Scientific Reports

Exact Analytical Model for Bose-Einstein Condensate at Negative Temperature

Ajay Nath, Jayanta Bera, Suranjana Ghosh, Utpal Roy

Published Jun 2, 2020• 15 citations

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.

DOI: 10.1038/s41598-020-65765-9

Related papers

A unified model for an external trap in a cigar-shaped Bose–Einstein condensate

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.

Journal of Physics A Mathematical and TheoreticalSep 24, 201418 citations

Droplet to soliton crossover at negative temperature in presence of bi-periodic optical lattices

Maitri R. Pathak, Ajay Nath

It is shown that the phenomenon of negative temperature essentially occurs in Bose-Einstein condensate due to the realization of the upper bound energy state utilizing a combination of expulsive harmonic oscillator and optical lattice potentials. We study the existence of quantum droplets at negative temperature and droplet-to-soliton crossover in the binary Bose-Einstein condensate mixture in the presence of bi-periodic optical lattices and expulsive-BOL confinements. Based on the beyond mean field approximation, we employ the extended Gross-Pitäevskii equation and calculate the exact analytical form of wavefunction solutions for BOL, expulsive-BOL confinements. An interesting transition of quantum droplets from positive to negative temperatures and the droplet-to-soliton crossover by modulating the disorder in BOL potential are illustrated. The affirmation of such crossover is performed by exploring the profile of atomic condensate density which smoothly transits from being a flat top density in optical lattice confinement to a bright soliton for BOL trap. Further, we confirm the crossover by exploring the energy per particle and the variation in the root mean square size of the condensate with respect to the potential depth of the BOL trap. Eventually, all of this aid us to construct a phase diagram in a space between the amplitude of BOL potential depth and particle number which reveals the formation of droplet and soliton phases. In expulsive-BOL confinement, it is seen that the impact of the expulsive trap is insignificant on atomic condensate density in the droplet phase and it becomes prominent in the soliton region. Further, the variation of total energy reveals that the amplitude of the expulsive oscillator strengthens the droplet phase and leads to an increase in the negative temperature of the considered system.

Scientific ReportsOct 29, 20227 citations

Dynamics and Stability of Bose-Einstein Condensates: the Nonlinear Schrodinger Equation with Periodic Potential

Bernard Deconinck, Béla A. Frigyik, J. Nathan Kutz

The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case.

arXiv:cond-mat/0106231Jun 12, 20010 citations

Stability of Bright Solitons in Bose-Einstein Condensate

Muhammad Irfan Qadir, Aleen Ijaz

We consider a system of effectively one dimensional cigar shaped Bose Einstein condensate. We present a numerical study for the existence and stability of travelling bright solitons in the time dependent nonlinear Schrodinger equation that describes the dynamics of Bose-Einstein ¨ condensate. Furthermore, the effects of strength of the trap on the stability of bright solitons are investigated when the condensate is placed under the influence of a trapping potential.

Punjab University Journal of MathematicsMay 17, 20250 citations

Bose–Einstein condensate in a bichromatic optical lattice: an exact analytical model

Ajay Nath, Utpal Roy

We provide an exact analytical model for the dynamics of a 1D Bose–Einstein condensate loaded in a bichromatic optical lattice. Although a host of exact solutions result from this novel method, we mainly concentrate on the solitonic excitations. The trapping potential and its depth of lattice frustration can be varied by tuning the power and the wavelengths of the two overlaying laser beams. Both attractive and repulsive regimes are thoroughly investigated. In the attractive domain, we obtain bright soliton, which reveals interesting variations with the depth of lattice frustration. Localization of the matter wave density is demonstrated as one of the applications in this regime. In the repulsive domain, dark soliton is obtained when the potential resembles an optical lattice. With appropriate tuning of the potential parameter, the dark soliton becomes modulated with an oscillatory background and gradually transforms to bright solitary trains.

Laser Physics LettersOct 13, 201425 citations

Exact Nonlinear Dynamics in Spinor Bose-Einstein Condensates

Jun’ichi Ieda, Miki Wadati

Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we

InTech eBooksJan 1, 20101 citation