Exact Analytical Model for Bose-Einstein Condensate at Negative Temperature

Ajay Nath,Utpal Roy,Suranjana Ghosh,Jayanta Bera

doi:10.1038/s41598-020-65765-9

Abstract

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.

Highlights

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
We report a large class of exact solitary wave solutions for 1D-Bose-Einstein condensate (BEC) at negative temperature by exploiting a composite potential
Different combinations of external traps are explicated to broaden the scope for future applications

Summary

Introduction

The localization of condensate density, which is the characteristic feature of a disordered potential, is observed corresponding to the variation of trap parameters in the negative temperature domain. We present the model for constructing exact solution of 1D-Gross Pitäevskii equation (GPE) at negative temperature under the composite confinement (a linear trap, an expulsive oscillator and a BOL trap) in presence of space- and time-modulated cubic nonlinearity and gain/loss. The axial compression of the atomic number density is observed with the variation of trap parameters, i.e., the power and wavelength of the lasers, and the expulsive oscillator frequency.

Results

Conclusion