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 analyze the mean-field yrast spectrum of a two-component Bose gas in the ring geometry with arbitrary interaction asymmetry. Of particular interest is the possibility that the yrast spectrum develops local minima at which persistent superfluid flow can occur. By analyzing the mean-field energy functional, we show that local minima can be found at plane-wave states and arise when the system parameters satisfy certain inequalities. We then go on to show that these plane-wave states can be yrast states even when the yrast spectrum no longer exhibits a local minimum. Finally, we obtain conditions which establish when the plane-wave states cease to be yrast states. Specific examples illustrating the roles played by the various interaction asymmetries are presented.

Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schrödinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring, however the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a constant value.

Considering a Bose-Einstein condensed gas confined in one dimension with periodic boundary conditions, we demonstrate that, very generally, solitary-wave and rotational excitations coincide. This exact equivalence allows us to establish connections between a number of effects that are present in these two problems, many of which have been studied using the mean-field approximation.

A Bose-Einstein condensate produced by a Hamiltonian which is rotationally or translationally symmetric is fragmented as a direct result of these symmetries. A corresponding mean-field unfragmented state, with an identical energy to leading order in the number of particles, can generally be constructed. As a consequence, vanishingly weak symmetry-breaking perturbations destabilize the fragmented state, which would thus be extremely difficult to realize experimentally, and lead to an unfragmented condensate.