Vol. 2 No. 1 • Spring / Summer 2006 Rapid Response to Supersolidity: ‘Is It There or Is It Not?’ May Be the Answer as Well as the Question “O, that this too too solid fl esh would melt 4 can be increased to 25 times that of earth’s Thaw and resolve itself into a dew!” (1.2) atmosphere at sea level. What may be emerging is a new phase of matter—a “supersolid” both HERE HAMLET CONTEMPLATES a crystalline and superfl uid. At issue is the nature “phase transition” decades before the advent of “solid.” of classical thermodynamics and centuries Said Chan, “We thought a crystalline before quantum mechanics. Shakespeare, ever solid is something we all understand—rigid, the prescient observer, builds the metaphor reliable, stay-put. Our data is indicating, ‘no, for physical transformation by analogy not quite’ if the temperature is low enough.” ‘We thought a crystalline solid is something we all understand—rigid, reliable, stay-put.’ with changes in a macroscopic collection of Th eoretical solid-state physicists molecules he had witnessed—water which (Andreev, Lifshitz, Chester, and Leggett) changes from solid to liquid to vapor as have been envisioning supersolidity since temperature increases. the early 1970s. Fast forward almost exactly fi ve hundred “I think theoretical physicists would years since “Hamlet” was fi rst performed say what we have seen is not impossible, but at the Globe to the year 2004 and the Penn the probability of seeing a suffi ciently large State University laboratory of physicist Moses signature is very small. So in that sense we Nell Campbell Chan, where temperatures can be lowered have exceeded the expectations of theoretical The KITP has instituted a singular, new kind of program—Rapid Response—to address to 0.2 Kelvin (0.2 above absolute zero) and physicists,” said Chan. pressures on a quantum crystal of helium- breaking developments in science. Inaugural participants include Moses Chan (l), SEE RAPID RESPONSE ON PAGE 3 Phil Anderson, and David Ceperley. Microsoft’s Quantum Research Project Headed by Mathematician Takes up Temporary Residence at KITP

IN THE SPRING OF 1997, former graduate group has taken up temporary residence at the students at the University of California at San KITP until its permanent offi ces are ready in Diego invited Michael Freedman, a topologist the building, now under construction, that will who was awarded the Fields Medal in 1986 for house the California NanoSystems Institute his work on the Poincaré conjecture, to give a (CNSI), located next to the side of Kohn Hall talk at Microsoft Research in Redmond, Wash. with the KITP’s former main entrance. At the conclusion of that talk, an employee Why locate his topnotch research group then there, physicist Nathan Myrvold, off ered in Santa Barbara? Said Freedman, “Th e Freedman a job to work, more or less, on KITP is the center of the world for theoretical whatever he wanted. physics, I think. I wanted our group either Freedman’s talk must have indicated to be in KITP or an easy stone’s throw away. to Myrvold that what Freedman wanted And that’s the way it’s working out. Here at to work on was an idea he had in the late Santa Barbara I am in this new growing place 1980s for possible applications of topology to plus there is this physics institute, which is computation. cycling through programs that bring everyone Nell Campbell Freedman accepted the job off er and I would ever want to talk to right to me.” assembled a small group of mathematicians and Chetan Nayak (l) and Michael Freedman physicists to pursue the idea. Th at Microsoft SEE MICROSOFT'S QUANTUM PROJECT PAGE 6 High School Teachers Need Physics Now INSIDE… SOME 70 TEACHERS of physics came from to current KITP programming ensures that and Stuart Wolf of the University of Virginia. throughout the United States to the KITP’s what the teachers hear is what is happening in “I wanted speakers,” said Awschalom, From the director, p. 2 fi fth conference for high school teachers— physics now. “who could communicate eff ectively to both this one on “Nanoscience and Quantum As one teacher commented, “At the high the public and to high school teachers and Distinguishing fermions and bosons, p. 3 Computing.” school level we are largely concerned with 16th were also leaders in their fi eld, so that de facto David Awschalom, an experimentalist century physics (mechanics, etc.). It’s great to they are excited by what they are doing.” Divining quantum choreography, pp. 4–5 who directs the Center for Spintronics and get to hear research being done on some really Th e presenters’ enthusiasm for their Quantum Computing at UC Santa Barbara, exciting physics.” research was contagious, as the responses of Thinking about quantum mechanics, p. 5 put together the program for the March 24 According to another teacher, “Th is type the following four teachers indicate: KITP Teachers Conference in conjunction of conference is the most valuable in-service • “Only my second time to attend, but this has Topological quantum computing, pp. 6–7 with his role as an organizer of the KITP I have attended in 18 years of teaching. We been the most valuable workshop I’ve ever “Spintronics” conference and program for are starved for information on cutting-edge attended in the way it aff ected me personally. I Upcoming, p. 8 physicists (March 13 to June 23). science. To hear it from the top researchers in was revitalized.” Th e spring programming for physicists at the world is a great treat.” • “Th is type of conference rejuvenates our the KITP determines the topic for the annual Th e top researchers who entranced the interest in Modern Physics. Th ank you for Teachers Conference. Not only can attendees teachers are Robert Buhrman of Cornell, inviting us teachers.” of the physics programs be tapped as speakers, James Eisenstein and John Preskill of Caltech, but also, even more importantly, the tie-in Stephan von Molnar of Florida State University, SEE TEACHERS ON PAGE 2 From the Director his spring we have run two programs that get to the heart of quantum mechanics. One Tis “Spintronics,” which is centered on the attempt to use quantum spin of the electron to convey information and control devices. The other is “Topological Phases and Quantum Computing,” an attempt to use a quantum mechanical system to construct an incredibly powerful computer that could out-perform existing classical computers by Mastres Tony a wide margin. These programs illustrate to me how central quantum mechanics is in modern physics, clearly at the atomic and of course subatomic scales. In conjunction with the programs, we held a conference for high school teachers on Nell Campbell “Nanoscience and Quantum Computing,” that led me to think about quantum mechanics in terms of education. Above, Teacher Conference participants, Many—probably all—physicists still feel a bit uncomfortable with dressed casually in reds for the Santa quantum mechanics, shaped as we are in our education by classical Barbara event, Jon Anderson (l) from notions of determinism and reality. Yet quantum mechanics works so Minnesota, Randall Dunkin from Ohio, well that no one has come up with an alternative picture though many, and Mark Toney from Washington from Einstein onward, have tried. (state) with conference organizer David Some of my colleagues believe that eventually quantum mechanics Awschalom will have to be replaced by something more “real.” I myself regard this eventuality as unlikely. If there are conceptual revolutions in the future, Left, teachers Ed Kunitz (l) from Illinois, they are only going to make things worse not better—less classical, Patricia Spackman from Pennsylvania, and Steve Buster from Kansas. stranger than ever. I have an idea that the reason we fi nd quantum mechanics so Below, teachers Wayne Hild and Dan diffi cult is due to our poor training. Quantum mechanics is only 70 Stewart from California years old—that’s a short time in the history of physics for dramatic new concepts to sink into the consciousness of the fi eld. And we are Nell Campbell only learning, as we go along, to teach quantum mechanics better and better to our younger students, who understand it much better than the inventors did. Thus I think eventually—maybe 100 years from now, when quantum mechanics is taught in high schools (and we don’t fi rst teach classical physics and then tell the students, “That’s all wrong, think quantum mechanically”), then and fi nally then— we will feel comfortable with quantum mechanics. Of course by then we might have (probably will have) new conceptual revolutions that will make things appear mysterious and confusing once again. Endowment Fund You will have noticed that this second issue of the “KITP Newsletter” contains a remittance envelope to encourage readers—our dear friends and colleagues around the world—to contribute to the KITP endowment fund. Its purpose is twofold: to enable the KITP to initiate new and exciting programming eff orts—to experiment!— and to buff er us against the vicissitudes of federal funding. Please take a moment to consider and, we hope, to respond. Nell Campbell Director’s Council The Director’s Council has seen a shift in leadership. Fred Gluck and Joe Alibrandi, who are the founding co-chairs of the Council, have given over that role to John Mackall, who has replaced them as chair. We welcome a new member, Simon Raab. Teachers CONTINUED FROM PAGE 1 Finally, we all mourn the loss of Eli Luria, a good friend of the KITP, who served on the Director’s Council till his passing in March. • “I can use some of the info in class. But I love writing. Th eir overriding message was one of being brought up to date. Th is is energizing gratitude for being revitalized and connected to me.” with physics as a live, rather than a dead, • “Re-energized my passion for physics.” enterprise. Other teachers noted the benefi ts to their Each of the comments quoted in this article young students: is from a diff erent respondent to the question “Do you feel this type of conference is of value • “Th ese types of conferences are very unique to your teaching?” Here are four more: and most informative in regard to ‘frontiers of science.’ I fi nd them most helpful. My • “It is of extreme value to physics teachers. Th is Newsletter from the KITP students always look forward to my return to is one of the best connections between high tell them about what I have discovered and school teachers and the science and technology Volume 2, No. 1, Spring / Summer 2006 learned in science.” of the day.” • “Th is is the best part of my year. I bring back • “It is very important to bring current topics into Editor / Writer: Jacquelyn Savani excitement and knowledge, which I cannot your teaching.” [email protected] get elsewhere.” • “One of the top (perhaps the best) ways of • “I teach locally and have attended 3 of these communicating state-of-art science (both Design / Production: Charmien Carrier conferences. I have incorporated certain topics content and methodology) to teachers.” into my teaching (e.g., brief coverage of string • “Science teachers need to be with scientists as This newsletter is a publication of the part of our regular routine.” Kavli Institute for Theoretical Physics. theory when covering make-up of matter and energy). Plus each conference inspires me to a • “Defi nitely one of the best opportunities I’ve had higher level of excitement in my own continuing to expand my content knowledge in physics.” study of physics.” In addition to being available for the • “Both of the conferences I have attended have fi rst time as a Podcast, the whole Teachers reinvigorated my teaching.” Conference in audio only or in audio-visual • “Th is series of conferences has been the best format can be accessed via the KITP web site I’ve ever attended. I have used almost every at www.kitp.ucsb.edu by following the links presentation in my classes.” from (far right list) “Talks on Line.” • “Many good ideas for bringing modern topics to Since the teachers’ comments indicate the classroom were discussed. More so, the talks that a little eff ort does, in some cases, go such a were of great personal interest.” long way, please consider alerting high school Of the 70 teachers attending, 44 put physics teachers to this resource. their responses to the March 24 experience in

