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arXiv:1503.08906

Two-component Bose gas trapped by harmonic and annular potentials: Supercurrent, vortex flow and instability of superfluidity by Rabi coupling

Hayato Ino, Yoshihito Kuno, Ikuo Ichinose

Published Mar 31, 2015• 1 citation
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Abstract

In this paper, we study a system of two-component Bose gas in an artificial magnetic field trapped by concentric harmonic and annular potentials, respectively. The system is realized by gases with two-internal states like the hyperfine states of $^{87}$Rb. We are interested in effects of a Rabi oscillation between them. Two-component Bose Hubbard model is introduced to describe the system, and Gross-Pitaevskii equations are used to study the system. We first study the Bose gas system in the annular trap by varying the width of the annulus and strength of the magnetic field, in particular, we focus on the phase slip and superflow. Then we consider the coupled Bose gas system in a magnetic field. In a strong magnetic field, vortices form a Abrikosov triangular lattice in both Bose-Einstein condensates (BECs), and locations of vortices in the BECs correlate with each other by the Rabi coupling. However, as the strength of the Rabi coupling is increased, vortices start to vibrate around their equilibrium locations. As the strength is increased further, vortices in the harmonic trap start to move along the boundaries of the annulus. Finally for a large Rabi coupling, the BECs are destroyed. Based on our findings about the BEC in the annular trap, we discuss the origin of above mentioned phenomena.

DOI
10.48550/arxiv.1503.08906

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In this paper, we study a system of two-component Bose gas in an artificial magnetic field trapped by concentric harmonic and annular potentials, respectively. The system is realized by gases with two-internal states like the hyperfine states of 87^{87}87Rb. We are interested in effects of a Rabi oscillation between them. Two-component Bose Hubbard model is introduced to describe the system, and Gross-Pitaevskii equations are used to study the system. We first study the Bose gas system in the annular trap by varying the width of the annulus and strength of the magnetic field, in particular, we focus on the phase slip and superflow. Then we consider the coupled Bose gas system in a magnetic field. In a strong magnetic field, vortices form a Abrikosov triangular lattice in both Bose-Einstein condensates (BECs), and locations of vortices in the BECs correlate with each other by the Rabi coupling. However, as the strength of the Rabi coupling is increased, vortices start to vibrate around their equilibrium locations. As the strength is increased further, vortices in the harmonic trap start to move along the boundaries of the annulus. Finally for a large Rabi coupling, the BECs are destroyed. Based on our findings about the BEC in the annular trap, we discuss the origin of above mentioned phenomena.
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Characteristic features in phases of Bose-Einstein condensations (BEC) for systems of two-components in gas phases of Alkali-metal atoms trapped by harmonic potentials are discussed on the basis of numerical calculations by the use of Gross-Pitaevskii equation. Condensations with and without vortices are considered in order to make clear spatial distributions. The shape of spatial distribution is essentially dependent on the ratio of interaction strengths between intra-components and inter-components. We emphasize the possibility of coexistence of vortex-free state (where the angular momentum ℓ is 0.) for the one component in BEC and vortex state (ℓ z =1) for another component whose shape is the donut-like spatial distribution. Furthermore, fluctuations of these states are discussed. In partiucular, we concentrate our attention to the appearance of the core modes with ℓ z =0 symmetry for the component with a vortex. In connection with the behavior of the core modes, the contribution of the component without a vortex to the stability of the above vortex is discussed on the basis of numerical calculation.
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Summary form only given. I present results of the detailed asymptotic and numerical results on stability of unit and higher order vortices in coupled Gross-Pitaevskii equations, which model the experimental work. Low lying eigenfrequencies, including ones generating instability of the unit vortex placed in one component of a binary mixture of BEC, have been calculated applying perturbative theory in the limit of the weak interparticle interaction. Results of the perturbative theory have been verified and significantly extended using numerical analysis of the linearised equations for excitations and direct numerical simulation of the coupled Gross-Pitaevskii equations. Two main instability mechanisms have been identified and their dependencies on the relative number of the particles in the condensates and on the strength of the inter-species interaction have been studied. The first mechanism is the drift instability induced by the vortex free component of the condensate and resulting in the motion of the vortex out of the condensate center to its periphery. The second mechanism is the splitting of the higher order vortices into unit ones. Absolute and/or relative increase of the number of particles in the vortex free condensate component has been found to have stabilizing effect on both drift and splitting instabilities. Different scenarios of the splitting instabilities have been found.
In this thesis, I explore the behavior of rotating ultra-cold Bose gases, by diagonalizing the Hamiltonian. This method has the advantage of being exact in the limit of weak interactions, and thus is a useful complement to the more commonly used Gross-Pitaevskii (GP) equation, which relies on a mean-field approximation. It is generally known that an ultra-cold Bose gas shows some remarkable properties under rotation, such as quantized vortices and persistent currents, and these are one main reason why we choose to study rotation. Abstract A repulsively interacting Bose-Einstein condensate (BEC) in a harmonic trapping potential will form singly quantized vortices when rotated. Papers I-V are examples of different kinds of generalizations to this basic system, each showing its particular non-trivial new features. Abstract In Paper I we make the trapping potential weakly anharmonic, and confirm the existence of multiply quantized vortices in both repulsively and attractively interacting condensates, which were previously predicted in Gross-Pitaevskii calculations. Abstract In Papers II and III, we generalize to a two-component system in a harmonic trap. The vortices that form under rotation will in general be coreless, i.e. one component will form a vortex and rotate around the other component. In Paper II we give some analytical expressions for the dispersion relation and occupation numbers at low angular momenta, and in Paper III we show how multiply quantized vortices can be stable in these systems. Abstract Finally we investigate bosons in potentials which can support persistent currents, i.e. rotating states that do not decay in a finite amount of time. These are possible if there is an energy barrier separating the rotating state from the non-rotating ground state. In Paper IV, we have a two-component condensate in a one-dimensional potential and we calculate among other things the minimum interaction strength where persistent currents can occur. In Paper V, we study an experimentally relevant two-dimensional annulus. Again we find that persistent currents are possible above a certain interaction strength, and we find this strength as a function of the width of the annulus, as well as how it depends on the relative population of the two species.