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Journal of the Physical Society of Japan

Ground State Properties of a Toroidally Trapped Bose-Einstein Condensate

Takeya Tsurumi, Miki Wadati

Published Jun 15, 2001• 7 citations
Publisher

Abstract

Ground state properties of a toroidally trapped Bose-Einstein condensate are investigated analytically. Through the variational approach, effects of the geometrical curvature and the inter-atomic interaction are taken into consideration. It is shown that the curvature lowers the ground state energy, and that the condensate is attracted towards the axis of symmetry of the torus.

DOI
10.1143/jpsj.70.1512

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Ground state properties of a toroidally trapped Bose-Einstein condensate are investigated analytically. Through the variational approach, effects of the geometrical curvature and the inter-atomic interaction are taken into consideration. It is shown that the curvature lowers the ground state energy, and that the condensate is attracted towards the axis of symmetry of the torus.
We consider Bose-Einstein-condensed atoms confined in a toroidal trap. Under conditions of one-dimensional behavior, the density distribution of the atoms may be exponentially localized or delocalized, even for very small variations in the trapping potential along the torus. For similar reasons, small irregularities of the trap may also have a very pronounced effect on the density of the cloud. The excitation spectrum is also affected by the presence of some spatially varying potential and/or irregularities in the trap.
The ground state of a rotating Bose-Einstein condensate with attractive interaction in a quasi-one-dimensional torus is studied in terms of the ratio $\ensuremath{\gamma}$ of the mean-field interaction energy per particle to the single-particle energy-level spacing. The plateaus of quantized circulation are found to appear if and only if $\ensuremath{\gamma}<1$ with the lengths of the plateaus reduced due to hybridization of the condensate over different angular-momentum states.
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.
In light of the interference experiment of Bose–Einstein condensates, we present an anharmonic external potential model to study ground state properties of Bose–Einstein condensates. The ground state energy and the chemical potential have been analytically obtained, which are lower than those in harmonic trap. Additionally, it is found that the anharmonic strength of the external potential has an important effect on density and velocity distributions of the ground state for the Thomas–Fermi model.