36 00:02:02,360 --> 00:02:05,700 blocks we have in AMO physics. 37 00:02:05,700 --> 00:02:08,930 So defined by the building blocks. 38 00:02:08,930 --> 00:02:16,070 And in AMO physics, we build systems 39 00:02:16,070 --> 00:02:24,020 out of atoms, or molecules, and then photons, 40 00:02:24,020 --> 00:02:29,460 or light, and in general, electromagnetic fields-- 41 00:02:29,460 --> 00:02:33,070 electric, magnetic fields, microwaves and all this. 42 00:02:33,070 --> 00:02:36,420 So in other words, everything which is interesting 43 00:02:36,420 --> 00:02:39,990 and we can put together with those building blocks, 44 00:02:39,990 --> 00:02:41,830 this is AMO physics now. 45 00:02:41,830 --> 00:02:46,210 And this may redefine AMO physics in the future. 46 00:02:46,210 --> 00:02:53,740 Now, historically this meant that those building blocks, 47 00:02:53,740 --> 00:03:00,830 atoms and molecules, were available in the gas phase. 48 00:03:00,830 --> 00:03:03,550 So you had gases of atoms, gases of molecules, 49 00:03:03,550 --> 00:03:05,730 and you studied them. 50 00:03:05,730 --> 00:03:10,720 And almost all of AMO physics was actually 51 00:03:10,720 --> 00:03:17,780 about individual particles, individual atoms, 52 00:03:17,780 --> 00:03:21,500 individual molecules, because in the gas phase 53 00:03:21,500 --> 00:03:23,755 at high temperature, pretty much, 54 00:03:23,755 --> 00:03:25,840 you learned that in statistical mechanics 55 00:03:25,840 --> 00:03:28,040 each particle is by itself. 56 00:03:28,040 --> 00:03:30,750 And the partition function of the whole system 57 00:03:30,750 --> 00:03:32,940 is just factorized into partition functions 58 00:03:32,940 --> 00:03:34,860 of the individual particles. 59 00:03:34,860 --> 00:03:38,780 Well, maybe with some exception-- occasionally, 60 00:03:38,780 --> 00:03:40,190 particles collide. 61 00:03:40,190 --> 00:03:42,950 And the field of collisions-- collisions 62 00:03:42,950 --> 00:03:45,520 between atoms and atoms, atoms and ions, atoms 63 00:03:45,520 --> 00:03:48,630 and molecules, molecules and photons-- this 64 00:03:48,630 --> 00:03:52,900 was widely started in AMO physics. 65 00:03:52,900 --> 00:03:59,346 Well, now the field has really moved away 66 00:03:59,346 --> 00:04:02,714 from just individual particles and collisions 67 00:04:02,714 --> 00:04:03,630 between two particles. 68 00:04:06,140 --> 00:04:09,970 What is in the center of attention is few body physics. 69 00:04:14,040 --> 00:04:17,130 And that of course takes us to entanglement. 70 00:04:21,690 --> 00:04:24,000 For instance, people study entanglement 71 00:04:24,000 --> 00:04:26,430 of eight ions in ion traps. 72 00:04:26,430 --> 00:04:28,210 And of course this is deeply related 73 00:04:28,210 --> 00:04:29,555 to quantum information science. 74 00:04:32,080 --> 00:04:38,450 Or if you want to go from few body to many body, 75 00:04:38,450 --> 00:04:42,230 this is now starting to overlap with condensed matter physics. 76 00:04:42,230 --> 00:04:48,650 And this is now widely studied in the field of [INAUDIBLE] 77 00:04:48,650 --> 00:04:50,535 atoms and quantum gases. 78 00:04:55,760 --> 00:05:05,310 Now, when we talk about many body physics, 79 00:05:05,310 --> 00:05:11,235 we get, of course, into overlap with condensed matter physics. 80 00:05:14,810 --> 00:05:18,010 In condensed, I would actually say now 81 00:05:18,010 --> 00:05:21,750 a larger fraction of AMO physics and condensed matter physics 82 00:05:21,750 --> 00:05:25,140 overlap strongly, that we speak the same language, 83 00:05:25,140 --> 00:05:28,900 we study the same Hamiltonian, a lot of theorists 84 00:05:28,900 --> 00:05:33,760 apply the same methods to topics coming from either field. 85 00:05:33,760 --> 00:05:38,530 However, often in technology, how the systems are studied, 86 00:05:38,530 --> 00:05:41,090 there's a different culture, different tradition, 87 00:05:41,090 --> 00:05:43,040 and still two different communities. 88 00:05:46,210 --> 00:05:50,410 And the overlap comes about because there 89 00:05:50,410 --> 00:05:53,350 are systems in nature which you can 90 00:05:53,350 --> 00:06:01,050 say-- they are natural two or few level systems. 91 00:06:04,330 --> 00:06:08,260 Of course, we've helped nature a little bit by engineering. 92 00:06:08,260 --> 00:06:15,200 Those systems are, for instance, quantum dots or NV centers 93 00:06:15,200 --> 00:06:15,810 in diamond. 94 00:06:26,840 --> 00:06:29,750 Or another overlap with condensed matter physics 95 00:06:29,750 --> 00:06:36,030 is that AMO physics is now-- one frontier of AMO physics 96 00:06:36,030 --> 00:06:40,815 is the optical control of mechanical oscillators. 97 00:06:43,330 --> 00:06:49,190 Micro cantilevers, membranes, tiny mirrors in cavities, 98 00:06:49,190 --> 00:06:50,610 they have mechanical motion. 99 00:06:50,610 --> 00:06:52,670 And the mechanical motion is strongly 100 00:06:52,670 --> 00:06:55,271 coupled to the photon field. 101 00:06:55,271 --> 00:06:58,460 Of course, for fundamental AMO physicists, 102 00:06:58,460 --> 00:07:01,359 a mechanical oscillator is nothing else 103 00:07:01,359 --> 00:07:02,525 than an harmonic oscillator. 104 00:07:08,260 --> 00:07:13,760 So one can say-- and this is sort of my third attempt 105 00:07:13,760 --> 00:07:17,780 in defining for you what AMO physics is-- 106 00:07:17,780 --> 00:07:28,205 AMO physics is almost defining itself by low energy quantum 107 00:07:28,205 --> 00:07:30,440 physics. 108 00:07:30,440 --> 00:07:33,340 So all of the quantum mechanics which doesn't take place 109 00:07:33,340 --> 00:07:36,550 at giga and tera electron volt, which takes place 110 00:07:36,550 --> 00:07:39,656 at low energy, this is AMO physics. 111 00:07:39,656 --> 00:07:42,410 Of course, maybe not all of it. 112 00:07:42,410 --> 00:07:44,320 Usually when it is in [INAUDIBLE] solution, 113 00:07:44,320 --> 00:07:45,930 it's biophysics, and it's distinctly 114 00:07:45,930 --> 00:07:47,550 different from AMO physics. 115 00:07:47,550 --> 00:07:50,730 Or if the solid state is involved, 116 00:07:50,730 --> 00:07:52,830 then it's more condensed matter physics. 117 00:07:52,830 --> 00:07:55,850 But I would say there is one part of solid state physics 118 00:07:55,850 --> 00:07:57,800 which is already becoming interdisciplinary 119 00:07:57,800 --> 00:07:59,260 with AMO physics. 120 00:07:59,260 --> 00:08:06,390 And this is when the control of the system 121 00:08:06,390 --> 00:08:09,470 is not done by wires and carbon probes 122 00:08:09,470 --> 00:08:12,470 but it is done by lasers. 123 00:08:12,470 --> 00:08:14,780 So if you have a solid state system 124 00:08:14,780 --> 00:08:17,500 and you use all of the methods you apply to atoms, 125 00:08:17,500 --> 00:08:19,340 you use electromagnetically-induced 126 00:08:19,340 --> 00:08:22,930 transparency, coherence, all those concepts, 127 00:08:22,930 --> 00:08:25,410 then AMO physicists feel at home and they 128 00:08:25,410 --> 00:08:28,740 don't care if the two level system or the harmonic 129 00:08:28,740 --> 00:08:32,760 oscillator is an ion oscillating in an ion trap 130 00:08:32,760 --> 00:08:34,419 or whether it's a small cantilever, 131 00:08:34,419 --> 00:08:36,010 the methods and concepts are the same. 132 00:08:38,590 --> 00:08:42,110 So therefore, one could say AMO physics 133 00:08:42,110 --> 00:08:46,580 is sort of the playground where we can work on extensions 134 00:08:46,580 --> 00:08:51,940 of simple systems which we understand and cherish. 135 00:08:51,940 --> 00:08:55,390 And of course, our exactly solvable problems 136 00:08:55,390 --> 00:08:59,847 are the hydrogen atom-- my colleague, Dan Kepner, 137 00:08:59,847 --> 00:09:01,555 would have said, maybe the hydrogen atom, 138 00:09:01,555 --> 00:09:03,055 if you understand the hydrogen atom, 139 00:09:03,055 --> 00:09:05,540 you understand all of atomic physics. 140 00:09:05,540 --> 00:09:06,950 I'm not so sure. 141 00:09:06,950 --> 00:09:10,240 I would actually say, in addition to the hydrogen atom, 142 00:09:10,240 --> 00:09:12,990 you have to know the two-level system. 143 00:09:12,990 --> 00:09:15,370 And of course, you have to understand the harmonic 144 00:09:15,370 --> 00:09:16,340 oscillator. 145 00:09:16,340 --> 00:09:19,340 So these are three paradigmatic Hamiltonians, 146 00:09:19,340 --> 00:09:25,870 and a lot of understanding of much more complicated systems 147 00:09:25,870 --> 00:09:30,980 really comes from taking the best features of those three 148 00:09:30,980 --> 00:09:32,220 systems and combining them. 149 00:09:35,280 --> 00:09:37,440 If you have questions or comments, 150 00:09:37,440 --> 00:09:38,770 this is an interactive class. 151 00:09:38,770 --> 00:09:41,850 Feel free to speak out or interrupt me. 152 00:09:44,570 --> 00:09:51,650 OK so, now we know, or we don't know, what AMO physics is. 153 00:09:51,650 --> 00:09:57,255 Let me now address-- how has AMO physics developed? 154 00:10:04,200 --> 00:10:07,720 And I mentioned to you that AMO physics 155 00:10:07,720 --> 00:10:14,590 has done breathtaking evolution in my lifetime, 156 00:10:14,590 --> 00:10:18,000 or even in the shorter part of my life, 157 00:10:18,000 --> 00:10:20,060 which is my research career. 158 00:10:20,060 --> 00:10:27,450 Well, traditionally, almost all fields in science 159 00:10:27,450 --> 00:10:30,780 started with observing nature. 160 00:10:33,740 --> 00:10:37,740 The pursuit of science was born out of human curiosity 161 00:10:37,740 --> 00:10:40,350 to understand the world around us. 162 00:10:40,350 --> 00:10:43,090 And atomic physicists, well, they 163 00:10:43,090 --> 00:10:48,330 started to observe atoms and molecules, usually in the gas 164 00:10:48,330 --> 00:10:51,390 phase, and what they were doing. 165 00:10:51,390 --> 00:10:58,520 And already there was some evolution, 166 00:10:58,520 --> 00:11:02,780 because original observations at low resolution 167 00:11:02,780 --> 00:11:07,740 were taken to a completely new level when 168 00:11:07,740 --> 00:11:12,360 high-resolution methods were developed, when lasers came 169 00:11:12,360 --> 00:11:15,480 along, when people had light sources which had fantastic 170 00:11:15,480 --> 00:11:20,500 resolution and eventually finer and finer details 171 00:11:20,500 --> 00:11:25,100 of the structure of atoms and interactions between atoms 172 00:11:25,100 --> 00:11:27,980 were resolved. 