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Journal of Experimental and Theoretical Physics

The Andreev-Bashkin effect in a two-component Bose gas

S. I. Shevchenko, D. V. Fil

Published Jul 1, 2007• 9 citations
Publisher

Abstract

A microscopic theory is developed for the Andreev-Bashkin effect in a superfluid two-component weakly nonideal Bose gas. An expression is obtained for the matrix of superfluid densities in the general case of two gases with different densities, particle masses, and scattering lengths. A method for the observation of a drag between superfluid components is proposed.

DOI
10.1134/s106377610707028x

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A microscopic theory is developed for the Andreev-Bashkin effect in a superfluid two-component weakly nonideal Bose gas. An expression is obtained for the matrix of superfluid densities in the general case of two gases with different densities, particle masses, and scattering lengths. A method for the observation of a drag between superfluid components is proposed.
A microscopic theory of a nondissipative drag in a two-component superfluid Bose gas is developed. The expression for the drag current in the system with the components of different atomic masses, densities, and scattering lengths is derived. It is shown that the drag current is proportional to the square root of the gas parameter. The temperature dependence of the drag current is studied and it is shown that at temperature of order or smaller than the interaction energy the temperature reduction of the drag current is rather small. A possible way of measuring the drag factor is proposed. A toroidal system with the drag component confined in two half-ring wells separated by two Josephson barriers is considered. Under certain condition such a system can be treated as a Bose-Einstein counterpart of the Josephson charge qubit in an external magnetic field. It is shown that the measurement of the difference of number of atoms in two wells under a controlled evolution of the state of the qubit allows one to determine the drag factor.
We study a mixture of two superfluids with density–density and current–current (Andreev–Bashkin) interspecies interactions. The Andreev–Bashkin coupling gives rise to a dissipationless drag (or entrainment) between the two superfluids. Within the quantum hydrodynamics approximation, we study the relations between speeds of sound, susceptibilities and static structure factors, in a generic model in which the density and spin dynamics decouple. Due to translational invariance, the density channel does not feel the drag. The spin channel, instead, does not satisfy the usual Bijl–Feynman relation, since the f-sum rule is not exhausted by the spin phonons. The very same effect on one dimensional Bose mixtures and their Luttinger liquid description is analysed within perturbation theory. Using diffusion quantum Monte Carlo simulations of a system of dipolar gases in a double layer configuration, we confirm the general results. Given the recent advances in measuring the counterflow instability, we also study the effect of the entrainment on the dynamical stability of a superfluid mixture with non-zero relative velocity.
We investigate the propagation of spin waves in two-component mixtures of one-dimensional Bose gases interacting through repulsive contact potentials. By using quantum Monte Carlo methods we calculate static ground-state properties, such as the spin susceptibility and the spin structure factor, as a function of the coupling strengths and we determine the critical parameters for phase separation. In homogeneous mixtures, results of the velocity of spin waves and of its softening close to the critical point of phase separation are obtained by means of hydrodynamic theory and a sum-rule approach. We quantify the nondissipative drag effect, resulting from the Andreev-Bashkin current-current interaction between the two components of the gas, and we show that in the regime of strong coupling it causes a significant suppression of the spin-wave velocity.
In multicomponent superfluids and superconductors, co- and counterflows of components have, in general, different properties. A. F. Andreev and E. P. Bashkin [Sov. Phys. JETP 42, 164 (1975)] discussed, in the context of He3/He4{\mathrm{He}}^{3}/{\mathrm{He}}^{4}He3/He4 superfluid mixtures, that interparticle interactions produce a dissipationless drag. The drag can be understood as a superflow of one component induced by phase gradients of the other component. Importantly, the drag can be both positive (entrainment) and negative (counterflow). The effect is known to have crucial importance for many properties of diverse physical systems ranging from the dynamics of neutron stars and rotational responses of Bose mixtures of ultracold atoms to magnetic responses of multicomponent superconductors. Although substantial literature exists that includes the drag interaction phenomenologically, only a few regimes are covered by quantitative studies of the microscopic origin of the drag and its dependence on microscopic parameters. Here we study the microscopic origin and strength of the drag interaction in a quantum system of two-component bosons on a lattice with short-range interaction. By performing quantum Monte Carlo simulations of a two-component Bose-Hubbard model we obtain dependencies of the drag strength on the boson-boson interactions and properties of the optical lattice. Of particular interest are the strongly correlated regimes where the ratio of coflow and counterflow superfluid stiffnesses can diverge, corresponding to the case of saturated drag.
A well-known paradox in the theory of superfluidity is studied: superfluidity is linked to Bose condensation, but the superfluid density is always greater than the density of the Bose condensate. Based on the model of a weakly nonideal Bose gas, it is demonstrated that supercondensate particles, forming pairs which are correlated in momentum space—the two-particle condensate—make the missing contribution to the superfluid density. It is shown that in the case of slow spatial variations of superfluid flows it is possible to introduce a macroscopic wave function describing the entire superfluid component and not only the single-particle condensate. The characteristic features of weak superfluidity in Bose systems are studied and it is shown that the tunneling effect is a sensitive tool for studying the structure of the superfluid component. It is hypothesized that the superfluid component of real He II consists of the sum of one-, two-, three-, and many-particle condensates.