KITP Director’s Council The Director’s Council is made up of leaders in fi elds other than physics, but with an interest in physics, who meet several times a year to provide the KITP leadership with invaluable support and advice. Chaired by John Mackall, the Council also includes Joe Alibrandi, David L. Brown, Virginia Castagnola-Hunter, K.C. Cole, Michael Ditmore, Fred Gluck, Gus Gurley, Stuart Mabon, Simon Raab, and Derek Westen. For profi les go to: http://www.kitp.ucsb.edu/community/director.html.

In conformance with applicable law and University policy, the University of California is an equal opportunity employer. Inquiries regarding the University's equal opportunity policies may be directed to Joseph I. Castro, coordinator, 2 Affi rmative Action Offi ce, 1503 South Hall, Santa Barbara, CA 93106

Peter Malinowski CONTINUED FROM PAGE 1 Th e fact of the KITP Rapid Response places where atoms aren’t—would behave like In addition to experimental confi rmation seems to have speeded up the process a gas of particles, which itself could form a for the phenomenon of supersolidity, the other David Ceperley, a theoretical solid- of experimental confi rmation because condensate and behave like a superfl uid. But key development emerging from the Rapid state physicist at the University of Illinois at the experimentalists pushed to complete the simple picture sketched by those theoretical Responders’ consideration of the experimental Urbanna, said, “We thought the probability confi rming experiments in order to report speculations doesn’t quite stack up with Chan’s evidence for supersolidity is that how the was low because in a solid we think of atoms and discuss their fi ndings at the KITP mini- experimental results. crystal is grown appears to be important. as localized at the sites. Push on one side of a program that brought together a more To begin with, said Ceperley, “Moses According to Ceperley, “Large defects measured the heat capacity in the crystal seem to be important to the of solid helium much phenomenon. Th is thing is at more than 25 more accurately.” Chan’s atmospheres pressure, and the holes—voids in experiments going on the crystal which we had theorized would give Rapid Response to Supersolidity at Penn State, while the rise to supersolidty—would have collapsed Rapid Responders were under that pressure.” lattice of atoms in a solid and the atoms should exotic type of attendee to KITP programs— meeting in Santa Barbara, revealed an unusual Since, the Rapid Responders reason, there just stay where they are and not move. But experimentalists—with the staple participant measurement of thermodynamic response. are strong theoretical hints that supersolidity then there were these theories that a supersolid —theorists. “Whenever there is some new cannot happen in a perfect crystal, there is a phase should exist. Th ere have been searches Take that old fi xture of ‘50s house parties, phenomenon happening,” said Chan, very strong likelihood that defects are key. So since the ‘70s that till 2004 have come up with the Lazy Susan tray, and load it with perfectly “physicists usually like to think about how it what kinds of defects might be in play if defects nothing.” smooth ball bearings instead of nuts or mints. corresponds to the energetics of the situation. understood as “holes,” very roughly analogous Chan did not fi nd supersolidity by chance. Now put a saucer on top of the ball bearings We put a certain amount of heat into the system to “holes” in the conventional semiconductor He said, “A colleague at UCSD [University of and rotate the Lazy Susan. If the ball bearings to see how much the temperature will rise. If paradigm, can’t withstand the pressure? California at San Diego], John Goodkind, had and saucer were to behave like a supersolid, the system can absorb a lot of energy without Well, there is something called “zero done some ultrasound measurements over the the saucer despite the moving Susan would raising the temperature, then the system has a point vacancy” or quantum mechanical years, and he saw something rather unusual. not move. large heat capacity. Over the history of physics, vacancy. Ultimately related to the uncertainty Th e signature he found, while complicated, So what is supersolidity? A deep physics, we have learned how to use this information to principle, zero point vacancy means that, to suggested a phase transition takes place in as opposed to a visually analogous explanation tell us what is going on in the system. If solid a very minute extent, since a thing’s location solid helium near 0.2 Kelvin. John Goodkind’s (via Lazy Susan laden with ball bearings helium were to behave like a typical solid, then cannot be pinpointed, it may not be there. fi ndings said to me, ‘Th ere’s something funny topped by a plate) requires understanding of the heat capacity would increase as the third Th e probability that a thing is not completely here; maybe we should take a look.’” the diff erence between two overriding types of power of the Chan decided to employ a technique quantum entities—the boson and the fermion temperature. developed by his PhD mentor, Cornell (See box below). But,” said University physicist John Reppy, in the 1970s. A supersolid refers to a diff erent phase of Chan, “we Th at approach enabled Chan to measure matter exemplifi ed in Chan’s experiments by a are seeing at directly the non-classical rotational inertia system of helium-4 atoms. Th e operative word the very low (signature of a supersolid) that Ceperely’s here may be “system” because it looks like a temperature, Illinois colleague and 2003 Physics Nobel very small amount of something else—leading where we laureate Tony Leggett had specifi cally calculated. What the experiments say about supersolidity and what the ‘Large defects in the crystal seem to be theorists thought are not, however, in complete agreement. important to the phenomenon.’ Such a confusing picture proved perfect for initiating a new kind of eff ort at the Kavli Institute for Th eoretical Physics at the University of to defects in the perfect crystalline structure of see the California at Santa Barbara—Rapid Response. a solid’s lattice—may be key. superfl uid Initially supported through Kavli Institute In helium-4 the atoms are bosons in response, a Nell Campbell funding, the Rapid Response program aims contrast to helium-3 in which the atoms are deviation to address breakthroughs such as Chan’s in a fermions. Th e nucleus of helium-4, about from the In the new KITP auditorium, William Mullin (l), Mark Robbins, and John Nell Campbell timescale of months instead of the customary 99.99986% of the helium on earth, contains third power Toner participate in the Rapid Response workshop on supersolidity. one to two years. two protons and two neutrons. Cooled to dependence Address how? By bringing together below 2.17 Kelvin, helium-4 becomes a on temper- from around the globe, some 30 afi cionados superfl uid, whose properties diff er from those ature below 0.2 Kelvin.” there depends on several things, but especially of supersolidity to tackle intensely the issues of an ordinary liquid. When, for instance, Th e big question is whether a phase mass, so that the lighter a thing (an atom associated with “Th e Supersolid State of cooled helium-4 is kept in an open vessel, a transition to supersolidity is occurring around of helium is quite light), the more likely it Matter” (Feb. 6 to 17, 2006). Chan and thin fi lm climbs the vessel’s sides and fl ows 0.2 Kelvin. During the Rapid Response isn’t there. Th eoretically, this vacancy can go Ceperley orchestrated the Rapid Response. over the vessel lip. Because of the lack of program, fi ndings issuing from Chan’s lab around and form a big loop such that when Th e fi rst exciting development of the two- viscosity (friction between the atoms of the failed to detect a peak or bump in the heat the system containing it is measured, it would week mini-program—and there were at least two vessel and the atoms of the fl uid), a superfl uid capacity curve that would signal the transition. appear that its mass is not there. And that mass developments that have, according to Ceperley, set in motion in the vessel will rotate forever. Th e fi ndings mystifi ed Ceperley and led at that is both there and not may be the signature “changed the nature of the discussion”—was What Chan did in his lab was to take least one prominent theorist participating of the supersolid’s superfl uidity. the announcement of confi rmation by three liquid helium-4 into its solid state by increasing in the Rapid Response program, Princeton Said Ceperley, “If supersolidity turns other experimental groups of Chan’s discovery. the pressure in order to get within the solid Nobel laureate Phil Anderson, to speculate out to have something to do with defects, All three groups were represented at the component of the system superfl uid behavior. that the transition occurs at absolute zero. then helium-4 will provide a simple system Rapid Response program: John Reppy from Essentially the solid contains a superfl uid and Written soon after the Rapid Response to understand how quantum defects work Cornell University; Keiya Shirahama of Keio that combination is the new state of matter— program ended, the fi rst draft of this article because there are defects in things like metals University, Japan; and Minoru Kubota of the supersolidity. reported no bump. Six weeks later, the bump such as copper, which are really complicated University of Tokyo. Th at was an important Th e main outlines of the theory for expected by theorists may be emerging from because they have all sorts of impurities. So milestone for supersolidity because it dispelled supersolidity before the Chan experiments the ongoing experiments in Chan’s lab. “We there is possible long-term impact of this for theorists the specter of experimental non- and the Rapid Response to them hypothesize are doing more measurements to nail this research on metallurgy.” reproducibility and therefore hesitancy about that, within the solid, holes or vacancies— down,” he said. Said Chan, “Another very curious thing pursuit of theoretical understanding. we have seen in our experiments is that when we mix a very little helium-3 (a fraction of a part per million) into helium-4, it has a very great deal of infl uence on what we see. Th ere is some indication that the supersolid response becomes very small the less the helium-3 (less ALL PARTICLES IN THREE-DIMENSIONAL SPACE are either bosons or fermions. What Fermions that are indistinguishable can’t be in the same state. Two electrons than one part per billion). Our theoretical distinguishes one from the other is not a simple matter: essentially it’s whether the of the same spin can’t be put on top of each other (the Pauli exclusion principle). friends say, ‘Well, maybe helium-3 as impurity particle’s spin is integer (e.g., 0, 1, and so forth) or half integer (e.g., 1/2, 3/2, and So in the case of two spin up electrons and two boxes, there is only one possible is the source for causing the defect in the so forth). These two classes of particles are distinguished behaviorally by diff erent state—each box contains one spin up electron. system or that this impurity has a great deal of statistics, which refer to the way physicists count the number of possible states in In relativistic quantum mechanics, there is a deep connection between the infl uence on the phenomenon.' collections of diff erent particles. spin of a particle and its statistics (the spin statistics theorem). “Th is work may have materials science A main new insight of quantum mechanics is that the same fundamental If the spin is one-half integer like the spin of the electron or the quark, then implications,” said Chan, “but perhaps most entities, whether the same elementary particles or the same atoms, are the particle is a fermion. If the spin is integer such as zero or one or two, then the importantly when we try to understand this indistinguishable. particle is a boson. phenomenon that is very counterintuitive— Let’s say we have two boxes and two identical entities, which are An atom consists of a nucleus and orbiting electrons. Since a nucleus, except such that a fraction of a solid can fl ow with indistinguishable. The problem is to count the states of that system because the for the simplest hydrogen atom, is made out of protons and neutrons, both of no friction—then we will understand what we mean by a solid because all the things we number of states determines the probabilities of the entity being located in a given which have spin one half, putting them together results in either a nucleus (and talk about in terms of defects are in all other state. In terms of quantum mechanics, there are three possibilities or states: both an atom) of integer spin for an even number of nucleons or a nucleus (and an solids.” entities can go into one box or both into the other box or one can go into each box. atom) of half integer spin for an odd number of nucleons. Helium-4 with two Th e NSF has provided funding for Chan’s A perspicacious child might ask whether each of the entities could protons and two neutrons has an even number of nuclei and is a boson. Helium- research since 1979. Ceperley, an expert at also be put in the other box, so that the number of possible states would be 3 with two protons and one neutron has an odd number of nuclei so that atom numerical simulations, is also affi liated with four. Classically, yes, but quantum mechanically, no, because the entities are is a fermion. Though both atoms contain two electrons, the number of nuclear the National Supercomputing Center at indistinguishable, and there is no way to make the diff erentiation that allows constituents determines that one is a boson and that the other is a fermion. Illinois. for the possibility of putting each in one or the other box. Interestingly, the properties of a fermionic gas are very diff erent from the In the case of atoms, the boxes are akin to the positions of the atoms in a properties of a bosonic gas. In the fermionic helium-3 gas, electrons tend to repel crystal. The number of ways of putting the atoms at positions in the crystal can each other. Bosons, on the other hand, like to be in the same state, which helps to be “counted” and gives rise to diff erent “statistics” that are diff erent for atoms account for the phenomenon of Bose/Einstein condensation or superfl uidity. that are bosons and for atoms that are fermions.

