Update: I definitely wasn’t expecting this! It’s nice to see something applied win the prize.
So Nobel Prize season is upon us once again. It’s always fun to try to guess who the winners will be — and because I know nothing about Medicine, Peace, or Economics, I’ll stick to making predictions on the Physics and Chemistry prizes. I happened to pick 2007’s Physics winners correctly by sheer luck: maybe it’ll happen again?
Actually, I don’t know Chemistry as a field broadly enough to make any reasonable predictions, either. Just for fun, I’m going to guess Richard Zare will win this year, for the extensive work he has done using lasers for all sorts of spectroscopy — in particular, he developed laser-induced fluorescence spectroscopy. The only problem with picking Zare is that his work might (?) be too closely related to that of last year’s Chemistry picks (Shimomura, Chalfie and Tsien) for their discovery and development of green fluorescent protein.
This year I’m guessing that the Physics prize will go to Aharanov and Berry for their work on quantum topological and geometrical phases (see, for example, the Aharonov-Bohm effect or Berry phase). There are a number of reasons for this guess. Every physics student learns about how a charged particle moving in a region of zero electric and magnetic field is still affected by the potentially non-zero electromagnetic vector potential A – that is, its wave function picks up a phase shift given by integrating A along its path. This is an incredibly deep and fundamental result of quantum mechanics: unlike in classical electrodynamics, in quantum electrodynamics the effects of this potential can be felt. For example, as Aharonov and Bohm proposed in 1959, two charged particles going in opposite directions around a circle encircling a solenoidal magnetic field interfere when they are recombined — in particular, their phase difference (which can be measured) is directly proportional to the magnetic flux penetrating the circle, even though they feel zero magnetic field along the path they traverse!
Indeed, this effect has been verified in numerous measurements since. The earliest example that I am aware of is this elegant experiment by Chambers in 1960, using an electrostatic “biprism” consisting of an aluminized quartz fiber flanked by two grounded metal plates (schematic here) to interfere two beams of electrons. This was followed up by further electron holography measurements using toroidal ferromagnets, as well as by work studying oscillations in the resistance of tiny metal rings as a function of the magnetic field being applied through their core. More recently, these magnetoresistance oscillations have been observed in individual carbon nanotubes with the field applied parallel to the tube axis, which I think is pretty cool. I remember when I first learned about this effect: it was one of the first times I was truly, genuinely, acutely thrown by quantum mechanics. And it has profound consequences — namely, it suggests that the electromagnetic vector potential is in some sense more “real” than the electric or magnetic fields on their own.
in 1984, Berry went one step further, pointing out that the Aharonov-Bohm effect is a particular example of geometric phase, and that a geometric phase often arises in many quantum situations. In particular, if a quantum system is changed very slowly (that is, adiabatically) such that it is eventually brought back to its initial conditions in parameter space, it turns out that it remembers the path it took: it picks up a phase factor that depends on the geometry of the path it took through parameter space. For example, if you subject a fixed electron to a constant magnetic field that changes in direction — say the magnetic field vector sweeps out an arbitrary closed loop on the surface of a sphere centered on the electron — it turns out that the electron state picks up a Berry’s phase proportional to the solid angle subtended by the path relative to the origin. That’s it. Isn’t that crazy?
The idea of a Berry phase (and the way in which it links physical effects to topological quantities) is quite general, and has found applications in many physical systems. For example, the quantum Hall effect can be understood as an example of Berry’s phase applied to 2D electronic systems, while the anomalous Hall effect for dilute magnetic semiconductors has recently been linked to Berry’s phase, as well. Graphene is a nice recent experimental system for studying Berry’s phase for electrons in two dimensions: electrons in graphene can be understood using the Dirac equation for spin-1/2 particles, and are characterized by “pseudospin”. Just as in the Berry phase example I gave earlier, an electron in graphene that completes a cyclotron orbit in an applied magnetic field has its pseudospin rotated by 360 degrees, and thus picks up a phase shift of pi in its wavefunction. The consequences of this have recently been observed in quantum Hall measurements of monolayer and bilayer graphene. In related work, topological insulators and the quantum spin Hall effect have recently begun receiving a huge amount of attention from the physics community, because of their unusual properties — while they are insulating in the bulk, they can support unique “surface states”. I don’t fully understand the theory of these, but the main framework within which they appear to be studied is by describing them as topologically ordered states, characterized by topological invariants such as Chern numbers and a non-trivial Berry phase.
An interesting side note: in all of these Aharonov-Bohm/Berry phase experiments, the quantum phase is measured through some kind of interference process. Recently, Manoharan’s group at Stanford has done some pretty cool STM experiments to directly measure quantum phase information, by comparing the STM signal of physically different but electronically identical quantum corral-type nanostructures.
One potential problem: the Aharonov-Bohm effect was apparently previously predicted by Ehrenberg and Siday ten years earlier, and Berry phase was apparently discussed by Pancharatnam some 28 years before Berry’s paper! On the other hand, history suggests that this may not be enough to deter the prize committee.
Update: apparently Thomson Reuters agrees with my pick for Physics…
