Aligned dipolar Bose-Einstein condensate in a double-well potential: From cigar-shaped to pancake-shaped

TL;DR

This paper explores the behavior of a dipolar Bose-Einstein condensate in a double-well potential, analyzing phase diagrams, stability, and excitations across different geometries from cigar-shaped to pancake-shaped.

Contribution

It provides a comprehensive mean-field analysis of dipolar BECs in double-well traps, including phase diagrams, stability criteria, and excitation spectra, with insights into geometric effects and collapse mechanisms.

Findings

Identification of three distinct phase regions: symmetric, asymmetric, and unstable.

Analysis of stability via Bogoliubov spectra and dynamical response.

Discovery of unique oscillation frequencies and collapse behaviors.

Abstract

We consider a Bose-Einstein condensate (BEC), which is characterized by long-range and anisotropic dipole-dipole interactions and vanishing s-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 $\lambda$, which is defined as the ratio between the axial and longitudinal trapping frequencies $\omega_z$ and $\omega_{\rho}$. 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 $\lambda$ and sufficiently high barrier height, the system consists of two connected quasi-two-dimensional sheets with density profiles whose maxima are located either at $\rho=0$ or away from $\rho=0$. 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.