3 Solid-State Physics: Quantum Fisher Frames History of Field for Focus on Strongly Correlated Electrons Choreography “There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.” (1.5) Even at the lowest temperature, inside every SO HAMLET, having just conversed piece of crystalline material, there is this with a Ghost, informs his friend, Horatio, miraculous electronic world with billions of incredulous, apparently, because well schooled electrons moving around. in Stoic philosophy, Horatio is a rationalist. “In the real world crystals are not perfect, Engagement with the implications of and their inhomogeneities affect the motion of quantum mechanics is like talking to a Ghost; electrons. But by and large, the field of strongly the experience shakes up notions of reality, correlated electrons is focusing on the simplest and things “un-dreamt” become possible problem of the idealized perfect crystal. If we when possibility is itself understood in terms can’t understand that, we are not going to of probability. understand the more complicated, imperfect, The difference between Hamlet’s ghost real world,” he said. and quantum mechanics is one of consensus. “What we have in crystalline solids are Maybe one or two physicists believe in the atoms arranged in an orderly way. Cooling possibility of ghosts, but almost all physicists the crystal slows the kinetic energy of its believe in quantum mechanics. After 100 constituent atoms. As an atom’s momentum years of unpacking its implications, physical gets smaller, its wavelength gets comparatively reality on a deep level has turned out to be larger, and once the wavelength becomes much stranger than a 19th-century physicist comparable to the distance between atoms could have dreamed. and the size of atoms, the atoms behave like KITP permanent member and solid-state waves. The atom is too massive to manifest theorist Matthew Fisher believes—counter that waviness at room temperature. Not so to the prevailing view in his field—that our the electrons.” everyday world contains aspects which may Treating the nuclei as a set of points, be far stranger than we can currently envisage a solid can be viewed as a collection of or even imagine. “The correlated motion of electrons. “I’m interested,” said Fisher, “in electrons inside some crystalline materials what the electrons are doing because they are provides the platform where such exotica so light that even at room temperature they might be lurking, largely uncharted,” he said. are behaving quantum mechanically. The In a culture where “thinking outside the electron particles are also behaving as waves. box” has become a cliché for creativity, Fisher The wavelength is the length over which the sees his approach to solid state physics as— wave oscillates, and is inversely proportional quite literally—thinking from the outside to the electron’s momentum.” At room about what is going on inside the “box,” temperature the electron’s wavelength is “Let’s imagine,” suggests Fisher, “that high temperature superconductors, physicists which, in his case, is the ordered array of typically very long—much longer than the we just turn off the Coulomb interaction; began to realize that collections of electrons atoms in the crystalline lattice of a solid. His distance between atoms. So electrons can nevertheless two up spin electrons have an can be much, much more interesting and preferred metaphor for this box is a dance look wavy and quantum mechanical at room exclusion interaction; they cannot sit on top complicated than described by Landau Fermi hall, in which electrons of spin up and spin temperature, and they do. of one another. You might think,” said Fisher, liquid theory. down move through the lattice like couples of “If,” said Fisher, “one is interested in “it would be a very complicated problem to The quantum Hall effect represented 23 men and women. Fisher’s task, as he sees it, is understanding the behavior of crystalline solve for 10 electrons moving around as the first well-understood example of electrons trying to discern from outside the dance hall solids under ordinary conditions here on earth, waves that can’t—as particles—sit on top of behaving in a manner qualitatively different the dancing patterns being performed by the it is ultimately necessary to understand the one another. Miraculously one can solve that from the standard paradigm. “We understand swirl of electrons; he is trying, in other words, quantum mechanical motion of the electrons problem exactly because these wavelike states what the electrons are doing,” said Fisher, to guess nature’s quantum choreography. around every single atom.” each have different momenta, beginning with “and they are doing something amazingly Though his endeavors may seem By and large the electrons are in orbits low and running to high.” interesting simply because they are doing abstruse to laymen, Fisher’s box contains around the nuclei of atoms. And they are The filled set of momentum states from something other than ignoring one another. not hypothetical dust from an Andromeda arranged in shells, which fill up in the order of lowest to highest is called the “Fermi sea.” The Though the quantum Hall effect occurs only moon, but earth rocks—materials which are distance away from the nucleus. filled Fermi sea provides an exact description in special circumstances, our understanding of magnetic and paramagnetic and ferromagnetic “Take a piece of copper,” said Fisher. of the electrons’ dynamics in the absence of it has convinced us that qualitatively different and conducting and semiconducting and “Each copper atom is relatively inert with one Coulomb interactions. behavior is possible.” superconducting. extra electron sitting in the outermost shell. “Even more amazing,” said Fisher, This is the physics variously described That electron can easily move from the sphere “when you add Coulomb interactions in Divining the Dance as “solid state” or “condensed matter,” from of influence of one copper atom to another. many important materials such as copper, “Imagine a town hall with a dance going which all of our high technology of computer So,” said Fisher, “in the background of these silicon, iron, and gold, the qualitative on, but to which no physicists are admitted chips and light emitting diodes and lasers has billiard balls [the copper atoms with their filled behavior of the collective of electrons though couples enter and music is audible,” come. This is preeminently the physics for electron shells], you can easily get this fluid of remains the same. It is as if interactions said Fisher. “The problem for the physicists is applications and usefulness. Most current electrons moving around; that is a quantum between electrons do not matter.” to guess the dance pattern inside. high technology is sliced from what Fisher mechanical fluid called a ‘Fermi liquid.’ The The assumption that it is legitimate to “One way—one experiment—would be characterizes as the paradigm of solid-state remarkable thing about a Fermi liquid, even ignore the interactions between the electrons to start pushing people in the front door and physics. In this standard paradigm, the though it is a quantum mechanical fluid, is constitutes the backbone of the quantum see how quickly people come out the back dance hall is the setting for an orderly, well- that its behavior can be simply understood theory of solids—the standard paradigm of door. That way you could tell how crowded understood behavior, in which the dancing mathematically.” solid-state physics with roots stretching back the hall is. Or you could push in women, and electrons are, in the terms of his metaphor, Before quantum mechanics people didn’t some 75 years. see how quickly men come out or women; “ultimately rather lonely and disinterested in understand the behavior, including the low It starts with a zero-order description that way you could get some idea how tightly one another.” electrical resistance, of metals because they where electrons do not interact at all and bound the men and women are (This method were thinking of the electrons as billiard balls. then adds in the (presumed) weak effects of of probing is called ‘electical transport’). The Paradigm But an electron moving in this “periodic interactions. When two electrons within the “Another thing you might want to do potential” (array of atoms) will, according Fermi sea interact weakly with one another, “Even,” said Fisher, “if a material is cooled is listen to the vibrations of the music—akin to Fisher, “go into a very nice wave where it there are relatively few empty states available to observing scattered neutrons to infer the to very low temperatures where normally in can move through the periodic background to scatter into, and the number of such the classical picture everything stops moving, ‘vibrations’ of the electrons’ spin. of atoms as if the atoms are not there.” Felix accessible states diminishes rapidly upon “Or, perhaps you climb on the roof of electrons are so light that quantum mechanics Bloch (awarded a Nobel Prize in 1952 for first cooling. In the 1950s Lev Landau, the famous keeps them fluctuating and moving around. the dance hall and drop people in through a demonstrating and explaining the Russian physicist, developed the requisite skylight and listen to the commotion below phenomenon of nuclear magnetic mathematical description of this picture. This when they land on the floor amidst the resonance [NMR] in 1946) figured “Landau Fermi liquid theory” basically takes dancers. This might give one some idea of this out in the 1930s soon after the into account the residual interactions between how crowded the room is with dancers. This advent of quantum mechanics. low energy electrons without changing their tactic is analogous to tunneling electrons Add another electron and ask qualitative behavior. from a metallic tip into a solid, in order what happens. Can it, for instance, But Landau Fermi liquid theory does to determine the behavior of the electrons collide with the original electron? not always work, asserts Fisher. “In some inside the solid,” said Fisher. The Pauli exclusion principle says materials the interactions between electrons Within the standard Fermi liquid that electrons, being fermions, can be so strong that their behavior changes paradigm, how would one describe the dancing cannot do the exact same thing as qualitatively. You cannot even think in terms within the hall? “People walk straight through one another. More precisely, a spin of momentum states; the Fermi sea does not the room, bump into a wall, and bounce off,” up electron cannot be in the same have any sharp meaning.” said Fisher, describing people moving like state as another spin up electron. In First with the quantum Hall effect and zombies in a low-budget horror film. “Most addition, any two electrons because then the fractional quantum Hall effect condensed matter theorists today,” said Fisher, they are both negatively charged repel (both efforts netting Nobel Prizes, in 1985 Nell Campbell “do not believe that thinking in terms of one another—that’s the “Coulomb and 1998, respectively) and then even more more exotic quantum choreography will be dramatically in 1986 with the discovery of the Chalk Talks, a program of the Friends of KITP, interaction.” productive; 95 percent of the practitioners enables audience members to ask questions of presenting scientists in a relaxed and casual setting. 4 Inside Crystals

