I was excited to hear that Charlie Kane, Laurens Molenkamp and Shoucheng Zhang were among the recipients of the 2013 Physics Frontiers Prize. Their seminal works both theoretically predicting and experimentally discovering the topological insulator have profoundly influenced the direction of condensed matter physics over the past few years and have shaped my own research agenda at Caltech.
I first learned about the topological insulator from a talk Charlie Kane delivered at the 2006 American Physical Society March Meeting. It was around this time that graphene was exploding onto the scene following Andre Geim and Konstantin Novoselov’s demonstration that single sheets of it could be peeled from graphite using Scotch tape. Inspired by the highly unconventional charge transport properties that were being measured from graphene, Charlie had begun to think about whether its spin transport properties might also yield surprises. The huge surprise, as Charlie would reveal in his talk, was that graphene could theoretically exhibit a quantum spin Hall effect in which spin-polarized charge carriers flow without dissipation along the edges of an electrically insulating material. Such quantum spin Hall insulators (later renamed the 2D topological insulator), as Charlie and his colleague Eugene Mele proved, are a phase of matter distinct from ordinary electrical insulators by virtue of a quantum entanglement of its electrons. Continue reading →
Erwin Schrödinger. Discussions of quantum foundations often seem to involve his much abused cat.
The group of physicists seriously engaged in studies of the “foundations” or “interpretation” of quantum theory is a small sliver of the broader physics community (perhaps a few hundred scientists among tens of thousands). Yet in my experience most scientists doing research in other areas of physics enjoy discussing foundational questions over coffee or beer.
The central question concerns quantum measurement. As often expressed, the axioms of quantum mechanics (see Sec. 2.1 of my notes here) distinguish two different ways for a quantum state to change. When the system is not being measured its state vector rotates continuously, as described by the Schrödinger equation. But when the system is measured its state “collapses” discontinuously. The Measurement Problem (or at least one version of it) is the challenge to explain why the mathematical description of measurement is different from the description of other physical processes.
My own views on such questions are rather unsophisticated and perhaps a bit muddled:
1) I know no good reason to disbelieve that all physical processes, including measurements, can be described by the Schrödinger equation.
2) But to describe measurement this way, we must include the observer as part of the evolving quantum system.
3) This formalism does not provide us observers with deterministic predictions for the outcomes of the measurements we perform. Therefore, we are forced to use probability theory to describe these outcomes.
4) Once we accept this role for probability (admittedly a big step), then the Born rule (the probability is proportional to the modulus squared of the wave function) follows from simple and elegant symmetry arguments. (These are described for example by Zurek – see also my class notes here. As a technical aside, what is special about the L2 norm is its rotational invariance, implying that the probability measure picks out no preferred basis in the Hilbert space.)
5) The “classical” world arises due to decoherence, that is, pervasive entanglement of an observed quantum system with its unobserved environment. Decoherence picks out a preferred basis in the Hilbert space, and this choice of basis is determined by properties of the Hamiltonian, in particular its spatial locality. Continue reading →
The elementary school I attended hosted an annual book fair, and every year I went with my mother to browse. I would check out the sports books first, to see whether there were any books about baseball I had not already read (typically, no). There was also a small table of science books, and in 1962 when I was in the 4th grade, one of them caught my eye: a lavishly illustrated oversized “Deluxe Golden Book” entitled The World of Science.
My copy of The World of Science by Jane Werner Watson, purchased in 1962 when I was in the 4th grade.
As I started leafing through it, I noticed one of the cutest girls in my class regarding me with what I interpreted as interest. Right then I resolved to buy the book, or more accurately, to persuade my mother to buy it, as the price tag was pretty steep. Impressing girls is a great motivator.
Ignacio Cirac, Dave Wineland, and Peter Zoller receiving the 2010 Franklin medal.
A good thing about a blog is that when my friends win prizes I have the opportunity to say nice things about them. This seems to be happening a lot lately (Kitaev, Wineland, Kimble, Hawking, Polchinski, …).
Today’s very exciting news is that Ignacio Cirac and Peter Zoller have won the 2013 Wolf Prize in Physics “for groundbreaking theoretical contributions to quantum information processing, quantum optics, and the physics of quantum gases.” Continue reading →
When the Institute for Quantum Information (IQI) was founded in 2000, we needed a logo, and (then) graduate student Andrew Landahl volunteered to produce one:
IQI logo designed by Andrew Landahl in 2001.
