Quantum Phases of Vortices in Rotating Bose-Einstein Condensates

TL;DR

Results are presented indicating that, as a function of nu, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly correlated vortex liquid phases.

Abstract

We investigate the groundstates of weakly interacting bosons in a rotating trap as a function of the number of bosons, $N$, and the average number of vortices, $N_V$. We identify the filling fraction $ν\equiv N/N_V$ as the parameter controlling the nature of these states. We present results indicating that, as a function of $ν$, there is a zero temperature {\it phase transition} between a triangular vortex lattice phase, and strongly-correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.

Figures (2)

• Figure 1: Solid lines: Excitation energies at momenta measured relative to the groundstate, for $N_V=8$, $a/b=\sqrt 3 /4$ (inset shows the GP groundstate: dark = low boson density). The excitation energies at the RLVs of the triangular lattice (filled symbols) collapse at $\nu\sim 6$, signalling the onset of a groundstate quasi-degeneracy; all other momenta retain non-zero excitation energies (two such momenta are shown as open symbols). Dashed Line: The excitation energy at one RLV $(2,0)$ for $N_V=6$ and $a/b=1/\sqrt{3}$, showing that the collapse at $\nu\sim 6$ initiates an exponential decrease with $\nu$.
• Figure 2: Energy gap (\ref{['eq:gap']}) as a function of $\nu$ for $N_V=6$ vortices, at $a/b=1/\sqrt 3$. Upward spikes signal values of $\nu$ for which the groundstate is incompressible. The collapse of the gaps at $\nu\sim 6$ indicates the transition to the vortex lattice phase. (Inset shows the density of the GP groundstate.)