1 00:00:10,760 --> 00:00:12,160 So it's a it's a great pleasure 2 00:00:12,160 --> 00:00:15,160 to be giving this talk about anions, one of my favorite subjects. 3 00:00:15,160 --> 00:00:16,800 I there's a little comment down here. 4 00:00:16,800 --> 00:00:19,840 Respect the young because as you'll see, a lot of the great progress in 5 00:00:19,840 --> 00:00:23,560 this field was made by people who are mere spring chickens. 6 00:00:25,000 --> 00:00:29,360 So the the idea of anions is really, trying to answer a question, 7 00:00:29,680 --> 00:00:33,680 what happens when you exchange two identical particles in quantum mechanics? 8 00:00:33,720 --> 00:00:34,800 It's a it's an old question. 9 00:00:34,800 --> 00:00:38,120 It goes back to a now famous letter from, say, Chandra Bose 10 00:00:38,120 --> 00:00:41,120 to Albert Einstein, written when Bose was 30 years old. 11 00:00:41,200 --> 00:00:44,400 The letter says this about 100 years old, 101 years old. 12 00:00:44,400 --> 00:00:47,200 Now, I guess this year it says respected sir, I venture in 13 00:00:47,200 --> 00:00:50,200 to send you the accompanying article for your perusal and opinion. 14 00:00:50,480 --> 00:00:52,400 And he asked Einstein to help him get it 15 00:00:52,400 --> 00:00:56,160 published in for physique, which was the leading journal of the time. 16 00:00:56,400 --> 00:00:58,440 He says there are complete stranger to you. 17 00:00:58,440 --> 00:01:01,840 I do not feel any hesitation in making this such a request. 18 00:01:02,160 --> 00:01:05,600 So what Bose had done is he had derived, using the basic 19 00:01:05,600 --> 00:01:09,120 principles of statistical mechanics, the distribution function 20 00:01:09,360 --> 00:01:13,120 of how photons will fill modes in a cavity. 21 00:01:13,920 --> 00:01:15,560 Now Einstein read this paper. 22 00:01:15,560 --> 00:01:19,120 He realized that it was it was not only correct, but it could be, 23 00:01:19,120 --> 00:01:22,960 applied to lots of other things, to particles that were not photons. 24 00:01:23,120 --> 00:01:26,760 And in and in this way we developed Bose-Einstein statistics 25 00:01:26,760 --> 00:01:30,640 that applies to all particles that are what we call bosons. 26 00:01:30,640 --> 00:01:32,000 That includes photons, pions, 27 00:01:32,000 --> 00:01:35,440 gluons, phonons, excitons, and of course, the famous Higgs boson. 28 00:01:35,960 --> 00:01:37,040 The very next year, 29 00:01:38,080 --> 00:01:39,320 when Pauli was 30 00:01:39,320 --> 00:01:42,320 25 years old, he formulated his exclusion principle. 31 00:01:42,520 --> 00:01:44,040 This, to remind you, is the principle 32 00:01:44,040 --> 00:01:47,920 that says you can only put one fermion in each orbital. 33 00:01:48,200 --> 00:01:50,880 Two if you count one spin up and one spin down. 34 00:01:50,880 --> 00:01:55,160 And this principle, of course, is is fundamental to the periodic table 35 00:01:55,160 --> 00:01:59,240 and and all of chemistry and everything else in physics as well. 36 00:01:59,240 --> 00:02:03,240 Realizing that these particles don't obey the same kind of, 37 00:02:03,280 --> 00:02:07,320 statistics as photons, we therefore needed 38 00:02:07,320 --> 00:02:10,640 another type of distribution, another type of particle. 39 00:02:10,800 --> 00:02:14,640 And this is what we now call Fermi-Dirac statistics, which was derived 40 00:02:14,640 --> 00:02:17,840 first by neither Fermi nor Dirac, but 41 00:02:19,280 --> 00:02:22,160 it was derived by Pascal Yordan, 42 00:02:22,160 --> 00:02:25,080 who is 23 years old at the time. 43 00:02:25,080 --> 00:02:28,680 So, there's kind of a long story about why it is that it wasn't 44 00:02:28,680 --> 00:02:30,120 named after Jordan. 45 00:02:30,120 --> 00:02:31,440 Jordan wrote his manuscript. 46 00:02:31,440 --> 00:02:33,160 He sent it to the journals. 47 00:02:33,160 --> 00:02:36,480 I for Zeke, the editor was Max born, who is a well-intentioned 48 00:02:36,480 --> 00:02:38,320 but rather forgetful guy. 49 00:02:38,320 --> 00:02:42,000 Max put it in his suitcase with the best 50 00:02:42,000 --> 00:02:43,680 to ever intention to take it out and read it. 51 00:02:43,680 --> 00:02:46,840 But then he forgot about it, and it stayed there for the better part 52 00:02:46,840 --> 00:02:51,680 of a year, during which the same result was published by Fermi and Dirac. 53 00:02:53,120 --> 00:02:55,080 So then we had Fermi-Dirac statistics, 54 00:02:55,080 --> 00:02:59,000 which applies to in particular electrons, but also to all particles 55 00:02:59,000 --> 00:03:01,360 that are fermions, including muons, quarks. 56 00:03:01,360 --> 00:03:02,680 And so forth. 57 00:03:02,680 --> 00:03:05,680 Now the scientific community is, 58 00:03:06,960 --> 00:03:10,560 is is usually pretty good about correcting errors of attribution. 59 00:03:10,560 --> 00:03:12,840 Max Born was very clear that he had made a mistake. 60 00:03:12,840 --> 00:03:14,160 He was very apologetic about it. 61 00:03:14,160 --> 00:03:16,640 He told everyone that he had made this error. 62 00:03:16,640 --> 00:03:20,160 He felt guilty about it for the rest of his life, having robbed Yordan 63 00:03:20,160 --> 00:03:23,840 of of credit that he rightly deserved and under most conditions, 64 00:03:24,000 --> 00:03:26,840 the scientific community would have renamed Fermi-Dirac statistics 65 00:03:26,840 --> 00:03:30,440 into Fermi-Dirac statistics or Yordan from Dirac statistics. 66 00:03:30,440 --> 00:03:31,800 But this didn't happen. 67 00:03:31,800 --> 00:03:33,080 And the reason it didn't happen 68 00:03:33,080 --> 00:03:38,520 is because a few years later, Yordan became very prominent Nazi and and pretty 69 00:03:38,520 --> 00:03:42,400 much no one liked him and no one felt the need to do him any favors. 70 00:03:44,280 --> 00:03:47,280 So, you know, 71 00:03:47,520 --> 00:03:51,240 there's there's more to this story, which is don't become a Nazi. 72 00:03:53,680 --> 00:03:56,680 This is my joke about American politics. 73 00:03:57,400 --> 00:04:01,360 So anyway, by 1930, the basics of quantum mechanics were. 74 00:04:01,360 --> 00:04:02,360 We're finished. 75 00:04:02,360 --> 00:04:05,280 Quantum field theory more or less finished by 1950. 76 00:04:05,280 --> 00:04:08,800 And during that time and since that time, you might wonder if people asked 77 00:04:08,800 --> 00:04:10,320 if there are other particles out there. 78 00:04:10,320 --> 00:04:14,320 There's bosons and there's fermions and is is there something else? 79 00:04:14,520 --> 00:04:18,160 And over and over people came to the same conclusion, which was no. 80 00:04:18,200 --> 00:04:21,280 All you have is bosons or fermions and nothing else. 81 00:04:21,280 --> 00:04:22,040 And if you open up 82 00:04:22,040 --> 00:04:25,680 your favorite quantum mechanics textbook, chances are that's what it says. 83 00:04:26,080 --> 00:04:30,240 Lots and lots of quantum mechanics textbooks have, have that answer in it. 84 00:04:30,360 --> 00:04:33,960 And they all give the same argument, which is very simple. 85 00:04:33,960 --> 00:04:35,880 And I'm going to give that argument right now. 86 00:04:35,880 --> 00:04:37,600 It's pretty, pretty easy argument. 87 00:04:37,600 --> 00:04:38,480 You define 88 00:04:38,480 --> 00:04:41,840 an operator called the exchange operator which switches the position 89 00:04:41,840 --> 00:04:42,640 of two particles. 90 00:04:42,640 --> 00:04:48,080 So the exchange operator applied to psi of r1, r2 gives you psi of r2 r1. 91 00:04:48,360 --> 00:04:51,160 If you apply this operator twice, you get back to where 92 00:04:51,160 --> 00:04:54,240 you started exchanging twice the identity. 93 00:04:54,480 --> 00:04:56,960 There's only two square roots of the identity. 94 00:04:56,960 --> 00:04:59,280 Therefore there's only two possibilities. 95 00:04:59,280 --> 00:05:01,440 If it's a plus one, you call it bosons. 96 00:05:01,440 --> 00:05:05,600 If it's a minus one, you call it fermions, and that's all you're allowed to have. 97 00:05:05,920 --> 00:05:07,800 This is a great argument. It's very simple. 98 00:05:07,800 --> 00:05:09,800 It's very clear. Unfortunately, it's also wrong. 99 00:05:11,640 --> 00:05:13,920 So this was not realized 100 00:05:13,920 --> 00:05:18,320 for quite a long time until 1976 with this beautiful paper 101 00:05:18,560 --> 00:05:21,800 by the Two Johns in Oslo, John Magna, Linus 102 00:05:21,800 --> 00:05:25,080 and Jon Wertheim, who are 28 and 30 years old at the time. 103 00:05:25,080 --> 00:05:28,080 Obviously, they're a little older in these photos. 104 00:05:28,880 --> 00:05:32,400 And they pointed out that if we lived in a two plus one 105 00:05:32,400 --> 00:05:35,640 dimensional universe, that's two spatial dimensions and one time 106 00:05:35,640 --> 00:05:38,880 dimension, then you could have other type of particles as well. 107 00:05:38,880 --> 00:05:43,040 And what they envisaged was the idea that if you exchange two particles, say 108 00:05:43,040 --> 00:05:47,960 counterclockwise here, the wave function would pick up a phase E to the I theta. 109 00:05:48,280 --> 00:05:50,800 Theta equals zero means no phase. 110 00:05:50,800 --> 00:05:51,840 That's bosons. 111 00:05:51,840 --> 00:05:54,360 Theta was pi into the I. Pi is minus one. 112 00:05:54,360 --> 00:05:55,680 That's fermions. 113 00:05:55,680 --> 00:05:59,360 But they pointed out that in fact, other values of theta, any value of theta 114 00:05:59,520 --> 00:06:01,680 is really also allowed by quantum mechanics. 115 00:06:01,680 --> 00:06:04,000 If you live in two to plus one dimensions. 116 00:06:04,000 --> 00:06:07,520 Now from this paper there's a number of things we can conclude. 