It served us well, and even today the Landahl Logo is emblazoned on hats worn by scientists all over the world.
In 2011, when the IQI became part of our larger new center, the Institute for Quantum Information and Matter (IQIM), a new logo was clearly needed. For a while, other business prevented us from focusing appropriate attention on this task, but this fall Spiros and I worked with the talented graphic designer Margaret Sanchez to create an image that would convey the essence of the IQIM in a visually appealing way.
We decided that the logo, rather than representing any concrete physical system, should instead portray the active role of the observer in the quantum measurement process. And so we eventually settled on:
As this year comes to a close, people around the world will be counting down the last few seconds of 2012. But, how come we never count up the first few seconds of the new year? What is it about the last few seconds of the year that makes them so special? Maybe it has to do with surviving a Mayan apocalypse, but that was just this year. I guess it always comes down to letting go of the good and of the difficult moments in our past. The champagne helps. Still, I would like to take a moment to pay tribute to the first few seconds of 2013 (the future) with a simple problem and a twist…
The question is simple enough: What is the longest sequence of consecutive numbers, such that each element of the sequence is a power of a prime number?
You will arrive at the answer soon after asking yourself the question: How often is a number divisible by both 2 and 3? The answer is every 6 numbers (since the number in question has to be divisible by ). So, the best one can do is to count the numbers from one to five. That is, if you count 1 as the power of a prime number, then the first five numbers have the incredible property of being the only such sequence of numbers (right?). [Note: Recalling that 1 is not a prime number (see Redemption: Part I, for a hint), we will allow ourselves to use 0 as a valid power to which we may raise a prime number, thus getting , which completes the argument.]
Now, here comes the twist…
Challenge: Is there a sequence of 10 consecutive numbers such that none of them is a power of a prime number?
To get the ball rolling, here are the first such sequences with one, two and three elements, respectively: [6], [14,15], [20,21,22].
Super Challenge: Can you find a sequence of 2013 consecutive numbers, such that none of them is a power of a prime number?
Impossible Challenge: Can you solve the first challenge, giving the sequence containing the smallest numbers satisfying the conditions of the problem?
Good luck and enjoy the rest of 2012! Who knows, maybe some genius will solve the above challenges before 2013 rolls around…
I heard of Jeff Kimble long before I met him in person. Legend had it that he was extremely rigorous with research and very tough on nonsense. So when I decided to approach him in October of 1996, at the annual OSA meeting in Rochester for a possible postdoc position, I was as nervous as I was excited. As a graduate student, I had learned theory of quantum optics from Marlan Scully, and learned advanced experimental techniques from Jan Hall. The experiences working with Jan laid a critical foundation for my scientific work. Likewise, Jeff had spent a sabbatical with Jan in 1985 that enabled their work on squeezing, as well as Jeff’s subsequent research in cavity QED, which provided me some comfort with this tall stranger. But, here was a guy who dealt with the annihilation operator as deftly in the lab as on paper; so I was hesitant. Then I listened to Jeff’s lecture on flying qubits and single-photon quantum logic gates – his speech for the Max Born Award. Armed with courage after surviving my own very first invited talk at OSA, I decided to give it a try.
I still remember most of our discussions from that first meeting, but none is as clear as my recollection of the pain from Jeff’s handshake. His grip was more than just firm; it actually squeezed the bones of my hand. So naturally, I took the handshake as a sign that he really wanted me to join his group. When an offer of a Caltech fellowship arrived three months later, I accepted it without hesitation. In 1997, I had no way of knowing that Jeff’s way of doing science would leave a profound mark on my career and that his deep friendship would continue to enrich my life and that of my family for many years.
I’m lazy. The only reason I ever do anything is that sometimes in a weak moment I agree to do something, and after that I don’t have the nerve to back out. And that’s how I happened to give the introductory lectures leading off the 12th Canadian Summer School on Quantum Information last June.
The video of the lectures recently became available on YouTube in two one-hour segments, which is my reason for posting about them now:
Here are the slides I used. The school is pitched at beginning graduate students who have a solid background in quantum mechanics but may not be very familiar with quantum information concepts.
