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Laser Physics

Effect of quantum fluctuations on bose-einstein condensation of bilayer atomic gases in rapid rotation

Y. Terakawa, Nobuhiko Yokoshi, Kenji Kamide, Daisuke Yamamoto, Susumu Kurihara

Published May 1, 2008• 0 citations
Publisher

Abstract

We investigate vortex states and quantum fluctuations of bilayer atomic gases in rapid rotation. Among mean-field solutions of the Gross-Pitaevskii equation, we consider two types of vortex configurations: the vortex core positions of the layers are coincident or staggered. It is found that the coincident type is energetically preferred in the practical parameter regime. We also calculate the dispersion relations of collective modes and the filling factor for bosons outside the condensates. In the double layer system, quantum depletion is found to be suppressed due to interlayer tunneling. This means that Bose-Einstein condensation is stabilized compared to the single layer case.

DOI
10.1134/s1054660x08050150

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We investigate vortex states and quantum fluctuations of bilayer atomic gases in rapid rotation. Among mean-field solutions of the Gross-Pitaevskii equation, we consider two types of vortex configurations: the vortex core positions of the layers are coincident or staggered. It is found that the coincident type is energetically preferred in the practical parameter regime. We also calculate the dispersion relations of collective modes and the filling factor for bosons outside the condensates. In the double layer system, quantum depletion is found to be suppressed due to interlayer tunneling. This means that Bose-Einstein condensation is stabilized compared to the single layer case.
In this paper we systematically study the double-layer vortex lattice model, which is proposed to illustrate the interplay between the physics of a fast rotating Bose-Einstein condensate and the macroscopic quantum tunneling. The phase diagram of the system is obtained. We find that under certain conditions the system will exhibit a phase transition which is a consequence of the competition between interlayer coherent hopping and the interlayer density-density interaction. In one phase the vortices in one layer coincide with those in the other layer. In another phase two sets of vortex lattices are staggered, and as a result the quantum tunneling between two layers is suppressed. To obtain the phase diagram we use the quantum Hall mean field and Thomas-Fermi mean field theories. Two different criteria for the transition taking place are obtained, which reveals some fundamental differences between these two mean-field states. The sliding mode excitation is also discussed.
We demonstrate that quantum fluctuations suppress Bose-Einstein condensation of quasi-two-dimensional bosons in a rapidly rotating trap. Our conclusions rest in part on the derivation of an exact expression for the boson action in terms of vortex position coordinates, and in part on a solution of the weakly interacting boson Bogoliubov equations, which simplify in the rapid-rotation limit. We obtain analytic expressions for the collective-excitation dispersion, which is quadratic rather than linear. Our estimates for the boson filling factor at which the vortex lattice melts are consistent with recent exact-diagonalization calculations.
The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmonic potential under forced rotation. By solving the non-linear Bogoliubov equations coupled with the Gross-Pitavskii equation, the elementary excitations and the total energy of the systems are calculated as a function of rotation velocity. There are two distinct criteria of vortex stability; The position of the excitation energy levels relative to the condensate energy level yields the local stability criterion, and the total energy relative to that of the non-vortex state yields the global stability criterion. The vortex stability phase diagram in the rotation velocity vs the particle density of the system is obtained, allowing one to locate the appropriate region to observe the singly quantized vortex.
In this article, we review developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single-component atomic Bose gas, which (at least at rest) forms a Bose–Einstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditions of rapid rotation, when the vortex density becomes large, atomic Bose gases offer the possibility to explore the physics of quantized vortices in novel parameter regimes. First, there is an interesting regime in which the vortices become sufficiently dense that their cores, as set by the healing length, start to overlap. In this regime, the theoretical description simplifies, allowing a reduction to single-particle states in the lowest Landau level. Second, one can envisage entering a regime of very high vortex density, when the number of vortices becomes comparable to the number of particles in the gas. In this regime, theory predicts the appearance of a series of strongly correlated phases, which can be viewed as bosonic versions of fractional quantum Hall states. In this article, we describe the equilibrium properties of rapidly rotating atomic Bose gases in both the mean-field and the strongly correlated regimes, and related theoretical developments for Bose gases in lattices, for multi-component Bose gases and for atomic Fermi gases. The current experimental situation and outlook for the future are discussed in light of these theoretical developments.
Rapidly rotating atomic gases provide a platform for studying phenomena akin to type-II superconductors and quantum Hall systems. Recently, these systems have attracted renewed interest due to technological advances in the trap anisotropy control, in-situ observation capabilities, and cooling and rotating complex atomic species such as dipolar gases. Understanding the vortex lattice formation and quantum melting is crucial for exploring quantum Hall physics in these systems. In this paper, we theoretically investigate the vortex lattices in anisotropic quantum gases. We formulate the rotating gas Hamiltonian in the Landau gauge, and consider the effects of additional perturbations such as the trap potential in the lowest Landau level (LLL). Focusing on the gases with short-range interactions, we obtain the many-body Hamiltonian projected to lowest Landau level. We consider the limit of full Bose-Einstein condensation and obtain the governing Gross-Pitaevskii equation to identify the possible vortex phases. We numerically solve the Gross-Pitaevskii equation using the imaginary time evolution, and demonstrate the possible vortex lattices as a function of anisotropy, rotation speed and interaction strength. We show that the number of states with a support in the LLL, which determines the number of vortices, follows a Thomas-Fermi type scaling albeit with slightly different coefficients from the usual condensates.
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.