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arXiv:cond-mat/0607692 · Physical Review A

Competing compressible and incompressible phases in rotating atomic Bose gases at filling factor ν=2

Nigel R. Cooper, Edward H. Rezayi

Published Jan 31, 2007• 24 citations
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Abstract

We study the groundstates of weakly interacting atomic Bose gases under conditions of rapid rotation. We present the results of large-scale exact diagonalization studies on a periodic geometry (a torus) which allows studies of compressible states with broken translational symmetry. Focusing on filling factor $\ensuremath{\nu}=2$, we show a competition between the triangular vortex lattice, a quantum smectic state, and the incompressible $k=4$ Read-Rezayi state. We discuss the corrections arising from finite size effects, and the likely behavior for large system sizes. The Read-Rezayi state is stabilized by a moderate amount of additional dipolar interactions.

DOI
10.1103/physreva.75.013627

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We study the groundstates of weakly interacting atomic Bose gases under conditions of rapid rotation. We present the results of large-scale exact diagonalization studies on a periodic geometry (a torus) which allows studies of compressible states with broken translational symmetry. Focusing on filling factor \ensuremathν=2\ensuremath{\nu}=2\ensuremathν=2, we show a competition between the triangular vortex lattice, a quantum smectic state, and the incompressible k=4k=4k=4 Read-Rezayi state. We discuss the corrections arising from finite size effects, and the likely behavior for large system sizes. The Read-Rezayi state is stabilized by a moderate amount of additional dipolar interactions.
We show that dipolar interactions have dramatic effects on the ground states of rotating atomic Bose gases in the weak-interaction limit. With increasing dipolar interaction (relative to the net contact interaction), the mean field, or high filling factor, ground state undergoes a series of transitions between vortex lattices of different symmetries: triangular, square, "stripe," and "bubble" phases. We also study the effects of dipolar interactions on the quantum fluids at low filling factors. We show that the incompressible Laughlin state at filling factor nu = 1/2 is replaced by compressible stripe and bubble phases.
We numerically study the system of rapidly rotating Bose atoms at the filling factor (ratio of particle number to vortex number) $\ensuremath{\nu}=1$ with the dipolar interaction. A moderate dipolar interaction stabilizes the incompressible quantum liquid at $\ensuremath{\nu}=1$. Further addition induces a collapse of it. We show evidence that states after the collapse are compressible states which have phases with stripes and bubbles. Low-energy spectra are consistently interpreted by the presence of particle-hole excitations in which a Bose atom hops between stripes or bubbles. We also investigate models constructed from truncated interactions and the models with the three-body contact interaction. They also have phases with stripes and bubbles.
We study the ground states of rotating atomic Bose-Einstein condensates with dipolar interactions. We present the results of numerical studies on a periodic geometry which show vortex lattice ground states of various symmetries: triangular and square vortex lattices, ``stripe crystal,'' and ``bubble crystal.'' We present the phase diagram (for systems with a large number of vortices) as a function of the ratio of dipolar to contact interactions and of the chemical potential. We discuss the experimental requirements for observing transitions between vortex lattice ground states via dipolar interactions. We finally investigate the stability of mean-field supersolid phases of a quasi-two-dimensional nonrotating Bose gas with dipolar interactions.
We investigate the ground states 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 nu identical with N/N(V) as the parameter controlling the nature of these states. We present results 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. The vortex liquid phases appear to be the Read-Rezayi parafermion states.
We discuss the effects of quantum fluctuations on the properties of vortex lattices in rapidly rotating ultracold atomic gases. We develop a variational method that goes beyond the Bogoliubov theory by including the effects of interactions between the quasiparticle excitations. These interactions are found to have significant quantitative effects on physical properties even at relatively large filling factors. We use our theory to predict the expected experimental signatures of quantum fluctuations of vortices and to assess the competition of the triangular vortex lattice phase with other phases in finite-sized systems.