Exact Analytical Model for Bose-Einstein Condensate at Negative Temperature

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.

Matter-wave Fractional Revivals in a Ring Waveguide

“…The variation of the revival time with the radius of the ring fosters quantum sensing applications. The work can be extended for 2D-disordered lattice for which the strong localization of condensate can be utilized to get better visibility during FR [60,61]. This work will also be a suitable guideline for a variety of other applications towards quantum information, quantum metrology, quantum logic gates and decoherence.…”

Distillation and Revival of Anderson Localization in Bose-Einstein Condensate

“…We carry out a dynamical stability check where the free evolution of the condensate with and without noise is compared at different times. We executed this analysis by numerically solving the GPE using Split-Step Fourier method [30,[46][47][48]. The absolute deviation of condensate density with noise from that without noise is estimated.…”

“…Adhikari et al carried out numerical studies on the localization of Bose-Einstein condensate (BEC) in BOL of 1,2 and 3 dimensions with different non-linearities [28]. The exact analytical model for BEC inside a BOL was reported by Nath et al [29,30], where the solutions for both attractive and repulsive nonlinearities were studied with precise trap engineering.…”

Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

“…The dynamical stability pertains to disturbance added to the wave function, while the structural stability implies deformation of the external trap. We addressed these problems separately by numerically solving the GPE with the help of the split-step Fourier method [21,24,32]. The results are presented in Figure 6.…”

“…In particular, the study of BEC under the action of geometrically frustrated OLs has drawn much interest [15][16][17][18]. Many complex phenomena have been found in this connection, including Anderson-like localization and negative absolute temperature [17,[19][20][21]. Optical superlattices subjected to frustration offer potential for the development of tools which can hold and mould robust matter-wave states, such as solitons [22][23][24][25][26].…”