situation where men and women like to be next mysterious behavior in materials such as the to one another, but can’t all be, so they all can’t high temperature superconductors and heavy be happy. This leads to interesting collective fermion materials. Each class might conceivably behavior, driven by compromises, much as have its own distinctive choreography.” He in complex human societies.” On triangular says he doesn’t have a feel for whether the lattices there are presently two experimental classes will themselves be classifiable into an materials, which are good candidates for being overarching pattern. critical spin liquids. Besides high temperature superconductors, Fisher has focused for over two decades strongly correlated electron systems hold another on building up an intuition for quantum tantalizing prospect for applications—in terms choreography. “I think that eventually of quantum computing. “Correlation” is we will successfully ascertain the correct basically the name of the game in quantum quantum choreography that underlies the computing. SEE QUANTUM CHOREOGRAPHY ON PAGE 7

Artist's representation of the conceptual process for divining quantum choreography

Illustrated by Peter Allen

prefer contemplating adding bells and whistles become separated. The lone man (an up spin to the true and tested Fermi liquid approach. electron) will quickly impose upon another— Thinking About Thinking About “Phil Anderson [Princeton physicist and stealing his partner—only to leave another

1977 Nobel laureate] was perhaps the first lonesome ‘gent.’ Similarly, for the woman (the Nell physicist who clearly envisioned that there spin down electron). The net effect is that at Quantum Mechanics was much more out there than such bells any time there will be an unpaired male and and whistles. Motivated by a particular class female traversing about the dance floor. Each Possible Good News for Aging Quantum Physicists of materials, he made a guess in the 1970s loner will carry the electron’s spin (spin one- that intuited what is, in the hindsight of my half) and has been christened a ‘spinon.’ “OUR INTUITION IS ALL ABOUT particles and positions; it is not about quantum present thinking, quantum choreography. “The electrons’ charge, which is simply waves,” said solid-state theorist Matthew Fisher, a permanent member of the It was a stroke of genius. He saw a kind of determined by the total number of people Kavli Institute for Theoretical Physics at UC Santa Barbara. “We don’t have dance pattern although at the time he did not irrespective of sex, will be uniform throughout understand it fully in mathematical terms. As the dance floor, so that the spinons are good experimental probes that measure particle waves very well. We’re good at soon as high temperature superconductivity effectively electrically neutral with respect to measuring particle positions, but not the phase of waves because we ourselves are was discovered over a decade later, he the background density of dancers. In particle solid, and solids by nature are good at measuring the positions of things. resurrected this quantum dance and physics the spin and charge of an electron are “What makes it so difficult for people to grasp quantum mechanics is the suggested that it should underlie the strange enslaved, always moving together. But in this necessity of thinking in terms of both particles and waves at the same time—the electronic behavior of these materials. strange hall filled with twirling dancers, the wave/particle duality. His insight was initially well received, but electron’s spin is effectively separated from its “If liquid helium atoms are cooled under pressure, they crystallize,” he said. has since largely fallen out of favor. A few charge—a phenomena called ‘spin-charge’ “In a crystal the atoms are basically behaving classically; there is some quantum diehards, though, have continued to refine, separation.” motion, but more or less the atoms stay still like an atom in a solid should. But develop and generalize the original quantum Fisher often prefers visualizing such reduce the pressure a little bit, and the atoms go into a liquid, into a Bose/Einstein choreography. In the past five years there has intricate quantum choreography in terms of condensate or superfluid. Suddenly the atoms are behaving very much like waves, been a good deal of progress in exploring “vortices,” places on the dance floor around toy models, which can be shown to manifest which dancers are twirling. “Particles are but the waves are kind of classical because all of the atoms are ‘waving’ coherently Anderson’s very first quantum dance waves and waves have phases, they can swirl like photons in a laser. proposed over 30 years earlier.” around in a current called a ‘vortex.’ I can “What’s really interesting are situations when large collections of quantum What about high temperature describe various dance patterns by focusing mechanical degrees of freedom [lots of variables such as position, spin, and charge] superconductivity? The researchers who on the quantum motion of the places where are behaving in a manner which is not easy to understand in terms of either a particle discovered it in 1986 got a Nobel Prize in they are rotating rather than looking at or a wave picture. Both types of behavior are simultaneously manifest. 1987. In the meantime 20 years have passed, individual electrons.” “Gaining intuition for those intrinsically quantum mechanical choreographies, and over 100,000 experiments have been There is much quantum choreography in which neither wave-like nor particle-like aspects are dominating, requires conducted. Is it understood yet? to divine. Spinning vortices and triangular thinking about both together. You really want to be thinking somehow ‘in between’ Replied Fisher, “We have not yet been (instead of square) lattice dance halls, where the two pictures.” sufficiently creative; I don’t believe that we (perhaps strangest of all) critical spin liquids Fisher won the prestigious Waterman Award in 1995, for demonstrating, have yet guessed the right choreography.” can take the floor. Quantum choreography is not easy. In such critical spin liquids, a female according to the specifications for nomination of candidates, “exceptional Even Fisher’s examples of how one might dancer can be paired, or entangled, with a individual achievement in scientific or engineering research of sufficient quality to go about guessing quantum choreography male clear across the dance floor. Dancing pairs place them at the forefront of their peers.” in terms, not of mathematics, but square come in all sizes, intertwined with one another. Fisher said he learned to think quantum mechanically by thinking dancing are not easy. And partners are continuously being swapped. mathematically first. “Just like the docey-doe in square dancing, Moreover, the “spinon”—the unpaired male “One’s intuition can with time transcend the mathematics. I would say that where a couple pairs together and dances or female dancer—moves across the dance mathematics is to physics, what grammar and syntax are to poetry. You can’t do about one another, electrons sometimes floor in a very complex manner, due to partner the latter well unless you have a deep grasp of the former. You can’t compose poetry like pairing. A quantum docey-doe of two swapping between well-separated pairs. “It is without language, and once you know a language it affects how you think. When you electrons is often akin to a ‘valence bond.’ impossible to describe the motion of this are thinking in images, you may be operating in a mixed mode somewhere between But sometimes, just like men and women spinon as a quantum mechanical particle,” words and vision. One’s thinking is so intertwined with one’s knowledge of language who tire of dancing with the same partner,” said Fisher. “It doesn’t behave like a boson; it said Fisher, “electrons become ‘swingers’ doesn’t behave like a fermion. It doesn’t behave that having done enough mathematics it’s hard to know what is physical intuition switching between different partners. The like a free particle at all. It is,” said Fisher, “an and what is mathematical because you now have an intuition for mathematics.” ‘resonating valence bond state’ proposed by element of a strongly interacting theory.” So physics may not just be a game for the 20 and 30 somethings, like so many Anderson in the 1970s is a quantum analog Such exotic quantum choreography of the prized behaviors of society, such as athletics and TV script writing? of square dancing’s ‘grand right and left’ in is possible largely due to the “frustration” “Twenty is, I think, too young, for great physics,” said Fisher. “At the other end, which everybody dances with everyone of inherent in the triangular lattice, according obviously, one eventually burns out. I do notice that the leaders in string theory are the opposite sex on the dance floor. to Fisher. “I am very excited by the quantum not only 30-year-olds, but also 40- and 50-year-olds. With the 50- and 60-year-olds “If the dance floor is disturbed antiferromagnet on the triangular lattice and who were great successes earlier on, their success tends to generate distractions in appropriately,” said Fisher, “a pair of dancers can other frustrated lattices,” said Fisher. “It’s a the form of new duties. And physics, above all else, takes incredible focus.”

