Analytic Study of a Bose-Einstein Condensate in Waveguide with an Obstacle Potential

Jianwen Song, Hai Wen-Hua, Zhong Hong-Hua +1 more

We investigate the exact solutions of one-dimensional (1D) time-independent Gross–Pitaevskii equation (GPE), which governs a Bose–Einstein condensate (BEC) in the magnetic waveguide with a square-Sech potential. Both the bound state and transmission state are found and the corresponding spatial configurations and transport properties of BEC are analyzed. It is shown that the well-known absolute transmission of the linear system can occur in the considered nonlinear system.

Elías Castellanos, Celia Escamilla‐Rivera, Mayra J. Reyes-Ibarra

Guangxi Hu, Jiping Ye, Xian Xi Dai +1 more

J. S. Stießberger, W. Zwerger

By considering the stability of potential flow of a superfluid around large obstacles of size R, we derive an analytical result for the critical velocity that is of order ${v}_{c}\ensuremath{\sim}\ensuremath{\Elzxh}/mR,$ scaling inversely with obstacle size, in contrast to what is obtained from a Landau criterion. Our results are compared with numerical solutions of the Gross-Pitaevskii equation and with recent measurements of the critical velocity in Bose-Einstein condensates of dilute atomic gases.

James Stickney, Alex A. Zozulya

Coherence properties of atomic Bose-Einstein condensates determine the performance of waveguide atom interferometers. We analyze the expansion of a Bose-Einstein condensate from a magnetic microtrap into a waveguide. We derive analytical expressions to describe the expansion, show how the expanded cloud maps onto transverse linear eigenfunctions of the guide, and calculate the dependence of the modal decomposition coefficients on the chemical potential of the cloud and the anisotropy of the trap. Analytical results are compared with three-dimensional numerical simulations of the expansion.

David Spierings, Ramón Ramos, Isabelle Racicot +1 more