117 00:06:07,760 --> 00:06:09,960 You might be tempted to conclude from this paper 118 00:06:09,960 --> 00:06:12,000 that everyone in Oslo is named John. 119 00:06:12,000 --> 00:06:15,720 This is this is in fact not correct, I assure you. 120 00:06:16,040 --> 00:06:17,720 But a little bit of a coincidence. 121 00:06:17,720 --> 00:06:19,240 They both happen to be named John. 122 00:06:19,240 --> 00:06:21,360 But there's other things that you should conclude. 123 00:06:21,360 --> 00:06:22,560 One thing you should conclude that 124 00:06:22,560 --> 00:06:25,560 there is something wrong with the argument I just gave you. 125 00:06:25,680 --> 00:06:27,320 And indeed, there is something wrong. 126 00:06:27,320 --> 00:06:28,160 When you define 127 00:06:28,160 --> 00:06:31,600 an exchange operator, you need to say how you exchange the particles. 128 00:06:31,920 --> 00:06:36,120 So to make that more clear, in two plus one is Shivaji 129 00:06:36,120 --> 00:06:39,120 actually mentioned this earlier, but I'll give the argument again 130 00:06:39,280 --> 00:06:40,800 in two plus one dimensions. 131 00:06:40,800 --> 00:06:44,520 If you exchange particles counterclockwise and you exchange them counterclockwise 132 00:06:44,520 --> 00:06:49,240 again, if you look at the world lines of the particles, the paths in space time, 133 00:06:49,480 --> 00:06:52,560 you will notice that the world lines have not it around each other 134 00:06:52,560 --> 00:06:55,840 and becomes more clear if you connect up the top to the bottom. 135 00:06:55,840 --> 00:07:00,160 And now you have two strands which are knotted, with each other. 136 00:07:00,600 --> 00:07:03,760 This is not the same as having not exchange the particles at all. 137 00:07:03,800 --> 00:07:06,720 So two exchanges is not equal to the identity. 138 00:07:06,720 --> 00:07:11,160 Now, the reason we got away with saying two exchanges is the same as the identity 139 00:07:11,160 --> 00:07:15,400 is because we usually think about three plus one dimensions, and in three plus 140 00:07:15,400 --> 00:07:18,720 one dimensions, two plus one and two exchanges actually 141 00:07:18,720 --> 00:07:21,920 is equal to the identity that comes from a topological statement 142 00:07:22,120 --> 00:07:25,640 that if you're living in a space with a total of four dimensions, 143 00:07:25,640 --> 00:07:28,800 four dimensional space, and you have one dimensional strands, 144 00:07:28,920 --> 00:07:31,520 you cannot make knots in one dimensional strands. 145 00:07:31,520 --> 00:07:33,920 Living in four dimensional space. 146 00:07:33,920 --> 00:07:36,720 If this is not obvious to you, ask me at the end. 147 00:07:36,720 --> 00:07:39,200 We can probably make it and make it obvious, but, 148 00:07:39,200 --> 00:07:42,200 But it is a true topological statement. 149 00:07:42,600 --> 00:07:43,360 Okay. 150 00:07:43,360 --> 00:07:47,800 So there's there's some other things we can conclude from this paper here. 151 00:07:48,280 --> 00:07:50,960 One thing that we can conclude, which is quite important, 152 00:07:50,960 --> 00:07:55,040 is that the scientific community isn't that good at realizing 153 00:07:55,040 --> 00:07:56,880 when something important has happened. 154 00:07:56,880 --> 00:07:59,600 This paper was more or less completely ignored 155 00:07:59,600 --> 00:08:01,800 for the first few years of its life. 156 00:08:01,800 --> 00:08:05,320 It was cited five times in the first five years of its of its life. 157 00:08:05,680 --> 00:08:09,000 And three of those citations are by the young Magna Linus himself. 158 00:08:09,360 --> 00:08:13,320 So pretty much no one was paying attention to this at all. 159 00:08:13,680 --> 00:08:14,920 But a few years later, 160 00:08:15,880 --> 00:08:16,920 this person, Frank 161 00:08:16,920 --> 00:08:20,200 Wilczek, did take notice and found it very interesting. 162 00:08:20,200 --> 00:08:24,440 Now, Frank Wilczek was already very famous for work he did when he was 22 years old 163 00:08:24,440 --> 00:08:27,480 in 1973, which would later win him a Nobel Prize. 164 00:08:27,520 --> 00:08:30,880 Asymptotic freedom in QCD, which turns out to be very important. 165 00:08:31,080 --> 00:08:35,000 So people were watching what he was doing, and once he got interested, 166 00:08:35,000 --> 00:08:38,000 then a lot of other people got interested in this as well. 167 00:08:38,000 --> 00:08:41,800 Another thing he did is he he gave a name to these types of particles. 168 00:08:41,800 --> 00:08:43,920 He called them anions, particles 169 00:08:43,920 --> 00:08:47,720 that have any statistics besides bosons and fermions. 170 00:08:47,720 --> 00:08:50,880 We'll check is particularly good at coming up with cute names. 171 00:08:51,360 --> 00:08:56,760 But what he was actually concerned with is the famous spin statistics theorem. 172 00:08:56,920 --> 00:09:00,480 To remind you what the spin statistics theorem is, it's a statement 173 00:09:00,640 --> 00:09:02,200 that if you have two identical particles 174 00:09:02,200 --> 00:09:04,640 and you exchange them, you accumulate some phase. 175 00:09:04,640 --> 00:09:08,200 Or if you take one of those particles and you rotate it around its axis by two 176 00:09:08,200 --> 00:09:12,520 pi, the phases that you accumulate in those two processes should be the same. 177 00:09:12,880 --> 00:09:13,960 For bosons. 178 00:09:13,960 --> 00:09:16,800 You get no phase for rotating it, no phase or exchanging. 179 00:09:16,800 --> 00:09:19,280 For fermions you get a minus one for rotating, 180 00:09:19,280 --> 00:09:21,840 you get minus one for exchanging, and for anyons 181 00:09:22,800 --> 00:09:24,120 there's the same thing hold up. 182 00:09:24,120 --> 00:09:25,400 And in fact it does. 183 00:09:25,400 --> 00:09:27,520 And that was kind of interesting. 184 00:09:27,520 --> 00:09:28,880 He notes in his paper. 185 00:09:28,880 --> 00:09:32,760 Although practical applications of these phenomena seem remote, 186 00:09:33,000 --> 00:09:35,120 they do have considerable methodological interest 187 00:09:35,120 --> 00:09:38,120 and shed some light on the spin statistics connection. 188 00:09:38,160 --> 00:09:41,000 So he couldn't imagine how you would ever be 189 00:09:41,000 --> 00:09:44,040 concerned with, two plus one dimensional universe. 190 00:09:44,040 --> 00:09:46,720 But it's a nice toy problem to play with. 191 00:09:46,720 --> 00:09:50,840 The same year, however, was the discovery of the so-called fractional quantum 192 00:09:50,840 --> 00:09:54,880 Hall effect, about which I will say a lot more in a moment, but it's an effect. 193 00:09:54,880 --> 00:09:58,200 It's observed an experiment in two dimensional electrons in high 194 00:09:58,200 --> 00:10:02,640 magnetic fields and low temperatures hint two dimensional electrons. 195 00:10:02,880 --> 00:10:05,280 So how do you get two dimensional electrons? 196 00:10:05,280 --> 00:10:11,240 Well, in this was this discovery was made when Horst Stormer was 33 years old. 197 00:10:12,440 --> 00:10:12,800 So to 198 00:10:12,800 --> 00:10:15,960 make two dimensional electrons, the way they did it was they sandwich 199 00:10:16,000 --> 00:10:20,640 the thin layer of gallium arsenide between layers of aluminum gallium arsenide. 200 00:10:20,640 --> 00:10:23,880 And they trapped electrons in this thin purple layer here. 201 00:10:24,080 --> 00:10:27,720 In fact, perhaps the more important discovery, even though the discovery 202 00:10:27,720 --> 00:10:29,760 of fractional quantum Hall effect was an important discovery, 203 00:10:29,760 --> 00:10:33,840 the more important discovery was made by Horace Stormer several years earlier, 204 00:10:34,200 --> 00:10:38,640 in which where he figured out how to make such semiconductor structures 205 00:10:38,640 --> 00:10:42,320 without introducing a lot of disorder into the gallium arsenide. 206 00:10:42,320 --> 00:10:44,520 This is a trick known as modulation doping. 207 00:10:44,520 --> 00:10:47,480 It's used industrially in all sorts of semiconductors. 208 00:10:47,480 --> 00:10:49,200 It was a very profitable patent 209 00:10:49,200 --> 00:10:52,800 for Bell Labs the company was working for for a long time in. 210 00:10:52,800 --> 00:10:54,760 The patent is now expired, I think. 211 00:10:54,760 --> 00:10:58,680 Anyway, in the modern era, there's other ways 212 00:10:58,680 --> 00:11:01,560 to make two dimensional electrons, and a really interesting one 213 00:11:01,560 --> 00:11:05,240 is the idea of using single atomic layers of carbon. 214 00:11:05,240 --> 00:11:06,520 What's known as graphene. 215 00:11:06,520 --> 00:11:10,640 Carbon can make a single layer in a little, honeycomb pattern like this, 216 00:11:10,640 --> 00:11:14,400 where each of these balls is a carbon carbon atom, all, all stuck together. 217 00:11:14,640 --> 00:11:20,000 It was discovered that you could do that in 2004 by Novoselov and Andrew Geim. 218 00:11:20,680 --> 00:11:23,160 Costello was 30 years old at the time. 219 00:11:23,160 --> 00:11:27,920 And this is another example of, of, of the theorem that the scientific 220 00:11:27,920 --> 00:11:31,680 community isn't very good at understanding when something important has happened. 221 00:11:31,840 --> 00:11:34,800 In fact, they had a lot of trouble getting their work published. 222 00:11:34,800 --> 00:11:36,160 It took them about a year to get it 223 00:11:36,160 --> 00:11:39,920 printed anywhere, and six years later, it already won a Nobel Prize. 224 00:11:40,120 --> 00:11:42,840 No one realized why this was really super interesting, 225 00:11:42,840 --> 00:11:45,840 but then all of a sudden everyone realized, yeah, this is super interesting. 