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arXiv:2103.16531 · Physical Review Letters

Dissipationless Vector Drag—Superfluid Spin Hall Effect

Andrzej Syrwid, Emil Blomquist, Egor S. Babaev

Published Aug 31, 2021• 8 citations
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Abstract

Dissipationless flows in single-component superfluids have a significant degree of universality. In ^{4}He, the dissipationless mass flow occurs with a superfluid velocity determined by the gradient of the superfluid phase. However, in interacting superfluid mixtures, principally new effects appear. In this Letter, we demonstrate a new kind of dissipationless phenomenon arising in mixtures of interacting bosons in optical lattices. We point out that for a particular class of optical lattices, bosons condense in a state where one of the components' superflow results in dissipationless mass flow of the other component, in a direction different from either of the components' superfluid velocities. The free-energy density of these systems contains a vector productlike interaction of superfluid velocities, producing the dissipationless noncollinear entrainment. The effect represents a superfluid counterpart of the Spin Hall effect.

DOI
10.1103/physrevlett.127.100403

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•Jan 1, 2018•0 citations
Dissipationless flows in single-component superfluids have a significant degree of universality. In ^{4}He, the dissipationless mass flow occurs with a superfluid velocity determined by the gradient of the superfluid phase. However, in interacting superfluid mixtures, principally new effects appear. In this Letter, we demonstrate a new kind of dissipationless phenomenon arising in mixtures of interacting bosons in optical lattices. We point out that for a particular class of optical lattices, bosons condense in a state where one of the components' superflow results in dissipationless mass flow of the other component, in a direction different from either of the components' superfluid velocities. The free-energy density of these systems contains a vector productlike interaction of superfluid velocities, producing the dissipationless noncollinear entrainment. The effect represents a superfluid counterpart of the Spin Hall effect.
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.
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 present a general method for constructing effective field theories for nonrelativistic superfluids, generalizing the previous approaches of Greiter, Witten, and Wilczek, and Son and Wingate to the case of several superfluids in solution. We investigate transport in mixtures with broken parity and find a parity-odd ``Hall drag'' in the presence of independent motion as well as a pinning of mass, charge, and energy to sites of nonzero relative velocity. Both effects have a simple geometric interpretation in terms of the signed volumes and directed areas of various subcomplexes of a ``velocity polyhedron'': the convex hull formed by the end points of the velocity vectors of a superfluid mixture. We also provide a simple quasi-one-dimensional model that exhibits nonzero Hall drag.
In a single-component superfluid under rotation a broken symmetry in the order parameter space results in a broken translational symmetry in real space: a vortex lattice. If translational symmetry is restored, the phase of the order parameter disorders and thus the broken symmetry in the order parameter space is also restored. We show that for Bose-Einstein condensate mixtures in optical lattices with negative dissipationless drag, a new situation arises. This state is a modulated vortex liquid which breaks translational symmetry in the direction transverse to the rotation vector.
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 Andreev-Bashkin drag interactions between the superflow of different components in the superfluid phase of a three-component Bose-Hubbard model without component-mixing interactions, relevant for cold atom systems subjected to an optical lattice. By means of directed worm algorithm path integral Monte Carlo simulations we produce the phase diagram of the superfluid drag density as a function of the nearest-neighbor hopping amplitude and the chemical potential in the case of component-symmetric parameters. In both one and two dimensions, we find an expected region of negative drag close to the tip of the first Mott lobe and a generalization of the two-component supercounterfluid phase in parts of this region. In addition, we also find a more trivial positive drag with strongest presence below the Mott lobe. Further, we investigate the dependence of the drag on the details of the intercomponent interactions strengths in the weakly-coupled regime. In accordance with mean-field results obtained by Stian Hartman, we find that, unlike in the two-component case, the drag is no longer independent of the sign of the intercomponent interaction strengths. In particular, the drag between component a and b can either be strengthened or weakened by increasing interaction strength between component a and c, depending on the sign of the interaction strength between b and c.