5 ■ ■ ■ ■ ■ Topological Quantum Computing:

involving topological phases.” That latter seriously the problem of correcting errors. group, according to Nayak, has come to the Since the error correction process can itself KITP program to learn, for instance, “the introduce errors, the rate of errors must be low connections between their kind of error initially for the whole enterprise to work. correcting codes and what a topological The KITP hosted a four-month program quantum computer does.” in 1996 “Quantum Computing and Quantum Perhaps the key strength of the topological Coherence,” which catalyzed developments approach to quantum computing is that the in the newly emerging field of quantum underlying physical system automatically information processing because it enabled the corrects and protects against errors. pioneers, including Shor, to get together for the “These people,” said Nayak, “who have first time for sustained intellectual exploration. worked on the problem of error correction Another program in 2001 (“Quantum codes with respect to the other approaches to Information, Entanglement, Decoherence and quantum computing based on spin states and Chaos”) again enabled the principals to gather trapped ions, see the topological approach as for a slightly longer five-month stretch. an exciting 'outside the box’ approach. People Those two earlier programs focused on realize the difficulties involved in building approaches to quantum computing other than a quantum computer are great, to say the topological phases because that approach had least, so as a result some people think a linear yet to coalesce into a set of ideas to ground a progression isn’t necessarily going to get us program. A key difference between the earlier there. We have to try something sneaky if we programs and the current one reveals a key Nell Campbell want to build a quantum computer, and this difference between the approaches. The earlier Richard D. Eager (l) and Dan Malinow, both first year physics students at UCSB, chat is such an idea.” programs, especially the first one, focused with Caltech's John Preskill after his “pedagogical lecture” on “Fault Tolerant Quantum on, in effect, software issues, especially error Computation.” “Pedagogical lectures” are a distinctive feature of the KITP program Genesis of Quantum correction, while the latter program is focused “Topological Phases and Quantum Computation.” essentially on hardware. Computing The titles of both early programs Quantum computing arrived on the scene in underscore what was emerging as “INTERDISCIPLINARY” IS A WORD so radically different from the other approaches a big way with Bell Labs’ Peter Shor’s 1994 perhaps the principal stumbling block that has gotten a lot of press in the past decade’s that the overlap between the people pursing discovery of an algorithm for finding the prime to the other approaches to quantum reporting on prospects for scientific discovery. this approach and the other approaches has factors for large numbers via a hypothetical computing: “decoherence,” the seemingly The presumption is that the action is occurring indeed been small. quantum computer. He said, in effect, here is insurmountable problem of sustaining not just at the boundaries of disciplines, but The sustained opportunity for sharing what a quantum computer could do fast that evanescent coherent states of a collective of also at the intersections where the boundaries ideas is one reason for the dynamism and a classical digital computer can’t (unless it can quantum “particles,” especially when trying of two or more disciplines overlap. Such is distinctiveness of the program, according run for decades, centuries, millennia). to scale up to a real computer. Quantum surely the case with topological quantum to one of its organizers, condensed matter Who cares about the ability to find the systems generally decohere very rapidly; computing, as the KITP program (Feb. 21 to theorist Chetan Nayak, a participant in prime factors of large numbers? The answer is consequently, it is difficult to keep the rate May 19) has dramatically illustrated. Microsoft's topological quantum computing the vast national security enterprise engaged in for this type of error low. Its roughly 80 participants represent project temporarily lodged at the KITP and codes and code-breaking. Other approaches to quantum computing the confluence of four streams of research. scheduled to move into the new UC Santa Conventional computing operates in a have essentially analogized digital computing. There are condensed matter theorists who Barbara building housing the California binary mode with a bit of either 0 or 1. What Since the spin of an electron understood are experts on the fractional quantum Hall NanoSystems Institute (CNSI). The other two is different and makes quantum computation classically as up or down is understood quantum effect and other possible topological phases organizers are Sander Bais from the University a potentially richer computational approach is mechanically as any possible superposition of of matter. There are condensed matter of Amsterdam’s Institute for Theoretical that it takes advantage of the multiplicity of up/down, particle spin has, for instance, by experimentalists studying fractional quantum Physics and Caltech’s John Preskill, whose May quantum states to encode not just one piece analogy been envisioned as a candidate for Hall states in gallium arsenide devices. 3 public lecture “Putting Weirdness to Work: of information (for instance whether the spin the qubit. And a collection of spin qubits There are also theorists studying quantum Quantum Information Science” provided a of a particle is up or down), but more, such could encode vastly more information than computation: some coming from an atomic snapshot of the quantum approach. as the superposition of particle spin states. a collection of classical bits. In contrast, with physics background; others studying quantum One distinctive feature of both groups of (Quantum mechanically, particle spin isn’t a topological phase, the qubit is not a single information in the abstract. Straddling all of quantum computing researchers is the overlap necessarily up or down, but in a state that is electron, but rather a collective excitation of these groups are the proponents of topological they represent between condensed matter [classically speaking] a combination of up and the whole system, which is inherently stable quantum computing, a small core group which physics, especially theory, and mathematics. down states.) because of its topology. is collaborating intensely with experts from the Said Nayak, “Many people have come Shortly after Shor’s proof of usefulness, Such an excitation can be useful for other areas and attracting converts. here who study quantum computing abstractly he and others began tackling the problem of quantum computing when it is an “anyon,” The use of topological phases represents and in many cases have been thinking about error correction. The problem is that quantum which exists only in two-dimensional space an approach to quantum computing which is other realizations of quantum computers not information is delicate, so one must take very and has strange properties, such as “fractional