226 00:11:46,080 --> 00:11:51,120 Anyway, making single atomic layers of carbon is a modern way of, 227 00:11:51,440 --> 00:11:56,520 of making to much electron systems, about which you'll hear more, later. 228 00:11:57,520 --> 00:12:00,360 Anyway, so in 1982, this effect, 229 00:12:00,360 --> 00:12:02,360 fractional quantum Hall effect was discovered. 230 00:12:02,360 --> 00:12:05,520 The theory of fractional quantum Hall effect was laid out. 231 00:12:05,600 --> 00:12:08,160 Its basic parts by Bob Laughlin. 232 00:12:08,160 --> 00:12:10,360 He was 33 years old at the time, actually. 233 00:12:10,360 --> 00:12:13,600 Academically, he was even younger than 33 because he, 234 00:12:13,600 --> 00:12:16,920 was forced to join the military because of the draft. 235 00:12:16,920 --> 00:12:21,680 And he lost quite a few, a number of his, his young years and not studying physics, 236 00:12:21,680 --> 00:12:23,360 which is what you should be doing when you're young. 237 00:12:23,360 --> 00:12:25,520 Anyway. 238 00:12:25,520 --> 00:12:29,280 The the group of them would win the Nobel Prize in, in 1998. 239 00:12:29,400 --> 00:12:30,960 So what about fractional quantum 240 00:12:30,960 --> 00:12:34,880 Hall effect was so interesting that it deserves, a Nobel Prize. 241 00:12:34,880 --> 00:12:39,520 Well, the next year, two groups managed to show, theoretically, 242 00:12:39,760 --> 00:12:41,160 that the low energy particles 243 00:12:41,160 --> 00:12:44,760 that arise in fractional quantum Hall systems really are anions. 244 00:12:45,200 --> 00:12:47,280 The people involved in bird hopping. 245 00:12:47,280 --> 00:12:49,400 And my thesis advisor, as it turns out. 246 00:12:49,400 --> 00:12:51,440 And we'll check. 247 00:12:51,440 --> 00:12:56,520 We've already meant Rob Schriever is, well, he was 26 years old when he did 248 00:12:56,520 --> 00:12:59,520 his Nobel Prize winning work in 1957, 249 00:12:59,560 --> 00:13:03,600 that the BCS theory of superconductivity very important, 250 00:13:04,000 --> 00:13:07,000 major breakthrough in physics. 251 00:13:07,080 --> 00:13:10,080 And the graduate student who did all the work then either of us 252 00:13:10,240 --> 00:13:13,240 was 23 years old at at the time. 253 00:13:13,440 --> 00:13:17,080 So anyway, theoretically, we believe that in these fractional 254 00:13:17,080 --> 00:13:20,480 quantum Hall systems, we do have anions running around. 255 00:13:20,880 --> 00:13:24,080 So the history of the field just summarizing it. 256 00:13:24,120 --> 00:13:26,560 And by 1920s we had bosons and fermions. 257 00:13:26,560 --> 00:13:29,320 The first proposal of anions was in 77. 258 00:13:29,320 --> 00:13:32,320 By 1984, we believe we actually had 259 00:13:32,520 --> 00:13:35,520 an experiment system where anions exist. 260 00:13:35,760 --> 00:13:39,360 The theoretical community accepted this almost immediately. 261 00:13:39,360 --> 00:13:42,880 It became gospel among quantum condensed matter physicists. 262 00:13:42,880 --> 00:13:45,400 Everyone learns this in graduate school. 263 00:13:45,400 --> 00:13:46,440 It's sort of fundamental 264 00:13:46,440 --> 00:13:49,680 to a lot of our understanding of of modern condensed matter physics. 265 00:13:50,200 --> 00:13:55,200 But as Shivaji said, often theory outruns experiment. 266 00:13:55,400 --> 00:13:59,520 It took a very long time between before this statement was, 267 00:13:59,920 --> 00:14:03,360 it was confirmed experimentally, before we actually had an experiment 268 00:14:03,360 --> 00:14:07,000 where we could show that exchanging two of these particles 269 00:14:07,240 --> 00:14:10,400 would give you a phase which is not plus 1 or -1. 270 00:14:10,680 --> 00:14:13,160 So that's what I'm going to talk about. 271 00:14:13,160 --> 00:14:16,200 So, before going on, 272 00:14:16,600 --> 00:14:19,760 you might ask me, why are you interested in anions in the first place? 273 00:14:20,120 --> 00:14:23,120 Well, one reason is because it's a fundamental interest. 274 00:14:23,160 --> 00:14:26,280 As physicists, we're always concerned with what kind of things can exist, 275 00:14:26,520 --> 00:14:27,480 at least in principle. 276 00:14:27,480 --> 00:14:30,120 What are its properties? How can you use it? 277 00:14:30,120 --> 00:14:33,120 So it's just fundamentally interesting to begin with. 278 00:14:33,200 --> 00:14:37,040 Another thing is, maybe it's lurking in plain sight, maybe the 279 00:14:37,080 --> 00:14:39,720 I mean, there's lots of experimental systems where we don't actually know 280 00:14:39,720 --> 00:14:43,080 what's going on or we think we do, but we it's not entirely sure. 281 00:14:43,440 --> 00:14:45,960 Maybe there's anions running around in lots of systems 282 00:14:45,960 --> 00:14:47,520 and we just haven't realized it yet. 283 00:14:49,320 --> 00:14:51,600 There's also a, surprisingly 284 00:14:51,600 --> 00:14:55,560 large number of connections to fields like high energy physics, quantum gravity, 285 00:14:55,800 --> 00:14:59,400 pure mathematics, and topology, which are also interesting in their own right. 286 00:14:59,760 --> 00:15:03,240 But the field got a huge boost in 1997 287 00:15:03,240 --> 00:15:07,440 by this person, Alexei Khattab, who was 33 years old at the time. 288 00:15:07,920 --> 00:15:12,000 Who pointed out that if you ever have a physical system with anions in it, 289 00:15:12,120 --> 00:15:16,280 you have a really good way to make a quantum memory, which would be very useful 290 00:15:16,440 --> 00:15:20,000 for a quantum computer should you ever build a quantum computer. 291 00:15:20,680 --> 00:15:23,040 This idea to hold then working 292 00:15:23,040 --> 00:15:26,840 with Michael Freedman, shortly thereafter, they, 293 00:15:26,920 --> 00:15:30,520 they proposed the idea of a so-called topological quantum computer, 294 00:15:30,720 --> 00:15:33,840 where all the computations are done by moving, 295 00:15:33,840 --> 00:15:36,840 anions around anions of a particular type. 296 00:15:37,200 --> 00:15:42,160 Anyway, this idea was, so important that Microsoft invested. 297 00:15:42,560 --> 00:15:43,800 I mean, I'm estimating this number, 298 00:15:43,800 --> 00:15:47,840 but I think the estimate is probably fairly accurate, over $1 billion so far 299 00:15:47,840 --> 00:15:52,440 into trying to produce a quantum computer that runs on this, on this principle. 300 00:15:52,560 --> 00:15:56,360 So the other person who's involved here is Mike Freedman in 1981, when he was 301 00:15:56,360 --> 00:15:57,240 30 years old, 302 00:15:57,240 --> 00:16:00,240 he proved an important mathematical theorem that won the Fields Medal. 303 00:16:00,600 --> 00:16:03,000 That's like the Nobel Prize of Mathematics. 304 00:16:03,000 --> 00:16:05,040 The very same year, he also won the American 305 00:16:05,040 --> 00:16:07,760 Rock Climbing Championship, for whatever that's worth. 306 00:16:07,760 --> 00:16:09,520 So he's a tough guy to keep up with. 307 00:16:10,920 --> 00:16:13,000 Okay, so 308 00:16:13,000 --> 00:16:14,120 what's kind of interesting 309 00:16:14,120 --> 00:16:17,720 about the experimental confirmation, which came around, around 20, 20, 310 00:16:18,120 --> 00:16:22,000 35, 36 years after the proposal that we actually have anions 311 00:16:22,360 --> 00:16:25,680 is that it wasn't just one experiment that did this. 312 00:16:25,680 --> 00:16:27,920 It wasn't just one experimental system, 313 00:16:27,920 --> 00:16:31,920 a number of technologies, all matured at roughly the same time. 314 00:16:31,920 --> 00:16:35,160 And we had a bunch of experiments all doing showing the same thing. 315 00:16:35,480 --> 00:16:38,360 So the first experiment to come out was a so-called anion collider 316 00:16:38,360 --> 00:16:42,280 experiment done by Gwendoline Evans group in Paris, done with, two 317 00:16:42,280 --> 00:16:46,080 dimensional electron gases and gallium arsenide semiconductor hetero structures. 318 00:16:46,440 --> 00:16:49,400 Then there was the Atom Interference and Interferometer 319 00:16:49,400 --> 00:16:52,680 Experiment, done first at at Purdue by Mike Mann. 320 00:16:52,680 --> 00:16:54,960 First group in gallium arsenide hetero structures, 321 00:16:54,960 --> 00:16:58,400 and later done by the Harvard Group and the University 322 00:16:58,400 --> 00:17:02,040 of California, Santa Barbara group by Philip Kim and Andrea Yang. 323 00:17:02,280 --> 00:17:07,200 Done in graphene, carbon, two dimensional electron systems. 324 00:17:07,480 --> 00:17:10,320 And then in addition, there was simulation 325 00:17:10,320 --> 00:17:14,040 of anions on quantum computers and rudimentary quantum computers. 326 00:17:14,040 --> 00:17:14,680 And this had been done 327 00:17:14,680 --> 00:17:17,920 by a huge number of groups for people who are familiar with it, 328 00:17:18,200 --> 00:17:22,400 the toric code is basically an anion model or the surface code. 329 00:17:22,960 --> 00:17:26,520 This is basically the best error correcting quantum code we know of. 330 00:17:26,640 --> 00:17:28,680 So more or less, every quantum 331 00:17:28,680 --> 00:17:32,120 computing effort in the world is trying to build anion models 332 00:17:32,280 --> 00:17:35,280 more or less, and it's been achieved by a number of different groups. 333 00:17:35,520 --> 00:17:36,240 By this time. 334 00:17:37,280 --> 00:17:38,040 Okay. 335 00:17:38,040 --> 00:17:41,120 Of these, the the experiment that I think is the nicest 336 00:17:41,120 --> 00:17:44,480 and the easiest to explain is this one, the graphene version. 337 00:17:44,480 --> 00:17:45,960 It has some properties 338 00:17:45,960 --> 00:17:49,200 which I like very much, and the data is particularly beautiful. 