Analytical Models for Cigar-Shaped Bose-Einstein Condensate under a Variety of External Confinements

Stephan Middelkamp, JiaJia Chang, Chris Hamner +6 more

Alexandru I. Nicolin, Mihaela Carina Raportaru

Hugo L. C. Couto, Ardiley Torres Avelar, Wesley Bueno Cardoso

Ajay Nath, Utpal Roy

In recent years, the study of cigar shaped Bose?Einstein condensate (BEC) under a variety of external confinements has attracted a great deal of attention, from both theoretical and experimental researchers. We report a unified model for obtaining explicit solutions under various kinds of physically relevant space- and time-modulated external traps and nonlinearities for the cigar shaped BEC. Our novel mechanism paves the way to investigate the system for a family of potential functions unified as a physical parameter of the system. We apply and illustrate our results for a number of exactly solvable quantum mechanical potentials; harmonic, double-well, P?sch?Teller, Morse, Toda lattice and power-law as some of the applications of our model. Expressions of the condensate density are provided for these potentials. In addition, as an application of our model, we have illustrated the condensate dynamics for harmonic, double-well and P?sch?Teller potentials. In the presence of loss/gain for a P?sch?Teller potential, the condensate density shows an interesting collapse and revival.

Lydia Shannon, Courtney Lannert

Ajay Nath, Jayanta Bera, Suranjana Ghosh +1 more

We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative temperature. This work is motivated by the first experimental discovery of negative temperature in Bose-Einstein condensate by Braun et al. We have considered an external confinement which is a combination of expulsive trap, bi-chromatic optical lattice trap, and linear trap. The present method is capable of providing the exact form of the condensate wavefunction, phase, nonlinearity and gain/loss. One of the consistency conditions is shown to map onto the Schrödinger equation, leading to a significant control over the dynamics of the system. We have modified the model by replacing the optical lattice trap by a bi-chromatic optical lattice trap, which imparts better localization at the central frustrated site, delineated through the variation of condensate fraction. Estimation of temperature and a numerical stability analysis are also carried out. Incorporation of an additional linear trap introduces asymmetry and the corresponding temporal dynamics reveal atom distillation at negative temperature.