173 00:11:27,980 --> 00:11:31,780 But AMO physics is a field which has 174 00:11:31,780 --> 00:11:35,640 taken the pursuit of science much further. 175 00:11:35,640 --> 00:11:39,110 So there is not just observation of nature-- 176 00:11:39,110 --> 00:11:41,930 and I want to write that with capital letters-- 177 00:11:41,930 --> 00:11:43,475 there is CONTROL OF NATURE. 178 00:11:46,380 --> 00:11:48,500 And you maybe take it for granted, 179 00:11:48,500 --> 00:11:50,200 but you should really appreciate it, 180 00:11:50,200 --> 00:11:54,850 that controlling nature, having control over what you study, 181 00:11:54,850 --> 00:11:58,130 modify it, advance it, take it to the next level, 182 00:11:58,130 --> 00:12:00,650 is really something wonderful. 183 00:12:00,650 --> 00:12:03,190 It is completely absent in certain fields, 184 00:12:03,190 --> 00:12:04,180 like astrophysics. 185 00:12:04,180 --> 00:12:07,880 In astrophysics, all you can do is, you can observe. 186 00:12:07,880 --> 00:12:12,700 In atomic physics, we create the objects we can observe. 187 00:12:12,700 --> 00:12:20,200 So the control of nature, the control of our atomic physics 188 00:12:20,200 --> 00:12:22,750 system, developed in stages. 189 00:12:26,230 --> 00:12:31,980 The first kind of control was exerted about internal states. 190 00:12:31,980 --> 00:12:35,810 If you have an atom at thermal energies, 191 00:12:35,810 --> 00:12:38,380 it would only come in hyperfine states which 192 00:12:38,380 --> 00:12:40,390 are thermally populated, or molecules 193 00:12:40,390 --> 00:12:44,640 come in rotation states, and well your limited control 194 00:12:44,640 --> 00:12:47,390 was simply to raise and lower the temperature. 195 00:12:47,390 --> 00:12:51,520 But with the advent of optical pumping-- this actually 196 00:12:51,520 --> 00:12:55,010 happened already with classical light sources 197 00:12:55,010 --> 00:12:57,440 before the invention of the laser-- so 198 00:12:57,440 --> 00:13:02,790 with optical pumping, you can pump the internal population 199 00:13:02,790 --> 00:13:06,690 of molecules into, let's say, a single rotational state. 200 00:13:06,690 --> 00:13:11,210 So this is control over the internal Hilbert space. 201 00:13:11,210 --> 00:13:16,360 And this was actually rewarded with a Nobel Prize 202 00:13:16,360 --> 00:13:21,630 to Alfred Kastler in 1966. 203 00:13:21,630 --> 00:13:24,390 Of course, the next step after controlling 204 00:13:24,390 --> 00:13:26,950 the internal degrees of freedom is 205 00:13:26,950 --> 00:13:30,600 have control over the external degrees of freedom, 206 00:13:30,600 --> 00:13:33,415 and this means control motion. 207 00:13:37,590 --> 00:13:40,800 This was of course pursued by understanding 208 00:13:40,800 --> 00:13:43,250 the mechanical aspect of light. 209 00:13:43,250 --> 00:13:48,120 How do photons mechanically interact with atoms? 210 00:13:48,120 --> 00:13:50,740 This eventually led to laser cooling 211 00:13:50,740 --> 00:13:53,270 and Bose-Einstein condensation. 212 00:13:53,270 --> 00:14:02,230 And those developments were recognized with major prizes. 213 00:14:02,230 --> 00:14:04,730 Well there is more to it than controlling 214 00:14:04,730 --> 00:14:09,150 internal and external degrees of freedom. 215 00:14:09,150 --> 00:14:13,560 You can then also say, well, how much can we 216 00:14:13,560 --> 00:14:16,890 control the number of building blocks? 217 00:14:16,890 --> 00:14:21,490 And eventually AMO physics advanced 218 00:14:21,490 --> 00:14:25,180 to exert control onto single quantum 219 00:14:25,180 --> 00:14:31,740 systems-- single photons, single atoms. 220 00:14:31,740 --> 00:14:35,070 A single atom in a cavity exchanging a photon 221 00:14:35,070 --> 00:14:38,980 with a cavity thousands of times. 222 00:14:38,980 --> 00:14:42,510 So this control of single quantum systems 223 00:14:42,510 --> 00:14:46,280 was actually just recognized with a Nobel Prize 224 00:14:46,280 --> 00:14:49,020 a few months ago. 225 00:14:49,020 --> 00:14:53,590 Well, at this point I sometimes make the joke, 226 00:14:53,590 --> 00:15:03,130 we have gone from big ensembles in many, many quantum states 227 00:15:03,130 --> 00:15:09,040 to single photons, single atoms, in a single quantum state-- 228 00:15:09,040 --> 00:15:10,810 a single quantum state for many particles 229 00:15:10,810 --> 00:15:14,250 is Bose-Einstein condensation. 230 00:15:14,250 --> 00:15:18,770 So we have really gone down to single atoms, single photons, 231 00:15:18,770 --> 00:15:20,550 single quantum states. 232 00:15:20,550 --> 00:15:23,260 Well, what comes next? 233 00:15:23,260 --> 00:15:27,090 To have no atoms and no light in vacuum. 234 00:15:27,090 --> 00:15:30,180 Well, the vacuum has some very interesting properties. 235 00:15:30,180 --> 00:15:32,520 And if you talk to Frank Wilczek, 236 00:15:32,520 --> 00:15:36,210 the nature of the vacuum and dark energy 237 00:15:36,210 --> 00:15:40,180 is one of the big mysteries in physics and in science 238 00:15:40,180 --> 00:15:41,080 in general. 239 00:15:41,080 --> 00:15:44,550 But the study of that is definitely 240 00:15:44,550 --> 00:15:47,850 outside the scope of AMO physics. 241 00:15:47,850 --> 00:15:51,370 So what happens is, when we have gone down and have now 242 00:15:51,370 --> 00:15:54,370 control over the building blocks, 243 00:15:54,370 --> 00:15:57,840 now we can sort of go up again in a controlled way, 244 00:15:57,840 --> 00:16:02,130 create complexity by assembling a few photons, 245 00:16:02,130 --> 00:16:07,080 a few atoms into new entangled states, 246 00:16:07,080 --> 00:16:11,670 so we can now take our system into very different regions 247 00:16:11,670 --> 00:16:13,790 of Hilbert space. 248 00:16:13,790 --> 00:16:18,930 So what is defining now the control is, 249 00:16:18,930 --> 00:16:22,180 we want to use this pristine control over the building 250 00:16:22,180 --> 00:16:27,500 blocks to now put in something which hasn't existed naturally 251 00:16:27,500 --> 00:16:32,520 before, or when it existed it was completely obscured, 252 00:16:32,520 --> 00:16:39,296 completely hidden by thermal motion or by you 253 00:16:39,296 --> 00:16:43,110 can say homogenous broadening our lack of control. 254 00:16:43,110 --> 00:16:45,080 And the best buzzwords are here now 255 00:16:45,080 --> 00:16:49,330 entanglement and many-body physics. 256 00:16:52,150 --> 00:16:59,176 It's hard to capture that as in a diagram, but let me try that. 257 00:16:59,176 --> 00:17:00,800 I don't know actually what I'm drawing, 258 00:17:00,800 --> 00:17:03,050 but I think you get the message that this 259 00:17:03,050 --> 00:17:05,579 is sort of Hilbert space. 260 00:17:05,579 --> 00:17:09,040 And I have 2 x's. 261 00:17:09,040 --> 00:17:14,569 One is sort of entropy, high temperature, 262 00:17:14,569 --> 00:17:18,869 and the other one is complexity. 263 00:17:18,869 --> 00:17:25,060 And for quite awhile, people studied hot gases. 264 00:17:25,060 --> 00:17:28,569 So these are gases, there's a lot of entropy in it. 265 00:17:28,569 --> 00:17:32,480 The complexity is actually not particularly high. 266 00:17:32,480 --> 00:17:38,470 And everything is described by a statistical operator-- 267 00:17:38,470 --> 00:17:39,285 the density matrix. 268 00:17:42,810 --> 00:17:46,710 The pursuit of cooling, and actually, 269 00:17:46,710 --> 00:17:50,680 control-- gaining information about a system 270 00:17:50,680 --> 00:17:51,910 is also a way of cooling. 271 00:17:51,910 --> 00:17:54,140 If you know in which state the atom is, 272 00:17:54,140 --> 00:17:56,110 the entropy of the system is zero 273 00:17:56,110 --> 00:17:58,670 even if you haven't changed the state of the atom. 274 00:17:58,670 --> 00:18:06,650 So control and cooling, control measurement and cooling, 275 00:18:06,650 --> 00:18:09,730 has now taken us to the point where 276 00:18:09,730 --> 00:18:12,190 we have systems which have no entropy anymore. 277 00:18:12,190 --> 00:18:15,690 They are very, very well defined. 278 00:18:15,690 --> 00:18:21,390 And our goal now is to take these systems 279 00:18:21,390 --> 00:18:26,440 to much more complexity where wave functions become entangled 280 00:18:26,440 --> 00:18:30,270 and we have strong correlations in many-body systems. 281 00:18:30,270 --> 00:18:34,880 But this is now, maybe here, this 282 00:18:34,880 --> 00:18:37,650 is now described by wave functions. 283 00:18:37,650 --> 00:18:42,290 But here is the wave function of a single particle, 284 00:18:42,290 --> 00:18:48,459 and here we have highly correlated, highly entangled 285 00:18:48,459 --> 00:18:49,500 many-body wave functions. 286 00:18:53,320 --> 00:18:58,120 So at least for me-- but all predictions 287 00:18:58,120 --> 00:19:00,440 are notoriously incorrect when you 288 00:19:00,440 --> 00:19:02,560 look at them in a few years from now-- 289 00:19:02,560 --> 00:19:06,360 but for me, this is where the future of our field 290 00:19:06,360 --> 00:19:11,570 is moving, to get into interesting regions of Hilbert 291 00:19:11,570 --> 00:19:14,655 space where no person has been before. 292 00:19:20,090 --> 00:19:25,880 As an experimentalist, and with a lot of experimental graduate 293 00:19:25,880 --> 00:19:30,540 students in this room, I want to emphasize 294 00:19:30,540 --> 00:19:35,650 that a lot of those rapid developments of the field 295 00:19:35,650 --> 00:19:36,925 are driven by technology. 296 00:19:41,190 --> 00:19:44,235 So it's driven by technology advances. 297 00:19:49,570 --> 00:19:51,900 In the '50s and early '60s, people 298 00:19:51,900 --> 00:19:56,380 thought AMO physics is pretty much dead. 299 00:19:56,380 --> 00:20:01,040 Only a few people with gray hair continue what they have done 300 00:20:01,040 --> 00:20:03,850 and the field will eventually die. 301 00:20:03,850 --> 00:20:10,750 But then technological developments 302 00:20:10,750 --> 00:20:14,370 made it possible to do major conceptual advances. 