339 00:17:49,320 --> 00:17:51,960 So I'm going to show this one to you. 340 00:17:51,960 --> 00:17:55,280 So first I have to explain a little bit about fractional quantum Hall effect. 341 00:17:55,560 --> 00:17:58,560 As I explained you need two dimensional electrons 342 00:17:58,640 --> 00:18:01,280 minimal amount of disorder and get rid of it all together. 343 00:18:01,280 --> 00:18:02,280 That's great. 344 00:18:02,280 --> 00:18:06,640 The we put a magnetic field perpendicular to the plane of the sample, 345 00:18:06,960 --> 00:18:09,760 and you cool it down to very, very low temperature. 346 00:18:09,760 --> 00:18:12,800 It's, 1/10,000 of room temperature 347 00:18:12,800 --> 00:18:15,800 is more or less where these experiments are done. 348 00:18:15,920 --> 00:18:20,400 The number you want to keep track of is known as the filling fraction. 349 00:18:20,400 --> 00:18:24,800 It's basically the ratio of the density of electrons to the magnetic field 350 00:18:25,120 --> 00:18:28,560 made dimensionless by, a flux quantum 351 00:18:28,560 --> 00:18:32,160 h bar over over the charge of of of the electron. 352 00:18:32,160 --> 00:18:33,960 So this is a dimensionless ratio. 353 00:18:33,960 --> 00:18:36,720 And you can change it by changing the magnetic field. 354 00:18:36,720 --> 00:18:39,720 When this dimension, this ratio, the filling 355 00:18:39,840 --> 00:18:43,160 is approximately a ratio of small integers. 356 00:18:43,160 --> 00:18:46,560 So p over q could be one over three, two over five over seven. 357 00:18:46,960 --> 00:18:49,760 Then fractional quantum Hall effect can occur. 358 00:18:50,800 --> 00:18:53,040 How do you know when you have fractional quantum Hall effect. 359 00:18:53,040 --> 00:18:58,160 Well, you measure something and what you measure is some sort of resistance. 360 00:18:58,160 --> 00:19:01,240 So you run current through your sample and you measure 361 00:19:01,240 --> 00:19:04,240 a voltage in the same direction as the current. 362 00:19:04,280 --> 00:19:06,520 What you measure is zero voltage. 363 00:19:06,520 --> 00:19:10,000 Now if you remember for a second that power dissipated 364 00:19:10,320 --> 00:19:13,440 is current times voltage in the direction of the current. 365 00:19:13,720 --> 00:19:17,800 So if the voltage in direction is zero, then you have zero power 366 00:19:17,800 --> 00:19:21,120 dissipation, which means it's flowing without any loss whatsoever. 367 00:19:21,360 --> 00:19:26,000 It's like a superconductor or a superfluid of some sort, dissipation, less flow. 368 00:19:26,000 --> 00:19:27,600 And that's kind of interesting. 369 00:19:27,600 --> 00:19:29,240 More interesting is what happens 370 00:19:29,240 --> 00:19:32,240 if you measure the voltage perpendicular to the current flow. 371 00:19:33,040 --> 00:19:36,680 In this case, the ratio of the so-called half voltage, 372 00:19:36,680 --> 00:19:39,680 the voltage perpendicular, the current flow divided by the current. 373 00:19:39,720 --> 00:19:43,560 This is known as a high resistance is two pi h bar over e squared. 374 00:19:44,480 --> 00:19:48,360 Is the charge an electron times q over p these two integers down here? 375 00:19:48,360 --> 00:19:49,600 Exactly. 376 00:19:49,600 --> 00:19:54,320 Now when I say exactly, I mean exactly to the precision with which it can be 377 00:19:54,320 --> 00:19:58,560 measured, that's about one part and ten to the 10 to 1 part and ten to the 11. 378 00:19:58,840 --> 00:20:02,800 That's like measuring the distance from here to California to within a centimeter. 379 00:20:03,120 --> 00:20:06,000 It's an extraordinary amount of precision considering 380 00:20:06,000 --> 00:20:09,560 this is a sloppy, messy, solid state experiment. 381 00:20:09,760 --> 00:20:11,360 So there is disorder in the sample. 382 00:20:11,360 --> 00:20:13,080 You don't know the shape of the sample. Exactly. 383 00:20:13,080 --> 00:20:16,680 You stuck electrodes on the sample to measure resistances with, 384 00:20:17,040 --> 00:20:18,600 you know, a soldering iron. 385 00:20:18,600 --> 00:20:22,080 You know that that there's so many things about about this experiment 386 00:20:22,080 --> 00:20:22,920 that you don't control. 387 00:20:22,920 --> 00:20:25,080 Precisely. Don't control the magnetic field. Precisely. 388 00:20:25,080 --> 00:20:27,240 You don't control the temperature. Precisely. 389 00:20:27,240 --> 00:20:28,160 You don't control it. 390 00:20:28,160 --> 00:20:30,120 They're vibrations going to the laboratory. 391 00:20:30,120 --> 00:20:31,920 There's no light shining on your sample. 392 00:20:31,920 --> 00:20:33,800 There's all sorts of things that you don't control. 393 00:20:33,800 --> 00:20:38,520 And yet the result comes out exactly two pi h bar over E squared times Q over p. 394 00:20:39,240 --> 00:20:41,320 All right. So that's kind of cool. 395 00:20:42,960 --> 00:20:43,560 Here's some real 396 00:20:43,560 --> 00:20:46,560 data, taken by George Stormer. 397 00:20:46,760 --> 00:20:49,320 And what you have here is a longitudinal resistance 398 00:20:49,320 --> 00:20:52,640 down here and the whole resistance up here, 399 00:20:53,040 --> 00:20:56,960 every time the longitudinal resistance drops down to zero, 400 00:20:57,080 --> 00:21:02,080 you will see that the whole resistance shows a flat plateau, exact quantization. 401 00:21:02,440 --> 00:21:07,440 And these plateaus are labeled by their p over q ratio. 402 00:21:07,480 --> 00:21:12,080 So, for example, this one's two over five, this one's one over three and so forth. 403 00:21:12,080 --> 00:21:14,640 Each of these is a different fractional quantum Hall state. 404 00:21:14,640 --> 00:21:18,440 The one we're going to focus on is the simplest actually the one 405 00:21:18,440 --> 00:21:21,840 that was first observed in experiment is a so-called new because one third 406 00:21:22,040 --> 00:21:25,320 fractional quantum Hall state, which is the easiest to understand. 407 00:21:26,280 --> 00:21:29,600 So in the new equals one third fractional quantum 408 00:21:29,600 --> 00:21:31,360 Hall effect, you start with the ground state. 409 00:21:31,360 --> 00:21:32,760 Then you make some excitations. 410 00:21:32,760 --> 00:21:37,000 And those excitations are particles that surprisingly have fractional charge. 411 00:21:38,200 --> 00:21:40,560 You put in electrons of charge E 412 00:21:40,560 --> 00:21:43,920 and the excitations now have charge U over three. 413 00:21:43,920 --> 00:21:48,160 You have an emergent particle with a fraction of the charge of an electron. 414 00:21:48,160 --> 00:21:49,800 Now how does that happen? 415 00:21:49,800 --> 00:21:54,120 Well, the way you should sort of think about it is that the electrons 416 00:21:54,120 --> 00:21:57,480 form a completely uniform soup of, 417 00:21:58,560 --> 00:22:00,600 of uniform density electrons. 418 00:22:00,600 --> 00:22:03,600 And these particles are the defects of that soup. 419 00:22:03,760 --> 00:22:04,560 Okay. 420 00:22:04,560 --> 00:22:08,560 It's a pushes a fraction of a charge of the electron away from some region. 421 00:22:08,560 --> 00:22:11,760 And that defect becomes the new low energy particle. 422 00:22:12,320 --> 00:22:14,520 What's more interesting 423 00:22:14,520 --> 00:22:18,040 is that these particles are also anions. 424 00:22:18,040 --> 00:22:21,880 When you exchange them, you pick up a phase in the two pi over three. 425 00:22:21,920 --> 00:22:22,440 They're neither. 426 00:22:22,440 --> 00:22:25,440 Both bosons nor fermions. 427 00:22:27,280 --> 00:22:31,320 But surely you must say these particles really live in three dimensions. 428 00:22:31,320 --> 00:22:33,840 Our universe is three dimensional. How can you know? 429 00:22:33,840 --> 00:22:35,360 Maybe if you have squashed them down. 430 00:22:35,360 --> 00:22:37,120 So they're approximately two dimensional, 431 00:22:37,120 --> 00:22:39,840 but they're not really two dimensional, are they? 432 00:22:39,840 --> 00:22:43,640 Well, let's look a little more carefully about what we at what we've done. 433 00:22:43,800 --> 00:22:45,760 We have our sample like this. 434 00:22:45,760 --> 00:22:51,200 We've tried to squeeze our electrons down into our this little blue layer here. 435 00:22:51,520 --> 00:22:54,560 Let's use a little bit of, gratuitous animation 436 00:22:54,960 --> 00:22:58,320 and blow up, our, our system here. 437 00:22:58,560 --> 00:23:02,160 And the, the potential felt by the electrons is kind of 438 00:23:02,160 --> 00:23:05,480 a, you know, a particle in a box, kind of, square. 439 00:23:05,480 --> 00:23:07,200 Well, potential. 440 00:23:07,200 --> 00:23:09,760 So the electrons are living in here. 441 00:23:09,760 --> 00:23:13,840 Blow that up, look at it more closely, and we're putting the electrons in there 442 00:23:13,840 --> 00:23:15,440 and so. Well, it's still living in three dimensions. 443 00:23:15,440 --> 00:23:17,200 Maybe they're sort of confined a little bit 444 00:23:17,200 --> 00:23:21,040 in, in the well but they're still really living in three dimensions aren't they. 445 00:23:21,280 --> 00:23:23,200 Well think about that more carefully. 446 00:23:23,200 --> 00:23:26,680 Remember that they form discrete eigenstates in the z direction 447 00:23:26,680 --> 00:23:30,480 in that well, and they occupy some of the different eigenstates. 448 00:23:30,480 --> 00:23:34,960 At low temperature they all get frozen down into the lowest eigenstate. 449 00:23:34,960 --> 00:23:38,880 And you remove any ability for them to change their wavefunction 450 00:23:39,120 --> 00:23:40,200 in the z direction. 451 00:23:40,200 --> 00:23:42,480 Their z direction is completely frozen. 