Microsoft's Quantum Project CONTINUED FROM PAGE 1 “The people I wanted to recruit to work The Witten Effect Freedman got very excited. “I talked to Freedman found out about FQHE in with me (I know them all; every single person everyone I knew or could find at Harvard to a popular article written by UCLA physicist has been a collaborator) were all coming The impetus for Freedman’s idea to use ask if we could build a quantum computer Steve Kivelson and published in Scientific from universities. I thought it would be topological phases for quantum computing this way. I wanted to know what would American in 1996. “Then,” said Freedman, very difficult to assemble this group because came from his engagement with the ideas for we need to make this physics that Witten “I really got interested. I knew that there obviously the people you want for a project which theoretical physicist Edward Witten is talking about. In a sense I was asking were physical systems that were governed by like this are people who have a lot of options (a student at Princeton in the mid-1970s of the question two years too early. Everyone a Chern-Simons term that actually would in their lives. I am not the only person who KITP Director David Gross) was to win the was very negative. One source said, ‘What be producing observations potentially that realizes their brilliance. The people I wanted to Fields Medal in 1990. Witten thinks of as physics is not what you would be exactly what Witten had talked bring on board would look at this opportunity Freedman, on leave from UC San Diego learned in high school’; that, in effect, there about.” and say, ‘This is going to be the most vibrant in 1988, attended a seminar in the Harvard is no material system in the world that acts Afire with that realization, Freedman place to do my work and also culturally easy, Mathematics Department. Said Freedman, the way his equations dictate.” shortly thereafter accepted his former on a university campus.’” “We went through Witten’s paper” on quantum But there is—the fractional quantum Hall students’ invitation to talk at Microsoft Employees of the Microsoft group hold field theory and the Jones polynomial. “I had effect (FQHE). Though discovered in 1982, Research. Of course, his subject was the UCSB adjunct positions in the departments the idea then that the technology of Witten’s the FQHE systems known to physicists at the topological phases approach to quantum of Mathematics and Physics, “as is most paper could potentially be used to make a new time of Freedman’s quest in 1988 exhibited computing, whose exploration has now appropriate depending on our training,” kind of computer.” fractional but ordinary abelian statistics, and not become the main mission of the Microsoft said Freedman. “We all expect to be close Some British mathematicians showed the non-abelian statistics of the mathematical project. participants in the university life so we will in 1988 that evaluating the Jones polynomial structures discovered by theoretical physicists “The possibility was out there,” said advise graduate students, for example, and in was computationally difficult. At about the Greg Moore and Nathan Seiborg in 1987, Freedman, “as a very abstract mathematical fact we will probably support graduate students same time, Freedman said, “I was working which were integral to Witten’s work on the idea in Witten’s paper, but Witten proposed as well. We’ve already given a two-quarter very hard in this seminar to understand Jones polynomial and which Freedman’s idea no connection to the real world.” course in the Mathematics Department that Witten’s paper, where he was saying, in a for a quantum computer required. (“Non- In brief, it is an ironic tale of the interplay had 16 to 18 people in attendance at any given sense, that if you do the right kind of physical abelian” roughly pertains in group theory to a between two remarkable minds: the physicist meeting. Many physicists came; Matthew experiment, you do the Jones polynomial. pair that is noncommutative, such that “ab” is who had the great abstract mathematical Fisher and Andreas Ludwig [both UCSB So a light flashed on in my head, which not equivalent to “ba.”) insights (via sidetracking from string theory) faculty and theorists] and all their condensed said it looks stupid to calculate the Jones Moore, a string theorist (now at Rutgers and the pure mathematician who intuited the matter students trekked over to South Hall,” polynomial on an ordinary computer if there University in New Jersey), joined his Yale relevance of those insights to condensed matter where the Mathematics Department resides. is some laboratory physics you could do to colleague, condensed matter physicist physics and the “real world” of potentially get the answer. And that must mean that Nicholas Read, in the early 1990s to search transformative technology. there is a new kind of computer that hasn’t for FQHE states with non-abelian statistics. been thought of yet.” They found several.

6 The Devil is Not in the Details statistics,” ranging “anywhere” (thus its name) Th e charged excitations and the A specifi c scheme for how to do between bosonic and fermionic statistics (See Braiding delocalized neutral fermion are examples of quantum computation in the 5/2 fractional box, page 3). He described computation based on such “quasiparticles” in the fractional quantum Hall quantum Hall state came late in 2004 in a In 1997 Alexei Kitaev (then at the a physical system as “taking one excitation eff ect. As a result of the neutral fermions, the paper Nayak co-authored with Freedman Landau Institute in Moscow and now with around another or around several others,” charged quasiparticles are non-abelian anyons. and a condensed matter theorist who operates Microsoft’s quantum project and a KITP which is called “braiding.” Because of the According to Nayak, “Many of us believe that close to experiment, Sankar Das Sarma of program participant) wrote a “brilliant” paper system’s robustness against details, said Nayak, non-abelian anyons of this type exist in the 5/2 the University of Maryland, also a program explaining, according to Nayak, “how non- “it doesn’t really matter whether one excitation fractional quantum Hall state,” discovered in participant. Th eir architecture is fairly concrete, abelian anyons would have built-in error takes a perfect circular path around the other 1987 by some of the drop-in experimentalists and serious experimental eff orts are underway correction. I don’t think,” said Nayak, “that one or a wiggly path or even pauses to take attending the program: Robert Willett of to realize it. many people besides Michael Freedman [a a break and then completes the transit. All Lucent, Jim Eisenstein (now at Caltech), and In intermittent attendance at the three- topologist with a Fields Medal and head of that matters is that it goes around the other. Horst Stormer (now at Columbia), together month-long program and in more sustained the Microsoft project] realized that the Kitaev Th erefore the error rate associated with such with their collaborators. fashion at its concluding fi ve-day conference paper was a work of landmark importance. an operation is essentially zero.” (May 15 to 19) are condensed matter Alexei,” said Nayak speaking about Kitaev’s Said Nayak, “When you have a bunch KITP Gives Birth to experimentalists, including representatives expertise in mathematics and physics, “is one of these excitations, it turns