Mixtures of Bose Gases under Rotation

Abstract

We examine the rotational properties of a mixture of two Bose gases. Considering the limit of weak interactions between the atoms, we investigate the behavior of the system under a fixed angular momentum. We demonstrate a number of exact results in this many-body system.PACS numbers: 05.30. Jp, 03.75.Lm, One of the many interesting aspects of the field of cold atoms is that one may create mixtures of different species. The equilibrium density distribution of the atoms is an interesting problem by itself, since the different components may coexist, or separate, depending on the value of the coupling constants between the atoms of the same and of the different species. If this system rotates, the problem becomes even more interesting. In this case, the state of lowest energy may involve rotation of either one of the components, or rotation of all the components. Actually, the first vortex state in cold gases of atoms was observed experimentally in a two-component system [1], following the theoretical suggestion of Ref. [2]. More recently, vortices have also been created and observed in spinor Bose-Einstein condensates [3,4]. Theoretically, there have been several studies of this problem [5,6,7], mostly in the case where the number of vortices is relatively large. Kasamatsu, Tsubota, and Ueda have also given a review of the work that has been done on this problem [8].In this Letter, we consider a rotating two-component Bose gas in the limit of weak interactions and slow rotation, where the number of vortices is of order unity. Surprisingly, a number of exact analytical results exist for the energy of this system. The corresponding manybody wavefunction also has a relatively simple structure.We assume equal masses M for the two components, and a harmonic trapping potential2 )/2, with ρ 2 = x 2 + y 2 . The trapping frequency ω z along the axis of rotation is assumed to be much higher than ω. In addition, we consider weak atomatom interactions, much smaller than the oscillator energyhω, and work within the subspace of states of the lowest Landau level. The motion of the atoms is thus frozen along the axis of rotation and our problem becomes quasi-two-dimensional [9]. The relevant eigenstates are Φ m (ρ, θ)ϕ 0 (z), where Φ m (ρ, θ) are the lowestLandau-level eigenfunctions of the two-dimensional oscillator with angular momentum mh, and ϕ 0 (z) is the lowest harmonic oscillator eigenstate along the z axis.The assumption of weak interactions also excludes the possibility of phase separation in the absence of rotation [10], since the atoms of both species reside in the lowest state Φ 0,0 (r) = Φ 0 (ρ, θ)ϕ 0 (z), while the depletion of the condensate due to the interaction may be treated perturbatively.We label the two (distinguishable) components of the gas as A and B. In what follows the atomatom interaction is assumed to be a contact potential of equal scattering lengths for collisions between the same species and the different ones, a AA = a BB = a AB = a. The interaction energy is measured in unitsare the oscillator l...

Rapidly rotating atomic gases

“…Beyond mean-field theory, there exist exact results for the case of SU(2) invariant interactions, g ij = g, in the 2D LLL limit. For small values of angular momentum, L ≤ min(N 1 , N 2 ), the results of exact diagonalization studies on N = N 1 + N 2 ≤ 8 particles have been used to motivate a conjecture for the exact (analytic) groundstates [177]. The numerical studies show that the groundstate contains only single particle states with angular momenta m ≤ 1; such states can be shown to be exact eigenstates of the SU(2) interactions.…”

Quantum Hall effect of two-component bosons at fractional and integral fillings

“…There has been much recent study of bosonic quantum Hall states. [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] It has been shown that the vortex lattice that forms at large ν melts and that a series of FQH states appear at various filling factors, which include, for appropriately chosen interactions, Laughlin, 40 Jain, 41 Moore-Read, 42 and Read-Rezayi 43 states. While FQH effect in cold atom systems has not yet been observed in a convincing manner, substantial progress in that direction has been reported.…”

Rotational properties of two-component Bose gases in the lowest Landau level

“…Physically, this is the regime where the first vortices (in the two components) enter the system [25]. A recent study by Papenbrock et al [26] identified a class of analytically exact states in the yrast spectrum of this regime; these include the ground state and some (but not all) excited states.…”