452 00:23:42,480 --> 00:23:45,360 There's no freedom to change anything in the z direction, 453 00:23:45,360 --> 00:23:48,800 and so they can only move in there in the x and y direction, 454 00:23:48,840 --> 00:23:51,000 they become strictly two dimensional objects. 455 00:23:51,960 --> 00:23:53,280 Okay, 456 00:23:53,280 --> 00:23:56,360 so people might be thinking something else. 457 00:23:56,360 --> 00:23:57,480 Another objection. 458 00:23:57,480 --> 00:23:59,760 But surely these aren't fundamental particles, 459 00:23:59,760 --> 00:24:02,760 not like an electron is a fundamental particle, is it? 460 00:24:02,880 --> 00:24:05,200 Well, you know, maybe nothing is. 461 00:24:05,200 --> 00:24:09,600 You know, that we think of an electron as being a fundamental particle 462 00:24:09,600 --> 00:24:12,840 because on the energy scales available to our experiment, 463 00:24:13,360 --> 00:24:15,320 we have not seen it break up into other things. 464 00:24:15,320 --> 00:24:17,240 We have not seen it emerged from other things. 465 00:24:17,240 --> 00:24:20,040 But that just means the energy scales available to us. 466 00:24:20,040 --> 00:24:21,320 It looks fundamental. 467 00:24:21,320 --> 00:24:23,680 It's the same thing here 468 00:24:23,680 --> 00:24:26,400 in this low energy, low temperature system. 469 00:24:26,400 --> 00:24:29,840 If you were a low temperature person living in this two 470 00:24:29,840 --> 00:24:34,400 dimensional low temperature quantum, well, you would swear that 471 00:24:34,560 --> 00:24:38,200 the particles, the fundamental particles are charged E over three. 472 00:24:38,360 --> 00:24:42,360 And it's only when you got yourself out of that two dimensional, 473 00:24:42,360 --> 00:24:45,360 layer and could go up to higher energies that you would notice. 474 00:24:45,360 --> 00:24:46,320 Oh, actually, it's 475 00:24:46,320 --> 00:24:49,960 the electrons that are running around and the E over three is just emergent. 476 00:24:50,200 --> 00:24:53,040 We're always in the business of describing physical, 477 00:24:53,040 --> 00:24:56,080 physical systems at the relevant scale for the experiments. 478 00:24:56,080 --> 00:24:56,640 We can do. 479 00:24:57,840 --> 00:24:59,040 All right. 480 00:24:59,040 --> 00:25:03,000 So these were the this is sort of the history of the story. 481 00:25:03,000 --> 00:25:07,520 And the experiment I'm going to explain is this one here. 482 00:25:07,920 --> 00:25:11,800 So to explain this experiment and the remaining 15 minutes 483 00:25:12,160 --> 00:25:15,440 is I'm going to need to tell you a couple 484 00:25:15,440 --> 00:25:18,440 things more about fractional quantum Hall effect, but not much. 485 00:25:19,200 --> 00:25:22,200 So the first thing I have to tell you about is quantum Hall edge states. 486 00:25:22,280 --> 00:25:25,760 So here I have drawn the blue region and the white region, the blue regions 487 00:25:25,760 --> 00:25:28,720 where there are electrons. My fractional quantum Hall effect. 488 00:25:28,720 --> 00:25:30,800 And then the white region is outside of the sample. 489 00:25:30,800 --> 00:25:32,120 That's a vacuum. 490 00:25:32,120 --> 00:25:36,360 I know that there's going to be an electric field. 491 00:25:36,360 --> 00:25:39,960 Well, minus the electric field is going to point into this, into the sample. 492 00:25:40,200 --> 00:25:43,080 So there's an electric force holding the electrons in. 493 00:25:43,080 --> 00:25:44,280 How do I know it's there. 494 00:25:44,280 --> 00:25:46,680 Well if it wasn't there the electrons would leak out 495 00:25:46,680 --> 00:25:47,520 and they're not leaking out. 496 00:25:47,520 --> 00:25:49,640 So there's an electric field there. 497 00:25:50,680 --> 00:25:54,240 So and then there's a magnetic field perpendicular to the sample. 498 00:25:54,240 --> 00:25:58,880 And I know from basic and I'm that, whenever I have a crossed 499 00:25:58,880 --> 00:26:02,760 electric and magnetic field, there's a drift velocity have any charge. 500 00:26:03,280 --> 00:26:06,720 And you can, you can calculate the drift velocity just by finding the reference 501 00:26:06,720 --> 00:26:10,760 frame in which the Lorentz force e plus v cross b is turns out to be zero. 502 00:26:11,240 --> 00:26:14,280 So if I put a charge in particular one of these particles 503 00:26:14,280 --> 00:26:17,280 on the edge, it will drift along like this. 504 00:26:17,520 --> 00:26:23,800 And just because of the x b effect, now we're going to use that to our advantage 505 00:26:23,800 --> 00:26:26,800 to transport these particles around our system. 506 00:26:27,680 --> 00:26:30,680 So here's the the geometry of the sample we're going to use. 507 00:26:30,840 --> 00:26:34,840 We're going to take you know the the blue region again is quantum Hall fluid. 508 00:26:35,040 --> 00:26:36,560 And we're going to pinch it down 509 00:26:36,560 --> 00:26:40,440 in some region in what experimentalists call a quantum point contact. 510 00:26:40,720 --> 00:26:42,240 It's a point contact. 511 00:26:42,240 --> 00:26:45,840 And then they put the word quantum because they like the word quantum. So 512 00:26:47,280 --> 00:26:48,120 anyway, 513 00:26:48,120 --> 00:26:51,480 so if you put this you send these charges in along the edge 514 00:26:51,800 --> 00:26:55,440 and they, they kind of move along the edge bump, bump, bump, bump, bump like that. 515 00:26:55,680 --> 00:26:56,880 And most of them go through. 516 00:26:56,880 --> 00:27:00,800 But occasionally you'll discover that one of them comes along 517 00:27:00,800 --> 00:27:04,800 and then jumps across the narrow neck and gets back reflected instead. 518 00:27:05,200 --> 00:27:08,560 Okay, so we should think of this constriction as 519 00:27:08,600 --> 00:27:12,880 being a half silvered mirror to send some through and reflect some back. 520 00:27:13,200 --> 00:27:17,160 Just as a side comment, the first measurement of the fractional 521 00:27:17,160 --> 00:27:21,120 charge of these particles was done with a single point contact like this. 522 00:27:21,440 --> 00:27:25,480 You measure that when the, the current coming back at you 523 00:27:25,480 --> 00:27:26,840 and you measure some total current. 524 00:27:26,840 --> 00:27:29,880 But you notice that the noise in that current is indicating 525 00:27:29,880 --> 00:27:33,920 that the charges are coming back to you in units of E over three, rather 526 00:27:33,920 --> 00:27:35,000 than in units of E. 527 00:27:35,960 --> 00:27:38,720 And this experiment was done in the 90s by several groups. 528 00:27:38,720 --> 00:27:43,920 And it's now not not controversial that this works as, as as described. 529 00:27:44,520 --> 00:27:45,360 All right. 530 00:27:45,360 --> 00:27:46,920 This is the experiment I'm going to describe. 531 00:27:46,920 --> 00:27:50,960 It was proposed in 97 by our first speaker, Shivaji, 532 00:27:51,120 --> 00:27:54,120 and, his friends Claudio Sherman, Denise Reed, Steve 533 00:27:54,120 --> 00:27:57,120 Constant and Sheldon Wen. 534 00:27:57,120 --> 00:27:58,200 The idea 535 00:27:58,200 --> 00:28:02,160 is we're going to have two of these, point contact, 536 00:28:02,160 --> 00:28:05,880 one of them called T1 and one of them, called T2. 537 00:28:05,920 --> 00:28:08,640 This is going to act as a beam splitter and a mirror. 538 00:28:08,640 --> 00:28:11,560 And if you remember your optics, this is basically 539 00:28:11,560 --> 00:28:14,560 a fabric parallel interferometer. 540 00:28:14,600 --> 00:28:17,760 So the idea is that a particle can come along like this. 541 00:28:18,160 --> 00:28:20,200 It will split into two partial waves. 542 00:28:20,200 --> 00:28:22,640 One partial wave jumps across, 543 00:28:22,640 --> 00:28:25,840 the other partial wave goes on and is reflected around the cavity. 544 00:28:26,200 --> 00:28:29,120 And then they're interfere and go on their way. 545 00:28:29,120 --> 00:28:30,240 Okay. 546 00:28:30,240 --> 00:28:33,480 Now the, if you count both of those partial waves, 547 00:28:33,480 --> 00:28:36,480 the wave function of the particle coming back at you 548 00:28:36,720 --> 00:28:40,040 is the sum of the part that went across T1 here 549 00:28:40,440 --> 00:28:43,800 and the part that went across T2 here, but the part that went around 550 00:28:43,800 --> 00:28:48,600 T2 picks up an additional phase for having gone around the cavity. 551 00:28:48,880 --> 00:28:50,200 Okay. 552 00:28:50,200 --> 00:28:52,440 Then if you want to know the current coming back, 553 00:28:52,440 --> 00:28:55,240 you have to square the wave function the usual way. 554 00:28:55,240 --> 00:28:58,520 You know, probabilities are squares of amplitudes gives you t1 squared 555 00:28:58,520 --> 00:29:01,520 plus t2 squared plus two t1 t2 cosine phi. 556 00:29:01,560 --> 00:29:05,600 Assuming t1 and t2 are real for simplicity okay. 557 00:29:06,120 --> 00:29:09,240 So this is basically Fabry Perot interferometry physics. 558 00:29:09,400 --> 00:29:14,320 And the thing we're going to be interested in is this phase Phi down here. 559 00:29:16,440 --> 00:29:19,080 So there we're going to try to change that 560 00:29:19,080 --> 00:29:23,160 phase Phi and measure the change in the backscattered current. 561 00:29:23,160 --> 00:29:27,720 And the way we change Phi is by actually changing the shape of the cavity slightly 562 00:29:27,880 --> 00:29:29,000 by pushing on the edge. 563 00:29:29,000 --> 00:29:31,040 Oh, this is the particle going around the cavity. 564 00:29:31,040 --> 00:29:31,480 There it goes. 565 00:29:31,480 --> 00:29:33,960 So we're interested in the phase of the particle going around the cavity. 