303 00:20:14,370 --> 00:20:16,910 I've mentioned the conceptual advances-- let me now 304 00:20:16,910 --> 00:20:21,550 say a few words about the technology which has driven it. 305 00:20:21,550 --> 00:20:26,200 There was one phase of developing lasers which 306 00:20:26,200 --> 00:20:28,310 I experienced when I was a student. 307 00:20:28,310 --> 00:20:30,630 But those lasers were fantastic. 308 00:20:30,630 --> 00:20:33,720 They were very narrow already, very stable, 309 00:20:33,720 --> 00:20:37,260 but they were very expensive and very complicated. 310 00:20:37,260 --> 00:20:40,850 So if you had one laser, this defined your laboratory 311 00:20:40,850 --> 00:20:42,420 and then you studied a lot of things 312 00:20:42,420 --> 00:20:45,800 with the single laser you could afford. 313 00:20:45,800 --> 00:20:50,740 Well, you're probably not used to one big dye 314 00:20:50,740 --> 00:20:53,540 laser pumped with a big argon ion laser. 315 00:20:53,540 --> 00:20:57,230 It was a $250,000 investment for the lab. 316 00:20:57,230 --> 00:21:01,000 And of course, you couldn't afford a second laser. 317 00:21:01,000 --> 00:21:06,270 It required 50 kilowatts pf electrical power. 318 00:21:06,270 --> 00:21:08,620 And all this power had to be cooled away 319 00:21:08,620 --> 00:21:11,620 by gushing water through thick pipes. 320 00:21:11,620 --> 00:21:13,720 So it was an expensive undertaking 321 00:21:13,720 --> 00:21:18,680 but you could really do wonderful science with it. 322 00:21:18,680 --> 00:21:21,010 So what I've seen in the last 20 years 323 00:21:21,010 --> 00:21:25,670 is the proliferation of solid state lasers, 324 00:21:25,670 --> 00:21:29,930 starting with diode lasers and continuing 325 00:21:29,930 --> 00:21:32,140 until the present year. 326 00:21:32,140 --> 00:21:35,530 So now, in a lot of our laboratories here at MIT, 327 00:21:35,530 --> 00:21:36,350 we have 10 lasers. 328 00:21:36,350 --> 00:21:38,990 And we've stopped counting them, because adding a laser 329 00:21:38,990 --> 00:21:41,340 to the system is almost like adding 330 00:21:41,340 --> 00:21:48,130 an amplifier to a circuit or adding another circuit 331 00:21:48,130 --> 00:21:51,510 to a data acquisition system. 332 00:21:51,510 --> 00:21:56,360 But it's not just the simplicity of the lasers 333 00:21:56,360 --> 00:21:58,080 which we have now, the robustness-- 334 00:21:58,080 --> 00:22:00,770 to have 10 lasers in the lab, it's fine. 335 00:22:00,770 --> 00:22:02,990 Previously, if you had three lasers in the lab, 336 00:22:02,990 --> 00:22:06,240 you spent 90% of your time just keeping the lasers running. 337 00:22:06,240 --> 00:22:11,190 Those lasers, not so much continuous-wave lasers, 338 00:22:11,190 --> 00:22:15,840 but pulse lasers have also very, very different properties. 339 00:22:15,840 --> 00:22:24,520 Laser pulses got very, very short-- femtosecond 340 00:22:24,520 --> 00:22:27,280 or even attosecond. 341 00:22:27,280 --> 00:22:33,720 Shorter pulses means that the energy is now 342 00:22:33,720 --> 00:22:37,570 focused to a much shorter temporal window. 343 00:22:37,570 --> 00:22:41,360 Therefore, laser pulses of very, very high intensity-- 344 00:22:41,360 --> 00:22:45,250 if you focus a short pulse laser on an atomic system, 345 00:22:45,250 --> 00:22:48,600 you can easily reach an electric field 346 00:22:48,600 --> 00:22:51,985 of the laser which is stronger than the electric field 347 00:22:51,985 --> 00:22:53,240 of the atom. 348 00:22:53,240 --> 00:22:56,490 So in other words, if you have protons and electrons-- well, 349 00:22:56,490 --> 00:22:59,290 maybe the outer electrons, not get down to the single protons. 350 00:22:59,290 --> 00:23:03,200 But maybe an ionic core, and you've electrons. 351 00:23:03,200 --> 00:23:06,590 Now, you should first look at the motion of free electrons 352 00:23:06,590 --> 00:23:09,981 in the strong field of the laser and add the atomic structure 353 00:23:09,981 --> 00:23:10,730 as a perturbation. 354 00:23:10,730 --> 00:23:17,520 It really takes the hierarchy of effects upside down. 355 00:23:17,520 --> 00:23:23,960 So the appearance of high intensity lasers 356 00:23:23,960 --> 00:23:28,560 has given rise to a whole new field of atomic physics. 357 00:23:28,560 --> 00:23:30,190 Lasers got more precise. 358 00:23:33,450 --> 00:23:37,660 The invention of the frequency combs, 359 00:23:37,660 --> 00:23:40,700 recognized by the Nobel Prize in 2005, 360 00:23:40,700 --> 00:23:48,070 meant now that we can control laser frequencies 361 00:23:48,070 --> 00:23:51,700 at a level of 10 to the minus 17. 362 00:23:51,700 --> 00:23:59,880 And this has completely redefined precision metrology 363 00:23:59,880 --> 00:24:05,974 and has advanced the control over atoms and molecules 364 00:24:05,974 --> 00:24:06,890 I've mentioned before. 365 00:24:10,640 --> 00:24:14,220 Finally, another technical development 366 00:24:14,220 --> 00:24:19,260 which plays a major role in research being pursued here 367 00:24:19,260 --> 00:24:22,530 at MIT and elsewhere are the development 368 00:24:22,530 --> 00:24:25,440 of high finesse cavities. 369 00:24:25,440 --> 00:24:28,005 High finesse cavities in the microwave range-- 370 00:24:28,005 --> 00:24:30,240 then they're superconducting-- or high 371 00:24:30,240 --> 00:24:34,670 finesse optical cavities by having super mirrors. 372 00:24:34,670 --> 00:24:37,910 It is actually those super cavities 373 00:24:37,910 --> 00:24:43,910 which have enabled the study of single photon physics. 374 00:24:43,910 --> 00:24:47,080 Because after all, photons move away with the speed of light. 375 00:24:47,080 --> 00:24:50,110 And if you want to observe a photon in your laboratory, 376 00:24:50,110 --> 00:24:52,850 it has to bounce around zillions of times 377 00:24:52,850 --> 00:24:55,619 in order to have enough time for the photon 378 00:24:55,619 --> 00:24:56,785 to do something interesting. 379 00:25:18,780 --> 00:25:25,110 So sometimes a field at the frontier of science 380 00:25:25,110 --> 00:25:31,500 is defined by paradigms. 381 00:25:31,500 --> 00:25:39,840 If you want to explain to somebody why 382 00:25:39,840 --> 00:25:44,020 your field of interest is cool and exciting, 383 00:25:44,020 --> 00:25:48,320 you usually do it by picking a few really exciting examples. 384 00:25:48,320 --> 00:25:57,220 And I want to show you how, over the years, it has advanced. 385 00:25:57,220 --> 00:26:00,320 Definitely in the '50s and '60s, you 386 00:26:00,320 --> 00:26:05,730 would have mentioned that we understand now atomic structure 387 00:26:05,730 --> 00:26:09,750 of multi-electron atoms. 388 00:26:09,750 --> 00:26:11,780 Optical pumping just started. 389 00:26:11,780 --> 00:26:15,735 So these were flagship developments of AMO science. 390 00:26:18,310 --> 00:26:20,850 The cool thing to do in the '60s and '80s 391 00:26:20,850 --> 00:26:25,380 was, use the new tool, the laser, applied to atoms 392 00:26:25,380 --> 00:26:28,740 and do laser spectroscopy. 393 00:26:28,740 --> 00:26:32,150 Sub-doppler spectroscopy, sub-natural spectroscopy, 394 00:26:32,150 --> 00:26:34,050 resolving hyperfine structure-- wow. 395 00:26:34,050 --> 00:26:36,400 I mean, this was really exciting in those days. 396 00:26:42,660 --> 00:26:46,250 And well, the older people I have met, 397 00:26:46,250 --> 00:26:48,790 my teachers, my thesis adviser, these 398 00:26:48,790 --> 00:26:51,840 were people who started their research career 399 00:26:51,840 --> 00:26:54,100 before the laser was invented but then, 400 00:26:54,100 --> 00:26:57,170 as a young researcher, embraced this new tool 401 00:26:57,170 --> 00:26:58,870 and helped to redefine the field. 402 00:27:02,550 --> 00:27:08,140 Definitely in the '80s and '90s, the cool pictures 403 00:27:08,140 --> 00:27:10,910 were those of magneto-optical traps, 404 00:27:10,910 --> 00:27:14,280 atoms standing still and hovering around. 405 00:27:14,280 --> 00:27:21,590 So the new aspect where mechanical forces 406 00:27:21,590 --> 00:27:27,860 of light which led to laser cooling and trapped atoms. 407 00:27:30,450 --> 00:27:34,490 In the late '90s, of course, the excitement 408 00:27:34,490 --> 00:27:37,280 was about Bose-Einstein condensation. 409 00:27:37,280 --> 00:27:40,240 And it was really Bose-Einstein condensation 410 00:27:40,240 --> 00:27:46,360 which drove AMO physics from single atoms, maybe 411 00:27:46,360 --> 00:27:48,860 two atoms colliding, to many-body physics. 412 00:27:53,160 --> 00:27:57,530 It's always easier to analyze those things 413 00:27:57,530 --> 00:28:01,440 by looking backward, so if I'm now getting closer to the past, 414 00:28:01,440 --> 00:28:03,760 I have to be a little bit vague. 415 00:28:03,760 --> 00:28:12,010 But in the 2000s, I think hot topics were ultracold fermions 416 00:28:12,010 --> 00:28:18,925 and the study of entanglement and correlations. 417 00:28:25,290 --> 00:28:31,340 And what is the paradigm now or in the near future? 418 00:28:31,340 --> 00:28:34,940 Well, I think you have to help to define it. 419 00:28:34,940 --> 00:28:37,070 If you make an interesting discovery, 420 00:28:37,070 --> 00:28:40,520 this is what people will be pointing to and would say, 421 00:28:40,520 --> 00:28:44,740 this is what now defines AMO physics. 422 00:28:44,740 --> 00:28:47,510 Some candidates are, of course, if there 423 00:28:47,510 --> 00:28:51,306 is a major breakthrough in quantum computation-- 424 00:28:51,306 --> 00:28:56,200 let me put question marks here. 425 00:28:56,200 --> 00:29:01,220 In the field called atom science, 426 00:29:01,220 --> 00:29:06,810 we may actually do some progress towards topological states 427 00:29:06,810 --> 00:29:10,500 which have different symmetries and different properties. 428 00:29:10,500 --> 00:29:16,570 And another emerging frontier is micro-mechanical oscillators. 429 00:29:20,480 --> 00:29:22,100 The last couple of years, we just 430 00:29:22,100 --> 00:29:24,430 had the breakthrough for the first time. 431 00:29:24,430 --> 00:29:28,700 Mechanical objects were cooled to the absolute ground state. 