We show that the convergence behavior of the many-body numerical diagonalization scheme for strongly interacting bosons in a trap can be significantly improved by the Lee-Suzuki method adapted from nuclear physics: One can construct an effective interaction that acts in a space much smaller than the original Hilbert space. In particular for short-ranged forces and strong correlations, the method offers a good estimate of the energy and the excitation spectrum, at a computational cost several orders of magnitude smaller than that required by the standard method.Comment: 5 pages, 4 figure

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...

We propose a universal transformation from a many-boson state to a corresponding many-fermion state in the lowest-Landau-level approximation of rotating many-body systems, inspired by the Laughlin wave function and by the Jain composite-fermion construction. We employ the exact-diagonalization technique for finding the many-body states. The overlap between the transformed boson ground state and the true fermion ground state is calculated in order to measure the quality of the transformation. For very small and high angular momenta, the overlap is typically above 90%. For intermediate angular momenta, mixing between states complicates the picture and leads to small ground-state overlaps at some angular momenta.

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We examine the conditions that give rise to metastable, persistent currents in a trapped Bose-Einstein condensate. A necessary condition for the stability of persistent currents is that the trapping potential is not a monotonically increasing function of the distance from the trap center. Persistent currents also require that the interatomic interactions are sufficiently strong and repulsive. Finally, any off-center vortex state is shown to be unstable, while a driven gas shows hysteresis.Comment: 7 pages, RevTex, 5 figure