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arXiv:1404.0259 · Physical Review A

Self-trapping of a dipolar Bose-Einstein condensate in a double well

Sadhan K. Adhikari

Published Apr 14, 2014• 18 citations
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Abstract

We study the Josephson oscillation and self-trapping dynamics of a cigar-shaped dipolar Bose-Einstein condensate of ${}^{52}$Cr 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 $a$) 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.

DOI
10.1103/physreva.89.043609

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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 propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s -wave and dipolar interactions.
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.
We study a Bose-Einstein condensate of 52Cr^{52}\mathrm{Cr}52Cr atoms confined in a toroidal trap with a variable strength of sss-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system from a pancake-shaped condensate when it is large to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origin-displaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity fields, finding that these also show a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the zzz direction provides a qualitative measure of the difference between the velocity in the different density peaks.
Abstract We theoretically study the effects of trap-confinement and interatomic interactions on Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) for a Bose–Einstein condensate confined in a trap which has a symmetric double-well potential along z -axis and 2D harmonic potentials along x - and y -axis. We consider three types of model interaction potentials: contact, long-range dipolar and finite-range potentials. Our results show that by changing the aspect ratio between the axial and radial trap sizes, one can induce a transition from JO to MQST for contact interactions with a small scattering length. For long-range dipolar interatomic interactions, we analyze transition from Rabi to Josephson regime and Josephson to MQST regime by changing the aspect ratio of the trap for a particular dipolar orientation. For a finite-range interaction, we study the effects of relatively large scattering length and effective range on JO and MQST. We show that JO and MQST are possible even if scattering length is relatively large, particularly near a narrow Feshbach resonance due to the finite-range effects.
We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s-wave and dipolar interactions. © 2011 Europhysics Letters Association.