432 00:29:28,700 --> 00:29:32,850 So at least for that community it was, but for many of us, 433 00:29:32,850 --> 00:29:35,660 Bose-Einstein condensation was 15 years ago. 434 00:29:43,420 --> 00:29:44,045 Any questions? 435 00:29:50,360 --> 00:29:53,810 Well, eventually we have to talk about this course. 436 00:30:02,430 --> 00:30:06,845 So I've told you about, at least, 437 00:30:06,845 --> 00:30:10,730 a snapshot of where AMO physics is, how it has developed, 438 00:30:10,730 --> 00:30:12,510 and on what trajectory it is. 439 00:30:15,850 --> 00:30:29,830 In this course I want to present you the concepts behind many 440 00:30:29,830 --> 00:30:31,900 of the major advances in the field. 441 00:30:35,280 --> 00:30:39,390 So over the years, quite often a topic was added to the course, 442 00:30:39,390 --> 00:30:41,700 because I felt, hey, that's getting really exciting, 443 00:30:41,700 --> 00:30:43,741 that's what people want to do in research, that's 444 00:30:43,741 --> 00:30:45,500 what graduate students want to do here. 445 00:30:45,500 --> 00:30:49,330 And then the subject was added and other subjects 446 00:30:49,330 --> 00:30:51,050 were dropped. 447 00:30:51,050 --> 00:30:54,010 I know in the '90s, I was teaching aspects of laser 448 00:30:54,010 --> 00:30:56,320 cooling, sub recoil laser cooling, 449 00:30:56,320 --> 00:30:57,830 which was the latest excitement. 450 00:31:00,500 --> 00:31:04,580 This year, I may mention it for 30 seconds. 451 00:31:04,580 --> 00:31:07,060 So the course has evolved. 452 00:31:07,060 --> 00:31:10,780 It wants to stay connected to what is exciting, what is hot, 453 00:31:10,780 --> 00:31:13,890 and what prepares you for research at the frontier. 454 00:31:18,244 --> 00:31:25,820 8.422, the second part of the two-course cycle 455 00:31:25,820 --> 00:31:28,460 in the graduate course in AMO physics, 456 00:31:28,460 --> 00:31:32,740 is somewhat different, not radically different, 457 00:31:32,740 --> 00:31:40,790 but is somewhat different from part one, from 8.421. 458 00:31:40,790 --> 00:31:47,190 First of all, 8.421, 8.422 can be taken out of sequence. 459 00:31:47,190 --> 00:31:51,360 We alternate between AMO 1 and AMO 2. 460 00:31:51,360 --> 00:31:54,086 And whenever you enter MIT, you're 461 00:31:54,086 --> 00:31:55,460 probably in your second semester, 462 00:31:55,460 --> 00:31:57,380 take whatever we offer. 463 00:31:57,380 --> 00:32:01,966 So I expect-- let me ask you, who of you has taken AMO 1? 464 00:32:01,966 --> 00:32:04,340 Yes, statistically, it should be about half of the class. 465 00:32:07,150 --> 00:32:11,680 It can be taken out of sequence because that's 466 00:32:11,680 --> 00:32:13,260 the way how we've structured it. 467 00:32:13,260 --> 00:32:16,810 But to give you one example is, in 8.421 468 00:32:16,810 --> 00:32:18,940 you really have to learn about hyperfine structure. 469 00:32:18,940 --> 00:32:19,903 You have to learn about atoms, you 470 00:32:19,903 --> 00:32:21,736 have to learn about Lamb shift and all that. 471 00:32:21,736 --> 00:32:25,070 So you have to learn what all these atomic levels are. 472 00:32:25,070 --> 00:32:28,250 And here in that course, in 8.422, I will say, 473 00:32:28,250 --> 00:32:30,420 here's a two-level system and then I run with that. 474 00:32:30,420 --> 00:32:32,290 And we do all sort of entanglement, 475 00:32:32,290 --> 00:32:34,660 manipulation of two-level systems. 476 00:32:34,660 --> 00:32:38,390 So it helps you if you know where those two levels come 477 00:32:38,390 --> 00:32:42,230 from, but you don't really need the detailed knowledge 478 00:32:42,230 --> 00:32:44,950 of atomic structure, for instance, to understand that. 479 00:32:44,950 --> 00:32:47,780 So this is why the different parts of the course 480 00:32:47,780 --> 00:32:52,250 are connected, but in terms of learning the material, somewhat 481 00:32:52,250 --> 00:32:53,860 decoupled. 482 00:32:53,860 --> 00:32:55,860 I've spoken to many students who said 483 00:32:55,860 --> 00:32:59,410 there was no problem in starting with 8.422. 484 00:32:59,410 --> 00:33:02,980 The only sort of critical comment I've heard 485 00:33:02,980 --> 00:33:09,430 is that taking 8.422 first and then 8.421 is anti-climactic. 486 00:33:09,430 --> 00:33:11,900 You see all this excitement in the modern physics, 487 00:33:11,900 --> 00:33:14,565 and then, eventually, you have to work on the foundation. 488 00:33:20,230 --> 00:33:25,050 Prerequisites for this course-- the course announcement 489 00:33:25,050 --> 00:33:27,500 said 8.05. 490 00:33:27,500 --> 00:33:31,120 It is actually 8.05 and 8.06. 491 00:33:31,120 --> 00:33:33,780 The main part of 8.06 which we really need here 492 00:33:33,780 --> 00:33:37,430 is perturbation theory-- time independent, time 493 00:33:37,430 --> 00:33:39,690 dependent perturbation theory, and this is usually 494 00:33:39,690 --> 00:33:42,570 covered in 8.06. 495 00:33:42,570 --> 00:33:46,390 However, I've had students who took the course without 8.06. 496 00:33:46,390 --> 00:33:48,450 If you're really determined and want 497 00:33:48,450 --> 00:33:51,476 to acquire certain things by self-study, 498 00:33:51,476 --> 00:33:52,600 you can follow this course. 499 00:33:56,740 --> 00:34:11,540 So the topics we will cover include QED. 500 00:34:14,860 --> 00:34:21,639 I really want to talk about light-atom interactions 501 00:34:21,639 --> 00:34:25,070 from first principles. 502 00:34:25,070 --> 00:34:29,530 Sure, 95% of what we're doing is just 503 00:34:29,530 --> 00:34:31,570 done by saying we have a matrix element, which 504 00:34:31,570 --> 00:34:33,429 maybe the dipole matrix element. 505 00:34:33,429 --> 00:34:38,560 But you really have to know what are the approximations, what 506 00:34:38,560 --> 00:34:43,159 are the conditions, which lead to the dipole approximation. 507 00:34:43,159 --> 00:34:45,710 And I want to do that from first principles, 508 00:34:45,710 --> 00:34:47,590 and we do that starting on Monday. 509 00:34:50,179 --> 00:35:04,720 So a discussion of light-atom interaction has two parts. 510 00:35:04,720 --> 00:35:07,950 One is the simple part-- excitation and stimulated 511 00:35:07,950 --> 00:35:09,080 emission. 512 00:35:09,080 --> 00:35:13,420 Because this can be simply described by a unitary time 513 00:35:13,420 --> 00:35:19,430 evolution, and you can do a lot, if not everything, 514 00:35:19,430 --> 00:35:22,500 by using Schroedinger's equation. 515 00:35:22,500 --> 00:35:28,180 Things get much more complicated and richer 516 00:35:28,180 --> 00:35:35,000 if you include spontaneous emission or, more generally, 517 00:35:35,000 --> 00:35:39,060 if you include dissipation. 518 00:35:39,060 --> 00:35:40,895 Then we talk about open systems. 519 00:35:44,180 --> 00:35:47,490 And for fundamental reasons, we need a formulation 520 00:35:47,490 --> 00:35:50,620 using the density matrix, a statistical operator, 521 00:35:50,620 --> 00:35:51,740 and a master equation. 522 00:35:56,480 --> 00:36:01,740 One major part of the course is discussion and [INAUDIBLE] 523 00:36:01,740 --> 00:36:05,470 derivation of the mechanical forces of light. 524 00:36:11,870 --> 00:36:15,170 This will include a discussion of 525 00:36:15,170 --> 00:36:19,040 important experimental techniques using 526 00:36:19,040 --> 00:36:20,830 those mechanical forces. 527 00:36:20,830 --> 00:36:26,530 So various simple and sophisticated methods 528 00:36:26,530 --> 00:36:27,550 of trapping and cooling. 529 00:36:31,450 --> 00:36:36,820 We will spend some time in not talking about atoms at all. 530 00:36:36,820 --> 00:36:42,490 We're just going to talk about photons, about single photons. 531 00:36:42,490 --> 00:36:46,150 We want to understand where the photon nature of light 532 00:36:46,150 --> 00:36:48,390 makes light very, very different from 533 00:36:48,390 --> 00:36:50,360 a classical electromagnetic wave. 534 00:36:52,940 --> 00:36:57,510 Also, it's not the focus, we will 535 00:36:57,510 --> 00:37:04,080 come across basic building blocks of quantum information 536 00:37:04,080 --> 00:37:05,450 science. 537 00:37:05,450 --> 00:37:08,060 Pretty much when atoms and photons interact, 538 00:37:08,060 --> 00:37:10,880 this is a fundamental quantum gate. 539 00:37:13,440 --> 00:37:16,070 And we'll talk about the many-body physics 540 00:37:16,070 --> 00:37:17,295 off quantum gases. 541 00:37:23,480 --> 00:37:29,890 So maybe it becomes clearer what we 542 00:37:29,890 --> 00:37:35,860 are covering by saying what we are not covering. 543 00:37:39,260 --> 00:37:41,820 And this tells you that there is at least 544 00:37:41,820 --> 00:37:43,400 some selection of topics. 545 00:37:43,400 --> 00:37:46,120 It's not that we talk about everything. 546 00:37:46,120 --> 00:37:52,780 We will not talk about the physics above 10 electron 547 00:37:52,780 --> 00:37:53,280 volts. 548 00:37:55,980 --> 00:37:58,470 We will not talk about collisions-- 549 00:37:58,470 --> 00:38:01,515 or maybe I should say, high-energy collisions. 550 00:38:05,594 --> 00:38:09,560 We will, of course, talk about nanokelvin collisions, which 551 00:38:09,560 --> 00:38:11,290 is the physics of the scattering links 552 00:38:11,290 --> 00:38:13,830 and some s-wave collisions which are really 553 00:38:13,830 --> 00:38:15,950 relevant to understand quantum gases. 554 00:38:20,050 --> 00:38:23,120 We're not talking about any advanced topic 555 00:38:23,120 --> 00:38:24,015 in atomic structure. 556 00:38:26,910 --> 00:38:30,630 All we do about atomic structure is done in 8.421. 557 00:38:30,630 --> 00:38:34,980 And if you want to graduate in atomic physics at MIT, 558 00:38:34,980 --> 00:38:37,890 yes, you have to understand atomic structure 559 00:38:37,890 --> 00:38:39,940 at the level of the hydrogen atom. 560 00:38:39,940 --> 00:38:42,740 And maybe know a little bit about a new phenomena-- 561 00:38:42,740 --> 00:38:45,695 when another electron enters, when electrons interact 562 00:38:45,695 --> 00:38:49,520 and that's a helium atom-- but we're not going beyond it. 563 00:38:49,520 --> 00:38:53,950 Let me just mention here that there is, of course, 564 00:38:53,950 --> 00:38:56,510 more interesting things in atomic structure. 