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arXiv:0803.1140 · Physical Review A

Incompressible liquid, stripes, and bubbles in rapidly rotating Bose atoms at ν=1

Hidetsugu Seki, Kazusumi Ino

Published Jun 3, 2008• 8 citations
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Abstract

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.

DOI
10.1103/physreva.77.063602

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We numerically study the system of rapidly rotating Bose atoms at the filling factor (ratio of particle number to vortex number) \ensuremathν=1\ensuremath{\nu}=1\ensuremathν=1 with the dipolar interaction. A moderate dipolar interaction stabilizes the incompressible quantum liquid at \ensuremathν=1\ensuremath{\nu}=1\ensuremathν=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 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 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 study a harmonically trapped highly oblate two-component Bose-Einstein condensate, which consists of both dipolar and scalar bosonic atoms. When the dipoles are polarized along the symmetry axis of the trap, the dipolar atoms' density exhibits a flat-disk regime at the trap center. It is found that the dipolar component is easier to induce the first vortex when the trap is rotating about the symmetry axis, if the long-range dipolar interactions dominate over the contact interactions, and vice versa. Vortex lattices with the compensating triangular, square, and stripe structures can be formed respectively under rapid rotation. When the dipoles are polarized perpendicular to the rotation axis, the two components are generically phase separated into a kernel-shell structure due to the anisotropic dipole-dipole interactions. While the giant-hole states are induced under slow rotation, the compensating stripe vortex structures are stabilized under fast rotation. In particular, a stripe-splitting structure is found to be competing with the stripe ones. These features are expected to be observed in the mixture of 52Cr{}^{52}\mathrm{Cr}52Cr atoms in the two different spin states.
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=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 theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.