566 00:29:33,960 --> 00:29:36,040 That shows up here as phi. 567 00:29:36,040 --> 00:29:41,040 And we're going to change the this cosine phi by changing the shape of the cavity. 568 00:29:41,040 --> 00:29:45,240 So the the phase accumulated by the particle going around the cavity changes. 569 00:29:45,440 --> 00:29:48,920 So you do that with an electrode that sort of pushes the 570 00:29:49,320 --> 00:29:52,240 the electrons out of the way and changes the shape of the cavity. 571 00:29:52,240 --> 00:29:55,080 So this is this is all changed with an electrode 572 00:29:55,080 --> 00:29:56,320 and it will change cosine phi. 573 00:29:56,320 --> 00:30:00,120 And so the current you measure backscattered is going to oscillate 574 00:30:00,120 --> 00:30:01,000 sinusoidal. 575 00:30:01,000 --> 00:30:03,480 It's just like taking a fabric interferometer. 576 00:30:03,480 --> 00:30:06,920 You have to marry your half silver mirror and and a solid mirror 577 00:30:06,920 --> 00:30:09,920 and you just move them back and forth and you'll see interference fringes. 578 00:30:10,560 --> 00:30:11,400 Okay. 579 00:30:11,400 --> 00:30:14,080 Now the interesting part of this experiment is what happens 580 00:30:14,080 --> 00:30:17,360 if you add an anion to the center of the cavity. 581 00:30:17,880 --> 00:30:21,360 Well, if one particle has now gone around another particle, 582 00:30:21,360 --> 00:30:22,800 it picks up a braiding phase 583 00:30:23,840 --> 00:30:27,280 two pi over three braiding braiding phase. 584 00:30:27,280 --> 00:30:29,840 So without the particle, if you see the black curve 585 00:30:29,840 --> 00:30:32,200 with the particle you'll see a shifted curve. 586 00:30:32,200 --> 00:30:34,000 The blue curve okay. 587 00:30:34,000 --> 00:30:36,240 And if I add another particle to the middle 588 00:30:36,240 --> 00:30:39,240 this curve shifts again by another two pi over three. 589 00:30:39,600 --> 00:30:42,600 That's what we're going to try to see. Okay. 590 00:30:42,720 --> 00:30:45,480 So it sounds like an easy experiment right now. 591 00:30:45,480 --> 00:30:50,880 So it was about 15 years of effort trying to make this experiment work. 592 00:30:51,000 --> 00:30:53,080 And people eventually came to the conclusion 593 00:30:53,080 --> 00:30:56,040 that it's actually a very hard experiment. It might even be impossible. 594 00:30:56,040 --> 00:30:59,520 So the reason it is hard is sort of it's 595 00:30:59,560 --> 00:31:02,560 sort of a conflict between two two issues. 596 00:31:02,920 --> 00:31:05,560 For any finite temperature, there's a coherence 597 00:31:05,560 --> 00:31:08,560 length beyond which you don't see any interference. 598 00:31:08,640 --> 00:31:12,360 So where that comes from, is it the phase can be, 599 00:31:12,400 --> 00:31:16,080 stated as e to the I length times a wave vector. 600 00:31:16,520 --> 00:31:18,840 Now the wave vector is a function of energy. 601 00:31:18,840 --> 00:31:22,440 So you expand this k0 plus decayed e times d. 602 00:31:22,920 --> 00:31:28,320 So depending on the energy of the incoming particle, you get a different phase. 603 00:31:29,640 --> 00:31:30,840 But at any finite 604 00:31:30,840 --> 00:31:34,600 temperature, say even 30 Millikelvin D is big enough 605 00:31:34,800 --> 00:31:39,680 so that the the changes in this term end up scrambling the phase completely. 606 00:31:39,960 --> 00:31:44,240 And the only way you cannot scramble the phase is if you make L very small. 607 00:31:44,240 --> 00:31:47,640 So this is going to force you to do the experiment 608 00:31:47,640 --> 00:31:51,960 on a very small sample on the micron scale, even at 30 millikelvin. 609 00:31:51,960 --> 00:31:53,440 I mean, if you go to zero temperature, 610 00:31:53,440 --> 00:31:56,440 zero zero temperature, you could do it in a much bigger sample. 611 00:31:56,440 --> 00:31:59,880 But, you know, 30 Millikelvin is about the limit of what you can do experimentally. 612 00:32:00,480 --> 00:32:03,040 However, 613 00:32:03,040 --> 00:32:06,640 there's a conflict with that, which is that adding a single electric 614 00:32:06,640 --> 00:32:11,040 charge of E or a three to a micron sized object is a very strong perturbation. 615 00:32:11,240 --> 00:32:14,080 It changes the position of all the edge states. 616 00:32:14,080 --> 00:32:16,360 And then you're measuring something completely different. 617 00:32:16,360 --> 00:32:18,120 Once you once you add the U over three. 618 00:32:18,120 --> 00:32:21,320 So you're not seeing the change just from the statistics of the particle. 619 00:32:21,480 --> 00:32:24,040 You're seeing that the change from the Coulomb 620 00:32:24,040 --> 00:32:27,040 interaction of the particle with the particles running around. 621 00:32:27,200 --> 00:32:28,840 So this is problematic. 622 00:32:28,840 --> 00:32:32,640 And then on top of that, even at 30 millikelvin there's significant 623 00:32:32,640 --> 00:32:35,640 thermal noise from various sources that you have to wrestle with. 624 00:32:35,920 --> 00:32:39,640 So all of these things were addressed by Mike Manfred's group in 2020. 625 00:32:39,640 --> 00:32:42,640 Using gallium arsenide have a structure with lots and lots of tricks 626 00:32:42,720 --> 00:32:44,400 to get around these problems, and it was done 627 00:32:44,400 --> 00:32:46,840 successfully and a beautiful tour de force experiment. 628 00:32:46,840 --> 00:32:48,720 But that's not the experiment I'm going to describe. 629 00:32:48,720 --> 00:32:50,600 I'm going to describe this experiment, 630 00:32:50,600 --> 00:32:53,880 which, which was done more recently by the Harvard group. 631 00:32:54,120 --> 00:32:57,640 Thomas Work Meister is a graduate student who's, the, the lead author. 632 00:32:57,640 --> 00:32:58,240 And the reason 633 00:32:58,240 --> 00:33:01,720 I well, one reason I like it is because the data is really beautiful. 634 00:33:01,720 --> 00:33:04,080 And the other reason I like it is because it invokes 635 00:33:04,080 --> 00:33:08,720 some of the things that we had mentioned in this earlier paper, from 2006. 636 00:33:09,560 --> 00:33:12,720 So the idea of the experiment is we're going to do exactly that. 637 00:33:12,720 --> 00:33:14,600 Explain we're not going to change any edge voltage. 638 00:33:14,600 --> 00:33:16,440 We're not going to change the shape of the interferometer. 639 00:33:16,440 --> 00:33:17,880 We're just going to wait. 640 00:33:17,880 --> 00:33:21,000 So you just sit in your experiment and you measure some current back 641 00:33:21,000 --> 00:33:24,160 scattering and you would think, okay, just I'm not changing anything. 642 00:33:24,160 --> 00:33:27,120 The current back scattering should be exactly the same. 643 00:33:27,120 --> 00:33:28,840 It should just not change at all. 644 00:33:28,840 --> 00:33:29,960 But it does change. 645 00:33:29,960 --> 00:33:32,240 It sort of jumps around after a half a minute 646 00:33:32,240 --> 00:33:35,040 it jumps up to this level, and then another half a million jumps 647 00:33:35,040 --> 00:33:37,320 up to this blue level and jumps back down to this green level. 648 00:33:37,320 --> 00:33:39,800 It's jumping all over the place. It looks like it's a noisy sample. 649 00:33:39,800 --> 00:33:42,240 And typically what you do with noisy samples is you throw them out. 650 00:33:43,680 --> 00:33:45,680 But then if you look at this for a little longer, 651 00:33:45,680 --> 00:33:47,400 you realize that actually it's only jumping 652 00:33:47,400 --> 00:33:49,520 between three different levels the green level, 653 00:33:49,520 --> 00:33:51,320 the blue level and the purple level. 654 00:33:51,320 --> 00:33:54,120 So let's plot those three levels over here. 655 00:33:54,120 --> 00:33:57,720 And then once you've accumulated data to find what these three levels are, 656 00:33:58,080 --> 00:34:01,560 then you change the shape of the interferometer and you trace out 657 00:34:01,560 --> 00:34:06,600 three curves which are three sinusoidal curves shifted by two pi over three. 658 00:34:06,840 --> 00:34:09,840 This is exactly these three curves here. 659 00:34:09,960 --> 00:34:11,920 What you're seeing 660 00:34:11,920 --> 00:34:16,280 is you're seeing telegraph noise as one particle is jumping in 661 00:34:16,560 --> 00:34:19,400 and out of the are the interferometer 662 00:34:19,400 --> 00:34:22,400 are two particles are jumping in and out of the interferometer. 663 00:34:22,640 --> 00:34:23,360 And they are. 664 00:34:23,360 --> 00:34:27,120 The blue curve will be when you have one for seven particles 665 00:34:27,120 --> 00:34:30,280 in the interferometer the purple will be two, five, eight. 666 00:34:30,280 --> 00:34:32,680 And the green will be zero, three, six and so forth. 667 00:34:32,680 --> 00:34:34,560 And it's jumping back and forth between them. 668 00:34:34,560 --> 00:34:37,520 But at any number of of particles in the interferometer, 669 00:34:37,520 --> 00:34:40,320 you're on one of these three sinusoidal curves. 670 00:34:42,200 --> 00:34:46,000 So how do we address these problems. 671 00:34:46,000 --> 00:34:47,320 Well, this one 672 00:34:47,320 --> 00:34:51,160 we got rid of the thermal noise by making lemonade out of lemons, I guess. 673 00:34:51,960 --> 00:34:53,480 So we used it to our advantage. 674 00:34:53,480 --> 00:34:54,600 But what about the conflict 675 00:34:54,600 --> 00:34:57,640 between the size of the the device and the Coulomb interaction? 