565 00:38:56,510 --> 00:39:02,000 For instance, if you go to highly charged ions, 566 00:39:02,000 --> 00:39:04,330 you have QED effects. 567 00:39:04,330 --> 00:39:07,520 You can discuss very interesting correlations 568 00:39:07,520 --> 00:39:10,060 between two electrons in an atom. 569 00:39:12,970 --> 00:39:16,520 And you can have very relativistic effects 570 00:39:16,520 --> 00:39:18,420 if you have highly ionized atoms. 571 00:39:23,060 --> 00:39:30,970 If you have bare uranium, then the electron 572 00:39:30,970 --> 00:39:35,360 in the lowest orbits becomes relativistic. 573 00:39:35,360 --> 00:39:38,810 You can even see, if you scale the fine structure constant-- 574 00:39:38,810 --> 00:39:44,000 which has an e squared in it-- with the charge of uranium 92, 575 00:39:44,000 --> 00:39:47,110 well, 1 over 137 times 92 gives about 1, 576 00:39:47,110 --> 00:39:48,900 so you really get into a new regime 577 00:39:48,900 --> 00:39:53,120 of coupling for atomic physics. 578 00:39:53,120 --> 00:39:57,320 But we won't have time to talk about it. 579 00:40:00,030 --> 00:40:03,810 And this may be an omission, because there 580 00:40:03,810 --> 00:40:06,540 is really interesting work going on. 581 00:40:06,540 --> 00:40:09,122 We're not talking about high intensity 582 00:40:09,122 --> 00:40:19,020 lasers and short laser pulses. 583 00:40:19,020 --> 00:40:22,410 This choice maybe mainly determined 584 00:40:22,410 --> 00:40:27,360 by that the experimental program in the physics department 585 00:40:27,360 --> 00:40:29,200 is not overlapping with that. 586 00:40:29,200 --> 00:40:32,015 But of course, you know we have world class researchers 587 00:40:32,015 --> 00:40:34,950 and short pulse lasers in the electrical engineering 588 00:40:34,950 --> 00:40:35,450 department. 589 00:40:38,440 --> 00:40:41,640 Any question about the syllabus? 590 00:40:41,640 --> 00:40:48,040 Questions about what to expect in the next 12, 13 weeks? 591 00:40:53,340 --> 00:40:57,716 Well, then let's talk about some technicalities. 592 00:41:08,070 --> 00:41:14,670 I'll keep it short because all this information is 593 00:41:14,670 --> 00:41:15,925 available on the website. 594 00:41:19,750 --> 00:41:22,520 We run the website of the CUA server. 595 00:41:22,520 --> 00:41:30,846 So it is cua.mit.edu/8.422. 596 00:41:30,846 --> 00:41:33,040 When I say all the information is available, 597 00:41:33,040 --> 00:41:36,020 I have to say-- not yet. 598 00:41:36,020 --> 00:41:38,260 I realized yesterday night that [INAUDIBLE] 599 00:41:38,260 --> 00:41:39,970 has re-modified the server. 600 00:41:39,970 --> 00:41:41,950 I didn't have access to the server. 601 00:41:41,950 --> 00:41:44,460 I just got it an hour ago. 602 00:41:44,460 --> 00:41:46,790 What you will find under this URL 603 00:41:46,790 --> 00:41:53,800 is the website from when the class was taught two years ago. 604 00:41:53,800 --> 00:41:57,130 And actually, more than 90 percent of the information 605 00:41:57,130 --> 00:41:59,290 is the same. 606 00:41:59,290 --> 00:42:01,030 I always try to improve the course, 607 00:42:01,030 --> 00:42:04,630 but I know it will be more incremental changes and not 608 00:42:04,630 --> 00:42:05,686 dramatic changes. 609 00:42:05,686 --> 00:42:07,560 So if you look at the website, you'll already 610 00:42:07,560 --> 00:42:11,254 get a taste what the course is, but within the next day or two, 611 00:42:11,254 --> 00:42:12,545 we'll have updated information. 612 00:42:21,350 --> 00:42:26,670 I know, at least for most of you, 613 00:42:26,670 --> 00:42:30,310 I have contact information for MIT registration. 614 00:42:30,310 --> 00:42:37,590 But if you are a Harvard student or a listener just sitting 615 00:42:37,590 --> 00:42:40,880 in and you haven't registered for the class, 616 00:42:40,880 --> 00:42:52,170 I would ask you to send an email to our secretary, Joanna, 617 00:42:52,170 --> 00:42:59,360 j_k@mit.edu, because I would like to have an email list 618 00:42:59,360 --> 00:43:05,180 for the class for corrections to the homework assignment or last 619 00:43:05,180 --> 00:43:07,780 minute announcements. 620 00:43:07,780 --> 00:43:09,900 And then we'll add you to the mailing list. 621 00:43:14,740 --> 00:43:20,050 The schedule of the class is, well, we 622 00:43:20,050 --> 00:43:24,400 meet at this time on Monday, Wednesday. 623 00:43:24,400 --> 00:43:32,730 And let me know disclose, I plan to occasionally teach 624 00:43:32,730 --> 00:43:36,379 on Fridays at the same time. 625 00:43:36,379 --> 00:43:38,170 Over many years, it has been my experience, 626 00:43:38,170 --> 00:43:40,450 if you have a class on Monday, Wednesday at one o'clock, 627 00:43:40,450 --> 00:43:42,575 you don't have another class Friday at one o'clock. 628 00:43:42,575 --> 00:43:44,100 Is that assumption correct? 629 00:43:46,670 --> 00:43:50,460 So within the next few days, I will tell you 630 00:43:50,460 --> 00:43:52,605 on the website which Friday I would like to teach. 631 00:43:52,605 --> 00:43:54,380 The reason is rather simple. 632 00:43:54,380 --> 00:43:57,690 Like every faculty member who's active in research, 633 00:43:57,690 --> 00:44:02,900 I have to go to funding agency workshops and conferences. 634 00:44:02,900 --> 00:44:06,280 I try to keep it to a minimum, but on average I 635 00:44:06,280 --> 00:44:07,880 will miss two or three classes. 636 00:44:07,880 --> 00:44:09,350 And instead of asking a [INAUDIBLE] 637 00:44:09,350 --> 00:44:11,480 or a graduate student to teach the class, 638 00:44:11,480 --> 00:44:13,810 I would like to teach the class myself. 639 00:44:13,810 --> 00:44:15,960 So I will have makeup classes on Fridays. 640 00:44:20,260 --> 00:44:22,380 OK, that's the schedule. 641 00:44:22,380 --> 00:44:40,610 Finally, talking about requirements, 642 00:44:40,610 --> 00:44:45,880 one requirement is homework. 643 00:44:45,880 --> 00:44:48,860 We have 10 wonderful problem sets 644 00:44:48,860 --> 00:44:50,920 with a lot of problems which I actually 645 00:44:50,920 --> 00:44:55,480 designed from current research. 646 00:44:55,480 --> 00:45:00,830 So you will actually recognize that a lot of problems 647 00:45:00,830 --> 00:45:05,010 are created based on some research papers which came out 648 00:45:05,010 --> 00:45:09,340 of my own group or other groups at MIT in the last few years. 649 00:45:13,160 --> 00:45:18,070 The good news is, there is no mid-term, there is no final, 650 00:45:18,070 --> 00:45:19,920 but there will be a term paper. 651 00:45:26,690 --> 00:45:30,805 And the term paper is due on the last day of classes. 652 00:45:40,890 --> 00:45:49,950 The teaching team are myself, Joanna Keseberg, 653 00:45:49,950 --> 00:45:55,820 our secretary-- that's also where you will be dropping off 654 00:45:55,820 --> 00:46:00,215 your homework-- and then we have assembled 655 00:46:00,215 --> 00:46:05,160 a wonderful team of five TAs. 656 00:46:05,160 --> 00:46:07,800 They are all advanced graduate students. 657 00:46:07,800 --> 00:46:12,600 And actually, I've picked TAs from all of the active groups 658 00:46:12,600 --> 00:46:13,490 here at MIT. 659 00:46:13,490 --> 00:46:15,490 From Martin Zwierlein's group, I. Chuang's 660 00:46:15,490 --> 00:46:17,410 group, Vladan Vuletic's group, and my group. 661 00:46:20,394 --> 00:46:23,880 Are any of the TA's around? 662 00:46:23,880 --> 00:46:36,760 Nick, Alexei, Jee Woo, Lawrence, and Molu. 663 00:46:39,410 --> 00:46:43,040 Each TA will be responsible for two weeks in the course, 664 00:46:43,040 --> 00:46:46,904 and the TA will indicate availability and office hours 665 00:46:46,904 --> 00:46:48,320 on the weekly homework assignment. 666 00:46:54,070 --> 00:46:56,700 Other details about the term paper, 667 00:46:56,700 --> 00:47:00,290 how long the term paper should be, 668 00:47:00,290 --> 00:47:04,070 the, kind of, what I regard as an honesty code, 669 00:47:04,070 --> 00:47:06,430 that you're not trying to get access 670 00:47:06,430 --> 00:47:10,030 to solutions from previous courses, 671 00:47:10,030 --> 00:47:11,830 all that is summarized on the website. 672 00:47:11,830 --> 00:47:14,260 And once I've updated the website, 673 00:47:14,260 --> 00:47:16,022 I'm sure you will read it. 674 00:47:16,022 --> 00:47:16,605 Any questions? 675 00:47:29,710 --> 00:47:33,710 OK, well, with that we will actually 676 00:47:33,710 --> 00:47:37,240 be ready to jump into the middle of the course 677 00:47:37,240 --> 00:47:42,280 and start with some heavy duty equations of QED. 678 00:47:42,280 --> 00:47:45,850 But no-- just joking. 679 00:47:45,850 --> 00:47:50,050 I think this would maybe spoil the introduction. 680 00:47:50,050 --> 00:47:53,100 What I actually like to do is, to make the transition 681 00:47:53,100 --> 00:47:55,470 from the introduction to the discussion 682 00:47:55,470 --> 00:47:59,560 of atom-photon interactions and quantum electrodynamics, 683 00:47:59,560 --> 00:48:01,660 I always like to start the course 684 00:48:01,660 --> 00:48:06,010 by giving you an appetizer by talking 685 00:48:06,010 --> 00:48:09,690 to you in a lighthearted but hopefully profound way 686 00:48:09,690 --> 00:48:17,660 about the system, which helps to showcase 687 00:48:17,660 --> 00:48:20,260 what are we doing in this course. 688 00:48:20,260 --> 00:48:22,750 And until a few years ago, I would 689 00:48:22,750 --> 00:48:26,610 have started with the simplest example of laser cooling, 690 00:48:26,610 --> 00:48:28,630 simply beam slowing or optical molasses, 691 00:48:28,630 --> 00:48:30,560 in the simplest possible picture, 692 00:48:30,560 --> 00:48:34,750 just to give you a taste of what we will be doing together 693 00:48:34,750 --> 00:48:36,750 during the semester. 694 00:48:36,750 --> 00:48:40,910 But as I said, AMO physics is moving along. 695 00:48:40,910 --> 00:48:46,880 And what I now want to use as an example which clearly 696 00:48:46,880 --> 00:48:50,470 synthesizes many aspects of this course 697 00:48:50,470 --> 00:48:53,000 are atoms in an optical lattice. 