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Journal of the Physical Society of Japan

Tunneling Dynamics of a Dipolar Bose–Einstein Condensate in a Double-Well Potential

Yuan-Sheng Wang, Qiuping Yang, Jing Wang

Published Apr 16, 2020• 1 citation
Publisher

Abstract

We investigate the tunneling dynamics of a three-dimensional (3D) cigar-shaped dipolar Bose–Einstein condensate (BEC) of 52Cr atoms in an axially-symmetric double-well potential (DWP). By introducing asymmetric basis functions, we improve the effective two-mode model. The results obtained by numerical solutions of the 3D Gross–Pitaevskii (GP) equation and the 3D two-mode approximation methods are basically in accordance with each other at different polarization angles.

DOI
10.7566/jpsj.89.053001

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We study the Josephson oscillation and self-trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of 52{}^{52}52Cr atoms polarized along the symmetry axis of an axially symmetric double-well potential using the numerical solution of a mean-field model, for dominating repulsive contact interaction (large positive scattering length aaa) over an anisotropic dipolar interaction. Josephson-type oscillation emerges for small and very large numbers of atoms, whereas self-trapping is noted for an intermediate number of atoms. The dipolar interaction pushes the system away from self-trapping towards Josephson oscillation. We consider a simple two-mode description for a qualitative understanding of the dynamics.
We investigate the impact of interplay between the contact interaction and the dipole-dipole interaction on the rotational properties of dipolar Bose-Einstein condensate, rotating in an axially confined double-well potential. The dynamics is governed by a quasi-two-dimensional Gross-Pitaevskii equation with phenomenological dissipation and non-local dipole-dipole interaction integral. In the present study, we consider using three different dipolar atoms namely 52Cr, 168Er and 164Dy with increasing order of dipole-dipole interaction strength respectively. From our numerical simulation, we see, at the critical frequency, the vortex core starts to emerge from the peripheries of the BEC. Further, we observe that the critical frequency of vortex nucleation decreases with an increase of dipole-dipole interaction strength and contact interaction strength and these interactions also enhance the number of vortices. We also find that the increase in average angular momentum per atom with rotational frequency suddenly shifts from linear to non-linear progression after attaining the critical rotational frequency. From the results obtained in the present study, it is quite clear that dipole-dipole interaction and contact interaction compliments with each other, has a considerable influence on the rotational properties of dipolar BECs.
Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.
We consider a Bose-Einstein condensate, which is characterized by long-range and anisotropic dipole-dipole interactions and vanishing sss-wave scattering length, in a double-well potential. The properties of this system are investigated as functions of the height of the barrier that splits the harmonic trap into two halves, the number of particles (or dipole-dipole strength) and the aspect ratio $\ensuremath{\lambda}$, which is defined as the ratio between the axial and longitudinal trapping frequencies ${\ensuremath{\omega}}_{z}$ and ${\ensuremath{\omega}}_{\ensuremath{\rho}}$. The phase diagram is determined by analyzing the stationary mean-field solutions. Three distinct regions are found: a region where the energetically lowest lying stationary solution is symmetric, a region where the energetically lowest lying stationary solution is located asymmetrically in one of the wells, and a region where the system is mechanically unstable. For sufficiently large aspect ratio $\ensuremath{\lambda}$ and sufficiently high barrier height, the system consists of two connected quasi-two-dimensional sheets with density profiles whose maxima are located either at $\ensuremath{\rho}=0$ or away from $\ensuremath{\rho}=0$. The stability of the stationary solutions is investigated by analyzing the Bogoliubov--de Gennes excitation spectrum and the dynamical response to small perturbations. These studies reveal unique oscillation frequencies and distinct collapse mechanisms. The results derived within the mean-field framework are complemented by an analysis based on a two-mode model.