out that there of the four groups who are now engaged in of those peculiarly Russian geniuses whose isn’t a unique ground state of the system with ‘Anyon’ friendly competition to make that device out conceptual insights fuse mathematics and those excitations present.” Rather there exists Nayak did his PhD at Princeton University of gallium arsenide. Another program drop- physics.” a rich manifold of states determined by the under Frank Wilczek, a particle theorist in, Loren Pfeiff er, heads the Lucent facility for Th e next important development topology of the system and the excitations. then at the Institute for Advanced Study in making gallium arsenide devices of the quality in the direct line of topological quantum Information can be stored and manipulated Princeton and now at MIT. Wilczek, who required by the experiments. computing came in a paper by Freedman in this manifold of states. In the system that shared the 2004 Nobel Prize with his Princeton With developments in topological and two mathematicians from Indiana is most exciting experimentally what most University thesis advisor, KITP director David quantum computing representing the now University, Zhengang Wang (a member in closely corresponds to a qubit, said Nayak, “is Gross, served from 1980 to 1988 as the fi rst rapid convergence of many types of theoretical the Microsoft project) and Michael Larsen. the presence or absence of a neutral fermionic permanent member at the KITP, where he fi rst and experimental expertise, one of the key Wang, like his PhD mentor Freedman, is a excitation associated with a pair of electrically dabbled in condensed matter theory. In 1982 features of the KITP program “Topological topologist, and Larsen is an expert on the charged excitations. Wilczek coined the term “anyon” to describe Phases and Quantum Computation” has been representation theory of groups. Th eir papers “When the charged excitations are quasiparticles in two-dimensional systems the pedagogical Th ursday afternoon sessions, demonstrated that a large class of non-abelian far apart, the fermion isn’t really localized whose quantum states range continuously designed to facilitate an expert in one fi eld anyons have just as much computational anywhere, so no local measurement you could between fermionic and bosonic. learning from a lecture by an expert in another power as ordinary qubit quantum computing. do or that the environment can do is going Nayak’s 1996 thesis research with Wilczek fi eld in a relaxed atmosphere that encourages As Freedman, Kitaev, and Wang showed, a to be able to tell whether it is there or not, focused on understanding the behavior of attendees to ask the kind of “stupid” questions topological quantum computer has no more and that’s essentially where the protection is possible non-abelian anyon excitations in the they might be wary of venturing in a more power than any other quantum computer; coming from. When these two excitations are 5/2 state. Th ey didn’t know it, but what Nayak formal seminar setting. therefore, the two approaches are equally far apart, the information is delocalized over and Wilczek were uncovering is, in today’s To get up to speed on the subject, Nayak powerful computationally. Th e big advantage the whole system. Th at is a miraculous thing; language, the qubit structure for topological said, “You can’t learn about it in a book. Th e of topological quantum computing is its very not only is it very beautiful mathematically quantum computing. only way for somebody on the outside of this low error rate. and conceptually, but it may also be useful for It turns out that the 12/5 state is an even game to become an insider is to talk a lot to the something,” said Nayak. better place to do quantum computing than right people, and they are [mostly] here.” What is a topological 5/2, but it is also a more delicate state. phase? Said Nayak, “Topology is the study of shape irrespective of length and angle. So for a topologist the doughnut really is a coff ee CONTINUED FROM PAGE 5 cup because even though the handle is small Quantum Choreography compared to the cup and a doughnut is all handle, by stretching and deforming the “Some people think the solid state physics done doughnut you can make it into a coff ee cup here in Santa Barbara is simply crazy; others are more and vice versa. Topologists are people who receptive,” said Fisher. “Th ere is a strong orthodoxy forget about all the details and look at the in the solid-state physics community [and more really important key features of a geometrical physicists are members of this community than any shape. Focusing on key features frees one other], an orthodoxy which is amazingly powerful from focusing on details wherein errors when it works. Expressing a strong preference for occur. With the storing of important physical exploring what does not fi t should not be taken information in topological features such as as dismissal of the original paradigm. Quantum shape, small errors in the geometry [like a blip mechanics didn’t mean Newton was a fool.” in the ceramic surface of a cup, which doesn’t But searching for a new paradigm has been interfere with the cup’s mission as container of challenging, and at times dispiriting. “About fi ve liquid] don’t matter.” years back, together with T. Senthil, after extending Translated to a physical system, a some of Phil’s early ideas, we proposed an experiment topological phase is one in which the electrons which could be used to unambiguously determine organize themselves in a state such that the whether or not the simplest resonating valence bond collective state of all the electrons doesn’t state was responsible for the behavior observed in the care about minor details. Th e only example underdoped cuprates. Th e theoretical foundations in nature (at least so far) is the fractional were suffi ciently clear to put forward a concrete Nell Campbell quantum Hall eff ect. However, the hunt is on and falsifi able prediction for an eminently doable for topological phases in other systems. experiment. We were shortly proved wrong. Discovered in the early 1980s by “It takes a certain personality,” he said, “to experimentalists Dan Tsui and Horst Stormer push optimistically, if not blindly, into creative new and explained by theorist Robert Laughlin, directions. Th ere is a real fear of being misguided. the fractional quantum Hall eff ect occurs But until ideas are suffi ciently well formulated to when electrons are cooled to low temperature enable testable predictions, one should persist. and put in high magnetic fi elds. Th ey organize Without taking the risk of being wrong, you can’t themselves in a highly correlated state in have new ideas.” which the ground state and low-energy excitations of the system don’t care about any local perturbations. Th e eff ect showed up in measurements of electrical resistance that is quantized, and the resistance doesn’t depend on details of the device (fabricated out of very high quality gallium arsenide initially made by Nell Campbell UCSB’s Art Gossard, then at Bell Labs), so the eff ect is robust. Top, Friends of KITP gather in the Kohn Hall “It turns out,” said Nayak, “that is exactly courtyard before attending a Chalk Talk in the the kind of physical system one is looking for main auditorium by KITP permanent member in quantum computing.” Matthew Fisher (above, r), who met Friends, such as John Mackall (above, l), chair of the KITP Director’s Council.