698 00:48:55,670 --> 00:49:06,470 So let me, in the last, next 20 minutes or so, 699 00:49:06,470 --> 00:49:12,270 make some connections to different topics of this course 700 00:49:12,270 --> 00:49:19,570 by using as a starting point a concrete, very simple system, 701 00:49:19,570 --> 00:49:21,680 but very, very rich and profound, 702 00:49:21,680 --> 00:49:24,910 and these are atoms in optical lattice. 703 00:49:24,910 --> 00:49:28,390 So the situation I want to use here 704 00:49:28,390 --> 00:49:34,120 is that you have two laser beams which interfere. 705 00:49:34,120 --> 00:49:38,820 And those laser beams form an optical standing wave. 706 00:49:43,400 --> 00:49:55,630 So next week we will learn how this electromagnetic wave 707 00:49:55,630 --> 00:49:59,350 interacts with atoms. 708 00:49:59,350 --> 00:50:02,900 So we have to put a few atoms into the system. 709 00:50:02,900 --> 00:50:06,460 And we will derive, from first principles, the QED 710 00:50:06,460 --> 00:50:14,100 Hamiltonian, which, after a lot of manipulation and eliminating 711 00:50:14,100 --> 00:50:22,210 complicated terms, will be the dipole interaction. 712 00:50:22,210 --> 00:50:25,380 But of course, each symbol here is an operator, 713 00:50:25,380 --> 00:50:27,333 and there's a long story behind that. 714 00:50:35,320 --> 00:50:42,280 In about two months, we will describe light-atom interaction 715 00:50:42,280 --> 00:50:46,170 with a formalism which uses a Bloch 716 00:50:46,170 --> 00:50:50,140 vector and the optical Bloch equations. 717 00:50:50,140 --> 00:50:53,650 There is a vector with three components which 718 00:50:53,650 --> 00:50:59,120 describes what is the state the atom is in. 719 00:50:59,120 --> 00:51:01,670 One component will tell us if the atom 720 00:51:01,670 --> 00:51:05,690 is in the upper or the lower state, 721 00:51:05,690 --> 00:51:08,970 whereas the other components tell us 722 00:51:08,970 --> 00:51:12,290 whether the dipole moment of the atom 723 00:51:12,290 --> 00:51:21,360 is in phase or out of phase with a driving 724 00:51:21,360 --> 00:51:22,610 electromagnetic field. 725 00:51:27,600 --> 00:51:40,670 Well, if there is part of the dipole moment which 726 00:51:40,670 --> 00:51:46,590 is in phase with a driving electric field, 727 00:51:46,590 --> 00:51:51,790 then the suitable expectation value 728 00:51:51,790 --> 00:51:55,490 defines a mechanical potential. 729 00:51:55,490 --> 00:51:58,630 And if the electric field is a standing wave, 730 00:51:58,630 --> 00:52:02,635 then we generate, through light-atom interaction, 731 00:52:02,635 --> 00:52:05,320 a periodic potential for the atoms. 732 00:52:08,960 --> 00:52:13,070 We will learn everything which we 733 00:52:13,070 --> 00:52:16,710 have to know about this potential. 734 00:52:16,710 --> 00:52:20,500 In a simple case, it is simply the Rabi frequency 735 00:52:20,500 --> 00:52:26,860 divided by the detuning of the electromagnetic wave. 736 00:52:26,860 --> 00:52:31,430 But we will find it very interesting 737 00:52:31,430 --> 00:52:34,490 to look at it from very different point of view. 738 00:52:34,490 --> 00:52:35,970 And maybe let me use this example 739 00:52:35,970 --> 00:52:40,600 to point out that I'm really a big friend of explaining 740 00:52:40,600 --> 00:52:44,910 the same physics from very, very different perspectives. 741 00:52:44,910 --> 00:52:48,350 And when we talk about optical standing waves, 742 00:52:48,350 --> 00:52:51,300 we will use a picture of a classical potential, 743 00:52:51,300 --> 00:52:54,680 like a mechanical potential, and the atom is just moving around. 744 00:52:54,680 --> 00:52:57,860 We will use a photon picture that every time the atom 745 00:52:57,860 --> 00:53:00,574 feels a force, photons are involved. 746 00:53:00,574 --> 00:53:02,490 You don't see them in the classical potential, 747 00:53:02,490 --> 00:53:06,020 but photons are behind it, and ultimately, the forces 748 00:53:06,020 --> 00:53:09,315 of the classic potential come from stimulated absorption 749 00:53:09,315 --> 00:53:10,290 emission of photons. 750 00:53:12,870 --> 00:53:16,280 I may go down to the microscopic level. 751 00:53:16,280 --> 00:53:18,910 And I may ask you, but in the end, it's an atom, 752 00:53:18,910 --> 00:53:21,270 but the atom consists of electrons. 753 00:53:21,270 --> 00:53:23,630 And the electrons are simply oscillating 754 00:53:23,630 --> 00:53:26,850 because it's driven by the electromagnetic field. 755 00:53:26,850 --> 00:53:29,560 It's actually something which most people are not aware of, 756 00:53:29,560 --> 00:53:32,320 but you can ask the question now-- 757 00:53:32,320 --> 00:53:38,010 is the force in the optical lattice on the atom, 758 00:53:38,010 --> 00:53:40,960 it's ultimately a force on the electron? 759 00:53:40,960 --> 00:53:42,885 Well, if you have a charged particle, 760 00:53:42,885 --> 00:53:45,890 you can have two kinds of forces-- an electric force 761 00:53:45,890 --> 00:53:48,510 or the Lorenz force. 762 00:53:48,510 --> 00:53:51,020 And I don't know if you would know the answer, 763 00:53:51,020 --> 00:53:54,320 but an atom is in an optical lattice, 764 00:53:54,320 --> 00:53:57,730 is the force just the [INAUDIBLE] 765 00:53:57,730 --> 00:54:00,540 the potential which the atom experiences, 766 00:54:00,540 --> 00:54:04,450 is that fundamentally due to the Coulomb force exerted 767 00:54:04,450 --> 00:54:06,450 by the electric field of the light, 768 00:54:06,450 --> 00:54:09,110 or is it due to the Lorenz force exerted 769 00:54:09,110 --> 00:54:10,560 by the magnetic part of the light? 770 00:54:13,840 --> 00:54:15,400 Who knows the answer? 771 00:54:15,400 --> 00:54:17,870 Who doesn't know the answer? 772 00:54:17,870 --> 00:54:18,970 OK, great. 773 00:54:18,970 --> 00:54:20,720 I was actually surprised when I derived it 774 00:54:20,720 --> 00:54:22,280 a few times for the first time. 775 00:54:22,280 --> 00:54:24,740 And it's not in the standard textbooks. 776 00:54:24,740 --> 00:54:29,270 So anyway, I hope, even for many of you who know already 777 00:54:29,270 --> 00:54:31,330 a lot about the subject, I hope I 778 00:54:31,330 --> 00:54:36,670 can add other perspectives for you. 779 00:54:36,670 --> 00:54:40,340 OK, so what I've discussed so far 780 00:54:40,340 --> 00:54:44,470 is that the standing wave of light 781 00:54:44,470 --> 00:54:54,330 creates now a periodic potential for the atom. 782 00:54:54,330 --> 00:54:57,730 And we will understand it from many, many different 783 00:54:57,730 --> 00:55:00,850 perspectives, from the photon type, quantum optics 784 00:55:00,850 --> 00:55:03,160 perspective, to the most classical description. 785 00:55:05,670 --> 00:55:09,520 So what immediately comes to my mind 786 00:55:09,520 --> 00:55:14,120 is that we now want to look at this periodic potential in two 787 00:55:14,120 --> 00:55:14,995 different situations. 788 00:55:19,930 --> 00:55:22,540 We can ask, well, whenever you have light, 789 00:55:22,540 --> 00:55:25,350 spontaneous emission is a possibility. 790 00:55:25,350 --> 00:55:31,030 And we may ask, what happens when spontaneous emission 791 00:55:31,030 --> 00:55:31,910 is not negligible? 792 00:55:35,330 --> 00:55:37,900 And we discuss that approximately 793 00:55:37,900 --> 00:55:40,960 in week nine of the course. 794 00:55:40,960 --> 00:55:46,090 Then what happens is, an atom has an excited and a ground 795 00:55:46,090 --> 00:55:47,410 state. 796 00:55:47,410 --> 00:55:50,520 And those in the excited and the ground state, 797 00:55:50,520 --> 00:55:54,140 do the atoms feel the periodic potential? 798 00:55:58,940 --> 00:56:06,240 Well, eventually, we have to generalize 799 00:56:06,240 --> 00:56:10,550 the notion of ground and excited state into [INAUDIBLE] states, 800 00:56:10,550 --> 00:56:14,000 and I will tell you all about it in a few weeks. 801 00:56:14,000 --> 00:56:18,010 But the situation can now be, when an atom is in the ground 802 00:56:18,010 --> 00:56:22,570 state, it has to move up the standing wave potential. 803 00:56:22,570 --> 00:56:25,200 Then it's getting excited with a laser. 804 00:56:25,200 --> 00:56:28,980 It has to move up again the standing wave potential. 805 00:56:28,980 --> 00:56:32,380 And then there may be spontaneous emission. 806 00:56:32,380 --> 00:56:35,210 So what I'm just describing here is a situation 807 00:56:35,210 --> 00:56:39,280 where the atom is mechanically moving up the potential. 808 00:56:39,280 --> 00:56:41,630 It's excited at the top of the potential. 809 00:56:41,630 --> 00:56:44,040 And it emits when it's on top of the potential. 810 00:56:44,040 --> 00:56:47,230 So the atom is doing mechanical work, 811 00:56:47,230 --> 00:56:50,950 and this is called Sisyphus cooling. 812 00:56:50,950 --> 00:56:57,240 This is the way, this is one method, one mechanism, 813 00:56:57,240 --> 00:56:59,760 of laser cooling which leads to the lowest 814 00:56:59,760 --> 00:57:03,550 temperatures in the laboratory before evaporative cooling is 815 00:57:03,550 --> 00:57:04,600 used. 816 00:57:04,600 --> 00:57:07,030 So that's some cool aspect we will come along 817 00:57:07,030 --> 00:57:09,710 by discussing motion in a standing wave, 818 00:57:09,710 --> 00:57:16,340 but taking into account that photons are emitted 819 00:57:16,340 --> 00:57:19,570 and really understanding when and where 820 00:57:19,570 --> 00:57:22,770 are the photons emitted. 821 00:57:22,770 --> 00:57:29,290 Well, the second situation is, of course, 822 00:57:29,290 --> 00:57:32,455 if spontaneous emission is completely negligible. 823 00:57:38,220 --> 00:57:43,470 Then we have a situation where all what matters 824 00:57:43,470 --> 00:57:46,830 is the potential, and we can completely 825 00:57:46,830 --> 00:57:51,550 forget that it's photons, it's quantum optics 826 00:57:51,550 --> 00:57:53,400 which has created this potential. 827 00:57:53,400 --> 00:57:56,150 We can simply use a classical potential 828 00:57:56,150 --> 00:57:59,710 in our description in our Hamiltonian. 