Vortex Lattice Locking in Two-Component Bose-Einstein Condensates

This is the title of my new paper that just came out. You can find a link here.

Unlike most of my papers, this one is very condensed-mattery (to invent a new word... think of it the way you would use the word "buttery") and doesn't have much mathematics at all. I do spend a lot of time working on condensed matter physics problems, but the style of my papers ordinarily reveals my nonlinear heart (or, rather, my nonlinear science/applied math heart). This particular paper was written jointly with my fellow scientists in Caltech's theoretical condensed matter group, and the flavor of the paper is correspondingly different---it's most definitely a physics paper rather than an applied math paper.

The first author is Caltech postdoc Ryan Barnett. Also on the list are Caltech faculty member Gil Refael and non-Caltech condensed matter theorist Hanspeter buchler (who goes by Hans Peter in publications).

Here is the abstract:

The vortex density of a rotating superfluid, divided by its particle
mass, dictates the superfluid’s angular velocity through the Feynman relation. To
find how the Feynman relation applies to superfluid mixtures, we investigate a
rotating two-component Bose–Einstein condensate, composed of bosons with
different masses. We find that in the case of sufficiently strong interspecies
attraction, the vortex lattices of the two condensates lock and rotate at the drive
frequency, while the superfluids themselves rotate at two different velocities,
whose ratio equals the ratio between the particle masses of the two species.
In this paper, we characterize the vortex-locked state, establish its regime of
stability, and find that it survives within a disk smaller than a critical radius,
beyond which vortices become unbound and the two Bose-gas rings rotate
together at the frequency of the external drive.


I view this as a form of synchronization, but instead of the better-studied frequency-locking, one actually needs to take the different masses of the species into account (it's a momentum-locking). One of the very important points we make is that if you look at a lot of papers, you'll see that they assume that two different masses are the same "without loss of generality" (and the literature on multiple-component Bose-Einstein condensates is absolutely riddled with that assumption). Of course, as we show in this paper, that's just not true, as there are very interesting phenomena that you'll simply miss if you always make that assumption.