676 00:34:57,960 --> 00:35:00,160 Well, here 677 00:35:00,160 --> 00:35:04,360 what they did was they screened the Coulomb interaction 678 00:35:04,360 --> 00:35:08,960 by slapping down a metal plate very close to the two dimensional electron 679 00:35:08,960 --> 00:35:12,040 gas that you're interested in, that if you put a metal right 680 00:35:12,040 --> 00:35:14,560 near you, two dimensional electron gas, and every time you have a charge 681 00:35:14,560 --> 00:35:17,920 in the two dimensional electron gas, you have a mirror charge in the 682 00:35:18,200 --> 00:35:19,360 in the metal plate. 683 00:35:19,360 --> 00:35:22,480 So instead of having coulombic interactions between E over three 684 00:35:22,480 --> 00:35:26,520 and were three over here you have dipolar interactions, much weaker 685 00:35:27,000 --> 00:35:30,280 dipolar interactions between this pair and this pair. 686 00:35:31,560 --> 00:35:33,080 Now doing that 687 00:35:33,080 --> 00:35:37,800 in gallium arsenide was really a very difficult trick because while 688 00:35:37,800 --> 00:35:41,600 the gallium arsenide the quantum wells are 100 nanometers to begin with 689 00:35:41,880 --> 00:35:47,720 and the, the the gallery, you know, the gallium arsenide world needs a cap. 690 00:35:47,720 --> 00:35:49,880 And then the metal plane can only be so close. 691 00:35:49,880 --> 00:35:54,360 But with graphene, it's super easy to do because graphene is only an atom thick. 692 00:35:54,480 --> 00:35:57,480 And you can plunkett right down on top of a piece of metal 693 00:35:57,520 --> 00:36:00,280 within a couple of angstroms, so you can screen the 694 00:36:00,280 --> 00:36:02,520 the Coulomb interaction extremely effectively. 695 00:36:02,520 --> 00:36:06,080 And that's why some of these new graphene experiments are so, so nice. 696 00:36:06,600 --> 00:36:08,160 Anyway, 697 00:36:08,160 --> 00:36:10,320 that more or less, ends the story. 698 00:36:10,320 --> 00:36:14,120 After about 36 years, we can finally, 699 00:36:14,120 --> 00:36:17,440 put a checkmark next to the experimental confirmation of. 700 00:36:22,560 --> 00:36:24,760 Okay, we can finally put a checkmark next 701 00:36:24,760 --> 00:36:29,520 to the experimental confirmation of of anion statistics. 702 00:36:29,520 --> 00:36:31,160 And I will thank you for listening. 703 00:36:31,160 --> 00:36:34,160 Just in time for. 704 00:36:49,800 --> 00:36:50,440 That. 705 00:36:50,440 --> 00:36:51,160 Yeah, actually. 706 00:36:51,160 --> 00:36:53,360 So, so they customize era three. 707 00:36:53,360 --> 00:36:55,040 Looks like the charge on a quark. 708 00:36:55,040 --> 00:36:58,040 So there's a legend that when, 709 00:36:58,800 --> 00:37:02,240 first Starman and Dan Sui were taking the first data on fractional quantum 710 00:37:02,240 --> 00:37:07,000 Hall effect, they, you know, they were served the way, you know, you 711 00:37:07,080 --> 00:37:10,680 you scan the magnetic field slowly, and and you see these plateaus form. 712 00:37:10,840 --> 00:37:12,000 They saw this plateau 713 00:37:12,000 --> 00:37:15,960 toe form at, you know, three times the other plateau that they'd seen. 714 00:37:16,280 --> 00:37:20,160 And Dan Sui immediately said, oh, quarks, 715 00:37:20,360 --> 00:37:23,360 you know, and it was it was completely a joke. 716 00:37:23,480 --> 00:37:28,080 But he realized immediately that the quantized one third 717 00:37:28,320 --> 00:37:31,640 would be consistent with a one third particle. 718 00:37:31,840 --> 00:37:34,680 It's not quarks, you know, the quarks are bound with enormous, 719 00:37:34,680 --> 00:37:39,720 enormous energy orders of magnitude, higher than anything in these experiments. 720 00:37:40,040 --> 00:37:43,760 But, but nonetheless, you know, it has that odd similarity 721 00:37:43,920 --> 00:37:45,440 that there are other fractional with quantum Hall, 722 00:37:45,440 --> 00:37:48,880 states where, where the, the charged particles are, 723 00:37:49,160 --> 00:37:52,840 you know, you're five or E over seven or any number like that. 724 00:37:53,120 --> 00:37:58,040 So three is, is sort of the, the minimal odd number on one. But 725 00:37:59,160 --> 00:38:00,600 yeah, it's, it's, it's a little bit. 726 00:38:00,600 --> 00:38:01,080 Yeah. 727 00:38:01,080 --> 00:38:03,720 It is a complicated combination of effects. 728 00:38:03,720 --> 00:38:06,720 So the question is what why are the width of the plateaus, what they are. 729 00:38:06,880 --> 00:38:09,720 So there's a theorem which says that 730 00:38:09,720 --> 00:38:13,240 if you had no disorder at all, there would be no plateaus anymore. 731 00:38:13,480 --> 00:38:15,680 So you need some amount of disorder. 732 00:38:15,680 --> 00:38:19,560 And it actually depends on not only the amount of disorder, the 733 00:38:20,160 --> 00:38:24,560 tendency to, grow, you know, initially grow wider as you reduce the disorder. 734 00:38:24,760 --> 00:38:28,640 But it also depends on the type of disorder, the the range of disorder. 735 00:38:28,640 --> 00:38:32,160 And in when, you know, quantum Hall effect, because of the precision, 736 00:38:32,160 --> 00:38:37,200 the effect is used for metrology, you know, for setting resistance standards. 737 00:38:37,200 --> 00:38:40,320 You know, if you want to ask how do you define an ARM really accurately? 738 00:38:40,320 --> 00:38:41,880 You do it this way. 739 00:38:41,880 --> 00:38:46,560 Use quantum Hall effect, and they use very special, samples 740 00:38:46,560 --> 00:38:51,160 with a particular type of disorder, which is known to give a, wide plateaus. 741 00:38:51,160 --> 00:38:53,080 So it's actually a combination of things 742 00:38:53,080 --> 00:38:54,840 that that goes into the width of the plateau. 743 00:38:54,840 --> 00:38:57,320 But it has to be sufficiently clean. 744 00:38:57,320 --> 00:39:00,320 But then the details of the disorder actually matter to. 745 00:39:00,400 --> 00:39:01,080 Yeah. 746 00:39:01,080 --> 00:39:05,040 So okay, so the question is why do you need, the integer ratios to be small. 747 00:39:05,400 --> 00:39:09,160 It's, it's only comes from the statement that as you get higher 748 00:39:09,520 --> 00:39:12,520 integers, the gaps tend to get smaller. 749 00:39:12,520 --> 00:39:15,560 And this is going to have to be the case because otherwise 750 00:39:15,560 --> 00:39:17,360 you're going to have a double staircase. 751 00:39:17,360 --> 00:39:19,280 You know, where there's a different quantum 752 00:39:19,280 --> 00:39:22,320 Hall effect that at each epsilon you change the magnetic field. 753 00:39:22,600 --> 00:39:26,120 So the the as you get to a cleaner and cleaner 754 00:39:26,120 --> 00:39:29,280 samples you, you a lots of more fractions. 755 00:39:29,280 --> 00:39:31,920 Do start emerging between other old ones. 756 00:39:31,920 --> 00:39:36,120 But the, the ones with the lower denominators are the ones that, 757 00:39:36,520 --> 00:39:38,120 that emerge first. 758 00:39:39,480 --> 00:39:40,160 Yeah. 759 00:39:40,160 --> 00:39:43,000 So, the question is about the rationality 760 00:39:43,000 --> 00:39:46,600 or irrationality of, of, of these, of these, these effects. 761 00:39:47,080 --> 00:39:51,040 So the so I wouldn't say this, this is, it's 762 00:39:51,040 --> 00:39:55,360 not a physical constant where we're measuring, it's, 763 00:39:56,040 --> 00:40:00,280 you know, we're measuring a number when we're measuring a number, the 764 00:40:01,160 --> 00:40:04,240 I guess I would say that the, 765 00:40:05,360 --> 00:40:08,320 you know, we are measuring a third of an electron 766 00:40:08,320 --> 00:40:13,560 to very high precision in, in some ways, although, to be honest, the, 767 00:40:13,560 --> 00:40:18,360 the experimental measurement that tells you directly that you're measuring, 768 00:40:18,920 --> 00:40:21,400 you know, the charge on these things is one third 769 00:40:21,400 --> 00:40:24,360 if you are is the unless 770 00:40:24,360 --> 00:40:28,040 you are saying that the Hall resistance itself, 771 00:40:28,120 --> 00:40:31,560 which is very easy to measure, is evidence that the charge 772 00:40:31,560 --> 00:40:34,560 is fractionalized and theoretically you might make the connection. 773 00:40:34,560 --> 00:40:38,520 But if you want a direct measurement of the of the charge on that particle, 774 00:40:38,520 --> 00:40:42,040 which you can do by noise measurements, or you can even these days, they can do it 775 00:40:42,040 --> 00:40:45,480 actually by by using an electron very sensitive electron meter. 776 00:40:45,480 --> 00:40:48,800 And you scan over the sample and you say, oh, there's a bump and its charge 777 00:40:48,840 --> 00:40:50,440 is about E over three. 778 00:40:50,440 --> 00:40:54,600 But those experiments are not accurate. 779 00:40:54,600 --> 00:40:57,840 Apart in ten to the ten, those experiments 780 00:40:57,840 --> 00:41:01,560 are accurate to say 5%, something like that. 781 00:41:01,560 --> 00:41:05,560 So it's consistent but it's not highly, highly accurate. 782 00:41:05,560 --> 00:41:07,880 The way the the resistance experiment is. 783 00:41:09,600 --> 00:41:10,560 Yeah okay. 784 00:41:10,560 --> 00:41:12,360 It's a very good question. 785 00:41:12,360 --> 00:41:14,200 So there was actually 786 00:41:14,200 --> 00:41:17,680 there was in the early days of fractional quantum Hall effect, 787 00:41:18,040 --> 00:41:22,360 it was believed to be a theorem that all denominators had to be odd. 788 00:41:22,680 --> 00:41:25,680 And that actually comes from the fact that the underlying, 789 00:41:25,800 --> 00:41:29,560 particle electrons that you're putting in is a fermion. 790 00:41:29,880 --> 00:41:33,760 And so it's a little bit of a complicated, connection. 791 00:41:33,760 --> 00:41:35,920 But from the fermionic statistics, 792 00:41:35,920 --> 00:41:38,520 the statement is that you would need to have an odd nominator, 793 00:41:38,520 --> 00:41:41,520 and three is the smallest odd denominator or higher than one. 794 00:41:41,760 --> 00:41:45,280 The what that one would gives 795 00:41:45,280 --> 00:41:48,600 you the integer quantum Hall effect, in which there is no fractional ization. 