829 00:58:02,300 --> 00:58:05,930 Now, again, we have two limiting cases. 830 00:58:08,750 --> 00:58:15,340 One case is when this potential, or optical lattice, 831 00:58:15,340 --> 00:58:18,630 is really deep. 832 00:58:18,630 --> 00:58:25,150 Deep means that atoms are sitting deep in the potential 833 00:58:25,150 --> 00:58:32,840 and they can oscillate around, but they cannot jump over 834 00:58:32,840 --> 00:58:35,810 to the next potential. 835 00:58:35,810 --> 00:58:42,190 So in this situation, you would say, well, that's boring. 836 00:58:42,190 --> 00:58:44,770 Nothing happens, the atom just stays put. 837 00:58:44,770 --> 00:58:46,370 But what is boring for some of you 838 00:58:46,370 --> 00:58:49,740 is exciting for some others, because these atoms 839 00:58:49,740 --> 00:58:52,110 are exquisitely controlled. 840 00:58:52,110 --> 00:58:56,040 They cannot collide, they cannot interact with other atoms. 841 00:58:56,040 --> 00:58:59,360 So these are really the most ideal situation 842 00:58:59,360 --> 00:59:01,910 you can imagine for atoms. 843 00:59:01,910 --> 00:59:06,020 Of course, if you have less than one atom per site. 844 00:59:06,020 --> 00:59:12,150 And this is the way how you want to prepare atoms 845 00:59:12,150 --> 00:59:16,170 for the most accurate interrogations. 846 00:59:16,170 --> 00:59:20,910 And you can build atomic clocks, optical atomic clocks, 847 00:59:20,910 --> 00:59:24,040 based on atoms insulated in such a lattice, which 848 00:59:24,040 --> 00:59:26,635 approach now 10 to the minus 17 accuracy. 849 00:59:32,190 --> 00:59:36,200 Well, if you drive a clock transition, 850 00:59:36,200 --> 00:59:39,550 if you take the atom from the ground to the excited state, 851 00:59:39,550 --> 00:59:43,420 you may face a situation I mentioned earlier 852 00:59:43,420 --> 00:59:46,590 that the periodic potential for the ground and excited state 853 00:59:46,590 --> 00:59:47,750 are different. 854 00:59:47,750 --> 00:59:50,460 And that would actually interfere with your clock, 855 00:59:50,460 --> 00:59:53,030 because the clock frequency depends now 856 00:59:53,030 --> 00:59:56,470 on what the lattice is doing to your atoms. 857 00:59:56,470 --> 01:00:03,360 However, and we discuss that in week four, 858 01:00:03,360 --> 01:00:11,860 there are what people call magic wavelengths, 859 01:00:11,860 --> 01:00:13,880 where you pick a certain wavelength 860 01:00:13,880 --> 01:00:22,750 for your optical lattice where the periodic potential is 861 01:00:22,750 --> 01:00:26,780 absolutely the same for ground and excited state. 862 01:00:31,210 --> 01:00:36,680 So that means you have, then, the perfect decoupling 863 01:00:36,680 --> 01:00:38,650 between the ticking of the clock, 864 01:00:38,650 --> 01:00:40,600 the internal structure of the atom 865 01:00:40,600 --> 01:00:44,870 and the mechanical motion of the atoms in the potential. 866 01:00:44,870 --> 01:00:55,290 And in that situation, you create a situation 867 01:00:55,290 --> 01:00:59,270 which has been studied since [INAUDIBLE], namely 868 01:00:59,270 --> 01:01:00,270 with trapped ions. 869 01:01:05,740 --> 01:01:09,855 If you have a single ion in an ion trap-- 870 01:01:09,855 --> 01:01:13,830 and ion trapping is pursued here at MIT in Ike Chuang's group-- 871 01:01:13,830 --> 01:01:17,990 you have just a single object completely isolated. 872 01:01:17,990 --> 01:01:23,730 And in the form of the aluminum ion, 873 01:01:23,730 --> 01:01:28,280 this has just been demonstrated to be 874 01:01:28,280 --> 01:01:31,390 the most accurate atomic clock in the world with 10 875 01:01:31,390 --> 01:01:34,150 to the minus 17 accuracy. 876 01:01:34,150 --> 01:01:37,880 So anyway, with optical lattices, 877 01:01:37,880 --> 01:01:41,690 avoiding spontaneous emission using magic wavelengths, 878 01:01:41,690 --> 01:01:46,120 we can only engineer with neutral atoms what 879 01:01:46,120 --> 01:01:48,500 has been available with trapped ions 880 01:01:48,500 --> 01:01:51,950 but we can simultaneously have 10,000 copies 881 01:01:51,950 --> 01:01:55,350 and look at 10,000 atoms which are all identical copies, 882 01:01:55,350 --> 01:01:56,790 identical systems with each other. 883 01:01:59,520 --> 01:02:01,590 So you see already from that example 884 01:02:01,590 --> 01:02:06,180 that there will be intellectual overlap and synergy 885 01:02:06,180 --> 01:02:09,920 between talking about neutral atoms in optical lattices 886 01:02:09,920 --> 01:02:15,610 and talking about trapped ions and how they are cooled 887 01:02:15,610 --> 01:02:17,510 and how they are manipulated. 888 01:02:17,510 --> 01:02:20,670 And we'll talk about trapped ions 889 01:02:20,670 --> 01:02:22,850 at the end of the course, sideband cooling 890 01:02:22,850 --> 01:02:24,550 of trapped ions, which is week 12. 891 01:02:30,660 --> 01:02:35,390 OK, so this is the simple but pristine situation 892 01:02:35,390 --> 01:02:39,400 that we have a deep lattice. 893 01:02:39,400 --> 01:02:43,940 The other limit is now that we have 894 01:02:43,940 --> 01:02:47,030 a weak, or shallow lattice. 895 01:02:47,030 --> 01:02:50,980 And the new physics which now comes into play 896 01:02:50,980 --> 01:02:55,240 is that atoms can move around-- they 897 01:02:55,240 --> 01:02:58,260 can tunnel from side to side. 898 01:03:01,010 --> 01:03:08,910 So towards the end of the course, 899 01:03:08,910 --> 01:03:14,180 I think the last months, approximately week 10, 900 01:03:14,180 --> 01:03:17,060 I will give you a short summary of what some of you 901 01:03:17,060 --> 01:03:23,410 may have already learned in the solid state course-- namely, 902 01:03:23,410 --> 01:03:34,990 band structure of atoms in optical lattices, Bloch states, 903 01:03:34,990 --> 01:03:37,960 effective mass, et cetera. 904 01:03:37,960 --> 01:03:41,870 This has now become language of atomic physics, 905 01:03:41,870 --> 01:03:48,280 because there is a very clean and straightforward realization 906 01:03:48,280 --> 01:03:51,270 of this physics using cold atoms. 907 01:03:54,020 --> 01:03:57,790 What we are mainly interested in, in our research, 908 01:03:57,790 --> 01:04:07,890 is when we have atoms which tunnel in this optical lattice. 909 01:04:07,890 --> 01:04:12,680 And for bosons, if the interactions get strong enough, 910 01:04:12,680 --> 01:04:16,980 the Bose-Einstein condensate is destroyed 911 01:04:16,980 --> 01:04:18,450 and what forms is a Mott insulator. 912 01:04:21,150 --> 01:04:22,970 This is a phase transition. 913 01:04:22,970 --> 01:04:26,680 And for fermions, we have a crossover 914 01:04:26,680 --> 01:04:28,900 from a metal to a fermionic Mott insulator. 915 01:04:32,680 --> 01:04:39,180 And with that, we are already overlapping conceptually 916 01:04:39,180 --> 01:04:45,750 with condensed matter physics, because the Mott insulator 917 01:04:45,750 --> 01:04:50,470 is a paradigm-- one of these paradigmatic examples where 918 01:04:50,470 --> 01:04:53,240 you understand some deep physics. 919 01:04:53,240 --> 01:04:56,520 It's a paradigm of condensed matter physics 920 01:04:56,520 --> 01:05:02,160 where you have only a partially-filled band. 921 01:05:02,160 --> 01:05:05,127 Common sense, or undergraduate textbooks, 922 01:05:05,127 --> 01:05:06,710 would say, partially-filled band, this 923 01:05:06,710 --> 01:05:08,730 means you've a metal, you've a conductor. 924 01:05:08,730 --> 01:05:11,550 But because of the interactions of the atoms, 925 01:05:11,550 --> 01:05:13,670 the system is an insulator. 926 01:05:13,670 --> 01:05:16,360 So this is where, really, the many-body physics 927 01:05:16,360 --> 01:05:19,180 profoundly changes the character of your system. 928 01:05:24,400 --> 01:05:25,590 Any questions? 929 01:05:30,090 --> 01:05:35,170 Well then, let me add one last aspect 930 01:05:35,170 --> 01:05:42,396 to my introductory example of optical lattices. 931 01:05:42,396 --> 01:05:44,770 In a sort of flyover, I described 932 01:05:44,770 --> 01:05:47,540 to you what is the physics we encounter when 933 01:05:47,540 --> 01:05:49,550 we have an optical lattice switched on 934 01:05:49,550 --> 01:05:52,950 and the atoms move around or they don't move around, 935 01:05:52,950 --> 01:05:55,150 and both cases are interesting. 936 01:05:55,150 --> 01:05:57,989 But if you think you've explored everything, well, 937 01:05:57,989 --> 01:05:59,780 then you think harder and say, hey, there's 938 01:05:59,780 --> 01:06:01,610 another angle we can get out of it. 939 01:06:01,610 --> 01:06:05,110 And this is, we can take the optical lettuce 940 01:06:05,110 --> 01:06:08,740 and simply pulse it on, switch it on and off. 941 01:06:11,380 --> 01:06:14,380 Well, what happens is, and then it 942 01:06:14,380 --> 01:06:17,390 becomes a time-dependent problem. 943 01:06:17,390 --> 01:06:22,910 It becomes something where we can shape and control 944 01:06:22,910 --> 01:06:26,690 the wave function of atoms in time-dependent way. 945 01:06:26,690 --> 01:06:28,240 Let me give you one example. 946 01:06:28,240 --> 01:06:30,980 If we start with very cold atoms-- can 947 01:06:30,980 --> 01:06:36,920 be a Bose-Einstein condensate-- and then, for a short time, 948 01:06:36,920 --> 01:06:45,010 we switch on the lattice, afterwards, we 949 01:06:45,010 --> 01:06:51,140 observe that we have still some atoms at zero momentum. 950 01:06:51,140 --> 01:06:57,680 But now we have atoms which have a momentum transfer of plus 951 01:06:57,680 --> 01:07:01,660 minus 2 h bar k. 952 01:07:01,660 --> 01:07:05,630 You can understand that-- and this again 953 01:07:05,630 --> 01:07:08,200 exemplifies that we want to look at the physics 954 01:07:08,200 --> 01:07:10,440 from different angles-- this can be 955 01:07:10,440 --> 01:07:18,020 described that you have an two-photon transition 956 01:07:18,020 --> 01:07:22,710 from the ground state with zero momentum to the ground 957 01:07:22,710 --> 01:07:27,520 state with two-photon recoil. 958 01:07:27,520 --> 01:07:30,590 So you can understand it in the photon picture. 959 01:07:30,590 --> 01:07:34,010 But you can also understand it by saying 960 01:07:34,010 --> 01:07:39,460 you have some matter waves which are now 961 01:07:39,460 --> 01:07:43,380 exposed to a periodic potential. 