Left, Friends of KITP, Glen Mitchel (l), Dr. Eugene Ellis, Gunnar Bergman, and Samuel Fordyce

Nell Campbell 7 Vol. 2 No. 1 • Spring / Summer 2006

Kavli Institute for Theoretical Physics NONPROFIT ORG. UC Santa Barbara U.S. POSTAGE PAID Santa Barbara, CA 93106-4030 SANTA BARBARA CALIFORNIA PERMIT NO. 104

ONGOING & UPCOMING For Physicists… For Friends of KITP… Programs Applications of Gravitational Star Formation* SEE WEB SITE: Lensing: Unique Insights into Tom Abel, Alyssa Goodman, Chris Spintronics* Galaxy Formation and Evolution* McKee, Paolo Padoan www.kitp.ucsb.edu/community/friends_upcoming_events.php David Awschalom, Gerrit Bauer, Leon Koopmans, Chung-Pei Ma, Ben Aug. 6 – Dec. 14, 2007 Michael Flatte, Daniel Loss, Allan Moore, Peter Schneider, Tommaso Treu MacDonald, Dan Ralph Sept. 18 – Nov. 03, 2006 *Indicates a program-related March 13 – June 23, 2006 conference was held (or is planned to be Evolution of Molecular Networks held) during the program. Molecular and Cellular Machines Eric Davidson, Michael Lassig, Tomoko David Bensimon, Robijn Bruinsma, Ohta, Nikolaus Rajewsky, Stephen Small Philip Nelson, Adrian Parsegian Jan. 15 – April 13, 2007 Mini-Programs April 3 – June 30, 2006 Cardiac Dynamics Accretion and Explosion: The Eberhard Bodenschatz, Emilia Physics of Galactic Nuclei* Astrophysics of Degenerate Stars* Entcheva, Robert Gilmour, Alain Martin Haehnelt, Scott Hughes, David Lars Bildsten, Rosanne Di Stefano, Karma, Valentin Krinsky Merritt, Roeland van der Marel Robert Kirshner, Craig Wheeler July 10 – Aug. 4, 2006 May 22 – July 28, 2006 Jan. 29 – June 1, 2007 The Nature and Dynamics of Attosecond Science* Strongly Correlated Phases the Earth’s Transition Zone: A Andre Bandrauk, Nathaniel Fisch, in Condensed Matter and Multidisciplinary Approach Anthony Starace Degenerate Atomic Systems* Adam M. Dziewonski, Stanley Hart, Nell Campbell July 31 – Sept. 15, 2006 Immanuel Bloch, Victor Gurarie, Louise Kellogg, Barbara Romanowicz Deborah Jin, Yong B. Kim, Leo Matthew Fisher (l), KITP permanent member, discusses his Chalk Stochastic Geometry and July 17 – Aug. 4, 2006 Talk, Quantum Crystals, Quantum Choreography and Quantum Radzihovsky, Peter Zoller “ Field Theory* Computing,” with Derek Westen, chair of Friends of KITP. Jan. 29 – June 15, 2007 The Quantum Nature of Ilya Gruzberg, Pierre LeDoussal, Spacetime Singularities Andreas Ludwig, Paul Wiegmann Biological Switches and Clocks Martin Bojowald, Robert H. Aug. 7 – Dec. 15, 2006 Reka Albert, Albert Goldbeter, Peter Brandenberger, Gary T. Horowitz, For information about events and membership, contact String Phenomenology* Ruoff, Jill Sible, John Tyson Hong Liu July 2 – Aug. 10, 2007 Michael Dine, Shamit Kachru, Gordon Jan. 8 – Jan. 26, 2007 Charmien Carrier at (805) 893-6349 or [email protected]. Kane, Joseph Lykken, Fernando Moments and Multiplets in Singular Geometries and For other Friends queries, contact Sarah Vaughan, Director of Quevedo, Eva Silverstein Mott Materials* Geometrical Singularities Development and Community Relations at (805) 893-7313. Aug. 7 – Dec. 15, 2006 Leon Balents, Matthew Fisher, Daniel L. Mahadevan, Tom Whitten, Khomskii, George Sawatzky, Oleg W. Zhang, Edward Spiegel Tchernyshyov July 16 – Aug. 3, 2007 Aug. 6 – Dec. 14, 2007

For details of programs go to our website: http://www.kitp.ucsb.edu/activities/