Andrew Childs, who knows my character flaws well, invited me to lecture at the school nearly a year in advance. Undaunted by my silence, he kept resending the invitation at regular intervals to improve his chances of catching me on a weak day. Sure enough, feeling a twinge of guilt over blowing off David Poulin when he made the same request the year before, and with a haunting sense that I had refused to do something Andrew had asked me to do on an earlier occasion (though I can’t recall what), one day in September I said yes, feeling the inevitable stab of regret just seconds after pushing the Send button. I consoled myself with the thought that this could be a Valuable Service to the Community.
Actually, it was fun to think about what to include in my lectures. The job was easier because I knew that the other lecturers who would follow me, all of them excellent, would be able to dig more deeply into some of the topics I would introduce. I decided that my first responsibility should be to convey what makes the topic important and exciting, without getting too bogged down in technicalities which were likely to be addressed later in the school. That meant emphasizing the essence of what makes quantum information different from ordinary “classical” information, and expounding on the theme that classical systems cannot in general simulate quantum systems efficiently.
The conditions under which I delivered the lectures were not quite ideal. Preparing PowerPoint slides is incredibly time consuming, and I believe in the principle that such a task can fill however much time is allotted for it. Therefore, as a matter of policy, I try to delay starting on the slides until the last moment, which has sometimes gotten me into hot water. In this case it meant working on the slides during the flight from LA to Toronto, in the car from Toronto to Waterloo, and then for a few more hours in my hotel room until I went to bed about midnight, with my alarm set for 6 am so I could finish my preparations in the morning.
It seemed like a good plan. But around 2 am I was awakened by an incredibly loud pounding, which sounded like a heavy mallet hammering on the ceiling below me. As I discovered when I complained to the front desk, this was literally true — they were repairing the air-conditioning ducts in the restaurant underneath my room. I was told that the hotel could not do anything about the noise, because the restaurant is under different ownership. I went back to bed, but lost patience around 3:30 am and demanded a different room, on the other side of the hotel. I was settled in my (perfectly quiet) new room by 4 am, but I was too keyed up to sleep, and read a book on my iPad until it was 6 am and time to get up.
I worked in my room as late as I could, then grabbed a taxi, showing the driver a map with the location of the summer school marked on it. Soon after he dropped me off, I discovered I was on the wrong side of the University of Waterloo campus, about a 20 minute walk from where I was supposed to be. It was about 8:15, and the school was to begin at 8:30, so I started jogging, though not, as it turned out, in the right direction. After twice asking passersby for help, I got to the lecture hall just in time, my heart pounding and my shirt soaked with sweat. Not in the best of moods, I barked at Andrew that I needed coffee, which he dutifully fetched for me.
Though my head was pounding and my legs felt rubbery, adrenalin kicked in as I started lecturing. I felt like I was performing in a lower gear than usual, but I wasn’t sure whether the audience could tell.
And as often happens when I reluctantly agree to do something, when it was all over I was glad I had done it.
Joe Polchinski was a Caltech undergrad, class of 1975 (before my time here). I first met Joe in 1982 when he arrived as a postdoc at Harvard, where I was then on the faculty, and it did not take long for me to recognize his genius. I was teaching a course that fall on advanced quantum field theory, and Joe sat in, at least for a while. One of my lectures was about renormalizability, and I talked about how the renormalization group can organize and simplify the horrible combinatoric task of taming the overlapping divergences in Feynman diagrams to all orders of perturbation theory. I had learned this idea from Curt Callan‘s wonderful 1975 Les Houches Summer School Lectures. Continue reading →
This is fantastic news! I assume the Prize recognizes Stephen’s great discovery that black holes radiate, one of the most transformative developments in theoretical physics during my lifetime. That’s just one of Stephen’s many important contributions. And of course his supreme skill as a popularizer and the unparalleled courage he displays in response to his disability have made him the most famous living scientist in the world. Congratulations, Stephen!
Stephen has a long-standing relationship with Caltech. He spent a sabbatical year here during 1974-75, when he wrote his famous paper formulating the black hole information paradox, and he has made more or less annual extended visits to Caltech since the 1990s. Stephen and I had many memorable discussions about black holes over the years, culminating when he conceded a bet, for which I received far more attention than I deserved. I’ve been proud to be Stephen’s friend for the past 30 years, and we’ve shared a lot of laughter.
). So, the best one can do is to count the numbers from one to five. That is, if you count 1 as the power of a prime number, then the first five numbers have the incredible property of being the only such sequence of numbers (right?). [Note: Recalling that 1 is not a prime number (see 
, which completes the argument.]
Quantum Frontiers 