962 01:07:43,380 --> 01:07:47,250 And you simply ask what happens to waves 963 01:07:47,250 --> 01:07:48,870 in a periodic potential? 964 01:07:48,870 --> 01:07:52,660 Well, that's the same what happens to optical waves 965 01:07:52,660 --> 01:07:55,295 when they encounter a grading, and that's 966 01:07:55,295 --> 01:07:56,420 the physics of diffraction. 967 01:08:00,760 --> 01:08:04,650 So in a nutshell, this happens when 968 01:08:04,650 --> 01:08:16,080 we use a pulse on an optical potential. 969 01:08:16,080 --> 01:08:18,740 And let me now finish by telling you that, 970 01:08:18,740 --> 01:08:24,319 again, in this situation, we discover the ambiguity 971 01:08:24,319 --> 01:08:28,350 or the two-sidedness of a lot of things we do in atomic physics. 972 01:08:28,350 --> 01:08:30,979 I've mentioned to you that the same experiment, 973 01:08:30,979 --> 01:08:34,390 the same experimental setup, cold atoms in optical lattice-- 974 01:08:34,390 --> 01:08:37,100 you turn up the lattice and you have the world's best 975 01:08:37,100 --> 01:08:40,170 atomic clock, atoms just isolated from each other. 976 01:08:40,170 --> 01:08:41,582 You turn down the lattice and you 977 01:08:41,582 --> 01:08:44,020 have an interesting condensed matter physics system. 978 01:08:44,020 --> 01:08:47,990 Let me just show you that the same two-sidedness 979 01:08:47,990 --> 01:08:50,910 of atomic physics-- precision and pristine control 980 01:08:50,910 --> 01:08:52,920 and interesting many-body physics-- 981 01:08:52,920 --> 01:08:56,810 happens when you pulse on optical lattices. 982 01:08:56,810 --> 01:09:02,990 So one application of those optical lettuces 983 01:09:02,990 --> 01:09:05,590 is atom optics. 984 01:09:05,590 --> 01:09:13,800 You have atoms and when they encounter an optical lattice, 985 01:09:13,800 --> 01:09:20,574 some atoms will just continue, will not be diffracted. 986 01:09:26,590 --> 01:09:28,899 They have zero momentums. 987 01:09:28,899 --> 01:09:34,310 Others are diffracted with a transverse momentum. 988 01:09:34,310 --> 01:09:39,979 You can then expose the atoms to a second zone 989 01:09:39,979 --> 01:09:44,740 where, eventually, momentum is transferred, 990 01:09:44,740 --> 01:09:48,189 and then the atoms come back together. 991 01:09:48,189 --> 01:09:52,069 So what we have here is an atom interferometer where 992 01:09:52,069 --> 01:09:56,105 atomic matter waves first go through a beam splitter, 993 01:09:56,105 --> 01:09:59,894 are reflected back towards each other, all by photon transfer, 994 01:09:59,894 --> 01:10:01,060 and then they're recombined. 995 01:10:07,130 --> 01:10:15,940 So this pulsed optical lattice acts as a beam splitter. 996 01:10:15,940 --> 01:10:24,880 It is the way how, today, the most precise atom 997 01:10:24,880 --> 01:10:27,760 interferometers are built. 998 01:10:27,760 --> 01:10:31,060 And this is used for precision measurement, 999 01:10:31,060 --> 01:10:36,510 for measurement of inertial forces, gravity, rotation, 1000 01:10:36,510 --> 01:10:45,760 acceleration, and it is used for navigation and accurate 1001 01:10:45,760 --> 01:10:49,450 observation of the changes of the gravitational field 1002 01:10:49,450 --> 01:10:52,010 of the Earth. 1003 01:10:52,010 --> 01:10:55,940 Since we just had a talk by Holger Mueller from Berkeley 1004 01:10:55,940 --> 01:10:58,350 day before yesterday over at Harvard, 1005 01:10:58,350 --> 01:11:01,980 he talked about the combination of atom interferometer 1006 01:11:01,980 --> 01:11:04,360 and frequency combs, another development-- 1007 01:11:04,360 --> 01:11:05,940 let me just mention that. 1008 01:11:05,940 --> 01:11:09,700 If you derive those laser frequencies 1009 01:11:09,700 --> 01:11:13,160 from an optical frequency comb, and with an optical frequency 1010 01:11:13,160 --> 01:11:15,740 comb you can pretty much count the frequencies. 1011 01:11:15,740 --> 01:11:20,440 So this laser is mode, I don't know-- 100,000 1012 01:11:20,440 --> 01:11:22,720 or whatever you are in the comb. 1013 01:11:22,720 --> 01:11:26,570 By doing that, by combining it, you can actually 1014 01:11:26,570 --> 01:11:32,000 build an atomic clock where-- let me just say, 1015 01:11:32,000 --> 01:11:36,070 plus combs-- can give an atomic clock 1016 01:11:36,070 --> 01:11:42,940 which is called the Compton clock because the frequency is 1017 01:11:42,940 --> 01:11:47,930 now given by the rest mass of the atom, 1018 01:11:47,930 --> 01:11:51,180 but divided by a big integer number. 1019 01:11:51,180 --> 01:11:56,190 So using completely unrelated developments in AMO science 1020 01:11:56,190 --> 01:11:59,810 which I've mentioned, the optical frequency comb, 1021 01:11:59,810 --> 01:12:03,145 combining it with the physics of a pulse standing wave, 1022 01:12:03,145 --> 01:12:07,030 you now have an atomic clock which is directly related 1023 01:12:07,030 --> 01:12:08,525 to the energy of the rest mass. 1024 01:12:16,780 --> 01:12:24,950 But finally, if you pulse on an optical standing wave 1025 01:12:24,950 --> 01:12:29,200 and your object are not individual atoms, 1026 01:12:29,200 --> 01:12:31,960 non-interacting atoms, your object 1027 01:12:31,960 --> 01:12:37,050 is the Bose-Einstein condensate or atoms which strongly 1028 01:12:37,050 --> 01:12:40,440 interact, then you're not transferring 1029 01:12:40,440 --> 01:12:43,130 recoil to individual atoms, you're 1030 01:12:43,130 --> 01:12:48,750 transferring momentum to a complicated many-body system. 1031 01:12:48,750 --> 01:12:53,940 And this means what we are measuring 1032 01:12:53,940 --> 01:12:56,420 is the dynamic structure factor. 1033 01:13:02,702 --> 01:13:04,660 If you have atoms, you want to do spectroscopy, 1034 01:13:04,660 --> 01:13:06,970 you want to know what energy levels are there, 1035 01:13:06,970 --> 01:13:08,470 and then you know your atom. 1036 01:13:08,470 --> 01:13:10,530 If you have a strongly-interacting system, 1037 01:13:10,530 --> 01:13:13,330 you also want to know what energy levels are there. 1038 01:13:13,330 --> 01:13:16,390 But each energy level in a homogeneous system 1039 01:13:16,390 --> 01:13:18,460 or in a periodic potential is associated 1040 01:13:18,460 --> 01:13:20,500 with momentum and quasi-momentum. 1041 01:13:20,500 --> 01:13:23,700 So in other words, if you have a more complicated system, 1042 01:13:23,700 --> 01:13:27,080 you want to figure out what are the possible states in terms 1043 01:13:27,080 --> 01:13:29,680 of momentum and energy. 1044 01:13:29,680 --> 01:13:32,610 And the optical standing wave, the pulsed optical standing 1045 01:13:32,610 --> 01:13:35,810 wave is the way how we impart momentum and energy 1046 01:13:35,810 --> 01:13:38,330 to a system. 1047 01:13:38,330 --> 01:13:41,800 What I actually just told you is a story 1048 01:13:41,800 --> 01:13:44,430 in my own research career. 1049 01:13:44,430 --> 01:13:46,190 I was a post-doc with Dave Pritchard. 1050 01:13:46,190 --> 01:13:48,010 He had trained at MIT in the '90s 1051 01:13:48,010 --> 01:13:50,070 by a pioneer in laser cooling. 1052 01:13:50,070 --> 01:13:52,110 And when we had Bose-Einstein condensates 1053 01:13:52,110 --> 01:13:56,790 in the late '90s, Professor Pritchard and myself, 1054 01:13:56,790 --> 01:13:57,969 we teamed up. 1055 01:13:57,969 --> 01:13:59,885 I was the expert on Bose-Einstein condensation 1056 01:13:59,885 --> 01:14:03,910 and he was the expert on atom interferometry. 1057 01:14:03,910 --> 01:14:06,460 So just by sort of exploring things, 1058 01:14:06,460 --> 01:14:08,630 we took Bose-Einstein condensates 1059 01:14:08,630 --> 01:14:10,940 and we pulsed on a standing wave. 1060 01:14:10,940 --> 01:14:14,790 What was on our mind was, hey, let's build an interferometer. 1061 01:14:14,790 --> 01:14:19,410 But I'm more of a many-body physics person. 1062 01:14:19,410 --> 01:14:21,775 I suddenly said, yes, but if we now 1063 01:14:21,775 --> 01:14:24,950 change the momentum and the frequency of this standing 1064 01:14:24,950 --> 01:14:26,400 wave, what happens? 1065 01:14:26,400 --> 01:14:28,245 And I suddenly realized that this 1066 01:14:28,245 --> 01:14:31,720 is a way to measure properties of a Bose-Einstein condensate 1067 01:14:31,720 --> 01:14:34,440 in a way which hadn't been done before. 1068 01:14:34,440 --> 01:14:36,790 So I realized-- and this is maybe 1069 01:14:36,790 --> 01:14:38,530 the last thing I want to tell you today-- 1070 01:14:38,530 --> 01:14:41,150 I realized in my own research and my collaboration 1071 01:14:41,150 --> 01:14:43,750 with Dave Pritchard, that we'd built an experiment, 1072 01:14:43,750 --> 01:14:47,460 and we just turned one knob at our experiment, 1073 01:14:47,460 --> 01:14:50,300 and the following day we were no longer doing 1074 01:14:50,300 --> 01:14:54,690 atomic interferometry, we were doing many-body physics. 1075 01:14:54,690 --> 01:14:57,670 So this is, I think, what makes our field exciting. 1076 01:14:57,670 --> 01:15:03,890 We are using the tools, the precision, and the control 1077 01:15:03,890 --> 01:15:07,590 of atomic physics, which leads to the most 1078 01:15:07,590 --> 01:15:11,677 accurate atomic clocks in the world-- 1079 01:15:11,677 --> 01:15:14,010 atomic clocks, which are the most accurate in the world. 1080 01:15:14,010 --> 01:15:17,520 And we are using those tools to do entanglement and many-body 1081 01:15:17,520 --> 01:15:18,130 physics. 1082 01:15:18,130 --> 01:15:21,800 And I think it's just a compelling combination. 1083 01:15:21,800 --> 01:15:23,550 Anyway, that's an appetizer, that's 1084 01:15:23,550 --> 01:15:26,006 an outlook over the semester. 1085 01:15:26,006 --> 01:15:31,500 Do you have any questions about the last examples I gave you 1086 01:15:31,500 --> 01:15:32,975 or the course in itself? 1087 01:15:37,870 --> 01:15:38,790 OK. 1088 01:15:38,790 --> 01:15:41,150 No homework assignment today. 1089 01:15:41,150 --> 01:15:43,750 And we'll meet Monday at the same time 1090 01:15:43,750 --> 01:15:45,890 here in this lecture hall.