796 00:41:49,080 --> 00:41:53,760 That turned out not to be true, actually, that people have measured 797 00:41:53,760 --> 00:41:58,040 even denominator fractions, and that comes from a more subtle effect 798 00:41:58,200 --> 00:42:02,280 where the electrons pair into bosons like a superconductor, 799 00:42:02,280 --> 00:42:05,840 and then that condenses so you can have even denominators too. 800 00:42:05,840 --> 00:42:10,800 It could be that the first one we measured was at one half, but it just turns out 801 00:42:10,800 --> 00:42:15,120 that the one half plateau is is weaker and a little bit harder to see. 802 00:42:15,120 --> 00:42:18,120 So they have been seen, but only in only weak, more weakly 803 00:42:18,120 --> 00:42:21,920 and, and, and more high, you know, key and cleaner samples. 804 00:42:21,920 --> 00:42:23,760 So if they can they can exist. 805 00:42:23,760 --> 00:42:25,120 Even denominators can exist. 806 00:42:25,120 --> 00:42:29,440 But some things, you know, people have, have observed something like 807 00:42:30,000 --> 00:42:33,360 80 or 100 different fractions and fractional quantum Hall experiments, 808 00:42:33,600 --> 00:42:36,560 of which all but a very few have our denominators. 809 00:42:38,240 --> 00:42:41,240 So there's 810 00:42:41,800 --> 00:42:43,840 there's a 811 00:42:43,840 --> 00:42:48,600 community in the world who wants to build, quantum computers out of anions. 812 00:42:48,920 --> 00:42:51,640 Now, initially, 813 00:42:51,640 --> 00:42:54,640 Microsoft was the home of this. 814 00:42:54,960 --> 00:42:56,440 Sorry, I should repeat the question. 815 00:42:56,440 --> 00:42:59,520 The question is, is where do you see this 816 00:42:59,520 --> 00:43:02,760 being applied to in, technology? 817 00:43:02,760 --> 00:43:05,760 And where do you see this being applied in fundamental physics? 818 00:43:07,360 --> 00:43:09,760 So in technology, there is this community 819 00:43:09,760 --> 00:43:13,280 that wants to, use anions to build quantum computers. 820 00:43:13,600 --> 00:43:17,440 And they initially started exploring fractional quantum Hall effect 821 00:43:17,640 --> 00:43:19,080 very intensively. 822 00:43:19,080 --> 00:43:22,080 And that's why people did this 15 years of experiments of, 823 00:43:23,160 --> 00:43:25,320 successful experiments actually. 824 00:43:25,320 --> 00:43:28,320 And they at some point after doing this for about eight years, 825 00:43:28,680 --> 00:43:30,680 Microsoft said, okay, that's not the way to do it. 826 00:43:30,680 --> 00:43:31,560 We're going to do something else. 827 00:43:31,560 --> 00:43:34,800 And they're still thinking about, so anion based 828 00:43:34,800 --> 00:43:37,960 quantum computers or Majorana based quantum computers are very similar. 829 00:43:39,120 --> 00:43:42,040 But they switched the platform to, 830 00:43:42,040 --> 00:43:45,840 using superconductor semiconductor structures. 831 00:43:45,840 --> 00:43:47,520 It's not quantum Hall effect anymore. 832 00:43:47,520 --> 00:43:48,960 So it has a lot of similarities. 833 00:43:48,960 --> 00:43:50,360 But no, it's not exactly the same. 834 00:43:50,360 --> 00:43:53,880 So that's something that they're really pushing very hard right now. 835 00:43:53,880 --> 00:43:55,840 And that could be a real technology. 836 00:43:55,840 --> 00:43:57,360 Although it's not fractional quantum modeling, 837 00:43:57,360 --> 00:43:57,760 although there are 838 00:43:57,760 --> 00:44:01,040 some people in the world, myself included, who would love to see fractional 839 00:44:01,040 --> 00:44:04,800 quantum Hall effect come back into the into the quantum computing game. 840 00:44:04,800 --> 00:44:09,480 And I still think that that's, you know, not an insane possibility, 841 00:44:09,880 --> 00:44:12,880 for fundamental physics. 842 00:44:13,360 --> 00:44:17,520 So in some ways, I have to ask maybe what do you mean by fundamental 843 00:44:17,520 --> 00:44:18,360 to begin with? 844 00:44:18,360 --> 00:44:21,880 But I would say that this this is fundamental physics as fundamental 845 00:44:21,880 --> 00:44:23,680 as anything else you will come up with. 846 00:44:23,680 --> 00:44:28,800 And, you know, seeing this, this principle that particles don't need to be, 847 00:44:29,160 --> 00:44:34,040 don't need to be bosons or fermions is a really fundamental advance. 848 00:44:34,040 --> 00:44:37,800 And and that is, is, you know, what I would call fundamental physics, 849 00:44:39,160 --> 00:44:41,320 I, I probably should have 850 00:44:41,320 --> 00:44:45,160 I mean, as I went further in, I mean, one to some extent, 851 00:44:45,160 --> 00:44:48,840 it's it's not, not fair because I think a lot of the modern modern work 852 00:44:49,160 --> 00:44:53,840 is, is much more frequently done in collaborations than it used to be. 853 00:44:54,160 --> 00:44:57,280 And so there will almost always be a student on the paper, 854 00:44:57,280 --> 00:45:02,400 a postdoc and a senior, you know, senior faculty member or several and so forth. 855 00:45:02,760 --> 00:45:07,520 And, then the question arises, you know, whose work was it? 856 00:45:07,560 --> 00:45:08,600 What's this? 857 00:45:08,600 --> 00:45:12,200 You know, is it really the graduate student who came up with the great idea? 858 00:45:12,480 --> 00:45:13,800 I mean, sometimes it actually is. 859 00:45:13,800 --> 00:45:15,600 And and the, you know, the faculty member 860 00:45:15,600 --> 00:45:17,960 is just the one who raised the money to pay the graduate student. 861 00:45:17,960 --> 00:45:21,400 But other times it's, you know, it's it's a more of a collaboration. 862 00:45:21,400 --> 00:45:23,360 So I think it becomes harder to, 863 00:45:23,360 --> 00:45:27,400 to say whether the ideas are still coming from, are coming from the young people. 864 00:45:27,400 --> 00:45:29,640 I my guess is that, in fact, a lot of the ideas 865 00:45:29,640 --> 00:45:31,600 still are coming from the from the young people. 866 00:45:31,600 --> 00:45:34,680 It's hard to prove that Nobel Prizes have become fractional. 867 00:45:35,160 --> 00:45:36,880 Yeah. Yeah, exactly. Yeah. 868 00:45:39,360 --> 00:45:42,640 So actually, there's a couple of things that I, that I can say 869 00:45:42,640 --> 00:45:46,200 that that where it's, it's not, it's not an irrelevant connection. 870 00:45:46,440 --> 00:45:50,760 So the underlying theory of anion models or its so-called topological quantum 871 00:45:50,760 --> 00:45:54,360 field theory is that you mentioned earlier where you throw out 872 00:45:54,360 --> 00:45:57,600 all space and all you care about is whether the one thing went around another. 873 00:45:58,000 --> 00:46:02,160 And topological quantum field theories were actually cooked up by, 874 00:46:02,160 --> 00:46:06,240 by string theorists in the, in the 1980s, more or less. 875 00:46:06,480 --> 00:46:09,760 And they were thinking about theories of quantum gravity in, in 876 00:46:10,160 --> 00:46:13,160 if you go down one dimension to a, 877 00:46:13,440 --> 00:46:15,640 two plus one dimensional universe instead of a three 878 00:46:15,640 --> 00:46:20,480 plus one dimensional universe, it is known that the gravity is very different. 879 00:46:20,480 --> 00:46:23,640 In two plus one dimensions, it becomes completely topological. 880 00:46:23,960 --> 00:46:26,040 And, you know, a lot of the structure goes away. 881 00:46:26,040 --> 00:46:31,440 And these kind of theories actually do describe universes in in lower dimensions. 882 00:46:31,800 --> 00:46:37,200 It's, it's beyond my pay grade to say whether any of that survives in our, 883 00:46:37,520 --> 00:46:38,240 three 884 00:46:38,240 --> 00:46:42,720 plus one dimensional universe or not, but it's definitely interesting to study. 885 00:46:44,520 --> 00:46:44,760 Yeah. 886 00:46:44,760 --> 00:46:45,760 What are the questions? 887 00:46:45,760 --> 00:46:51,040 What are the statistics of anions analogous to Bose-Einstein and fermions? 888 00:46:51,280 --> 00:46:54,120 You can write down a distribution function 889 00:46:54,120 --> 00:46:58,200 for anions statistics, which is somewhere between boson and fermion as well. 890 00:46:58,320 --> 00:47:02,200 There's another description of statistics that also arises which is 891 00:47:02,280 --> 00:47:06,600 which is interesting, which is, to ask the question, 892 00:47:06,600 --> 00:47:11,160 you have some Hilbert space and, you ask how big it is. 893 00:47:11,400 --> 00:47:14,600 And then when you add a particle to it, how much smaller did it get? 894 00:47:15,040 --> 00:47:18,120 You know, how many fewer orbitals are allowed 895 00:47:18,360 --> 00:47:19,800 for the next particle that comes in. 896 00:47:19,800 --> 00:47:22,800 So for bosons, if I put a particle in 897 00:47:23,240 --> 00:47:27,280 the next particle I put in, it has exactly the same in the options for fermions. 898 00:47:27,280 --> 00:47:30,840 If I put a particle in, the next particle has a left, has fewer options 899 00:47:31,160 --> 00:47:34,720 with anions, it's somewhere in between that you put two particles in, 900 00:47:34,720 --> 00:47:37,680 and then you reduce the number of options by one for example. 901 00:47:37,680 --> 00:47:42,320 So it does I mean always seems to interpolate between the the two possibilities. 902 00:47:46,520 --> 00:47:47,040 Okay. 903 00:47:47,040 --> 00:47:49,680 I think another question is that we just didn't find. 904 00:47:49,680 --> 00:47:51,240 So let's think okay.