The rotational properties of a mixture of two distinguishable Bose gases that are confined in a ring potential provide novel physical effects that we demonstrate in this study. Persistent currents are shown to be stable for a range of the population imbalance between the two components at low angular momentum. At higher values of the angular momentum, even small admixtures of a second species of atoms make the persistent currents highly fragile.PACS numbers: 05.30. Jp, 03.75.Lm, 67.60.Bc Introduction. One of the most fascinating phenomena associated with superfluidity [1] is the stability of persistent currents. In some remarkable experiments that have been performed recently, Bose-Einstein condensed atoms were confined in annular traps [2,3], in which persistent currents could be created and observed [4]. In an earlier experiment, the resistant-free motion of an object through a Bose-Einstein condensate below some critical velocity, was also observed [5].Motivated by these recent advances, in the present study we consider a mixture of two (distinguishable) Bose gases at zero temperature [6,7], that are confined to one dimension with periodic boundary conditions, i.e. in a ring potential, deriving a series of exact and analytic results.The main issue of our study concerns the rotational properties of this system and the stability of persistent currents. In higher dimensions it has been argued that mixtures of Bose gases do not support persistent currents, because there is no energy cost for the system to get rid of its circulation (i.e., the line integral of the velocity field around a closed loop that encircles the ring), as long as angular momentum can be transferred between the two species [8]. Here, we demonstrate that when the total angular momentum per atom varies between zero and unity, currents are stable for a certain range of the ratio of the populations of the two species. We calculate the critical strength of the coupling for a given value of this ratio, which we determine analytically and exactly. On the other hand, for higher values of the angular momentum per atom, persistent currents in one-component systems are very fragile, as even small admixtures of a second species of atoms destabilize the currents.Model. Assuming a ring potential (which corresponds to a very tight annular trap along the transverse direction [9]), the Hamiltonian of the system that we study for the two components that we label as A and B is H = H AA + H BB +Ũ AB

We examine the problem of stability of persistent currents in a mixture of two Bose gases trapped in an annular potential. We evaluate the critical coupling for metastability in the transition from quasi-one to two-dimensional motion. We also evaluate the critical coupling for metastability in a mixture of two species as function of the population imbalance. The stability of the currents is shown to be sensitive to the deviation from one-dimensional motion.

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 consider bosonic atoms that rotate in an anharmonic trapping potential. Using numerical diagonalization of the Hamiltonian, we get evidence for various phases of the gas for different values of the coupling between the atoms and of the rotational frequency of the trap. These include vortex excitation of single and multiple quantization, the phase of center-of-mass excitation, and the unstable phase.

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