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arXiv:cond-mat/0404567

Berry phase caused by nondissipative drag of superflow in a Bose qubit

D. V. Fil, S. I. Shevchenko

Published Apr 23, 2004• 0 citations
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Abstract

A microscopic theory of superfluid drag in a two-component Bose gas is developed. The drag factor is shown to be proportional to the square root of the gas parameter. Basing on the similarity between the drag force and vector potential of magnetic field we propose how the superfluid drag can be used to detect a Berry phase in a Bose counterpart of the Josephson charge qubit. We consider a system in which the drag component, situated inside the drive component, is confined in two half-ring traps separated by two Josephson barriers. Under cyclic adiabatic change of Josephson coupling parameters and an asymmetry of two traps a Berry phase is generated. This phase can be observed though measurements of relative number of atoms in two traps. The Berry phase depends on the drag factor and its detection can be used for determining the value of the drag.

DOI
10.48550/arxiv.cond-mat/0404567

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•Jan 1, 2018•0 citations
A microscopic theory of superfluid drag in a two-component Bose gas is developed. The drag factor is shown to be proportional to the square root of the gas parameter. Basing on the similarity between the drag force and vector potential of magnetic field we propose how the superfluid drag can be used to detect a Berry phase in a Bose counterpart of the Josephson charge qubit. We consider a system in which the drag component, situated inside the drive component, is confined in two half-ring traps separated by two Josephson barriers. Under cyclic adiabatic change of Josephson coupling parameters and an asymmetry of two traps a Berry phase is generated. This phase can be observed though measurements of relative number of atoms in two traps. The Berry phase depends on the drag factor and its detection can be used for determining the value of the drag.
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.
An effect of nondissipative drag of a superfluid flow in a system of two Bose gases confined in two parallel quasi-two-dimensional traps is studied. Using an approach based on the introduction of density and phase operators, we compute the drag current at zero and finite temperatures for arbitrary ratio of particle densities in the adjacent layers. We demonstrate that in a system of two ring-shaped traps the “drag force” influences the drag trap in the same way as an external magnetic flux influences a superconducting ring. This allows one to use the drag effect to control persistent current states in superfluids and opens up the possibility of implementing a Bose analog of the superconducting Josephson flux qubit.
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 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.
The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau’s criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.
Motivated by previous work on drag effects in superfluid Bose-Einstein condensates, the Bose-Hubbard model on the square lattice is considered using mean-field theory, and a method for computing the superfluid drag density that does not rely on Galilean invariance is employed to re-derive the drag in the weakly interacting two-component Bose-Einstein condensate. The same method is then used on the Bose-Hubbard model generalized to three-components. An exact analytic expression is not possible because of the complexity of the resulting diagonalization problem. However, Rayleigh-Schrödinger perturbation theory is used to fourth order, which yields an analytic perturbative expression for the zero temperature drag, in addition to exact numerical diagonalization to find the exact behaviour at zero and finite temperatures within mean-field theory. It is found that the presence of a third component can alter the drag in a non-trivial manner: The drag between the two initial boson components can be completely mediated by the third, and it can be both enhanced and diminished depending on the inter-component interaction strengths and signs. An attempt is also made at finding the drag in a weakly interacting two-component Bose-Einstein condensate with spin-orbit coupling, but complications arise, which are discussed. Finally, a phase diagram for the two-component condensate with interactions and spin-orbit coupling is constructed, describing the spin-imbalance, degeneracy, and distribution of spin at zero temperature. A qualitative discussion of the finite temperature behaviour suggests that the inhomogeneous weakly interacting and spin-orbit coupled superfluid Bose-Einstein condensate may in some regions in parameter space favor spin-imbalance as the temperature is increased.