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Chinese Physics B

Dynamics of bubble-shaped Bose–Einstein condensates on two-dimensional cross-section in micro-gravity environment

Tie-Fu Zhang, Cheng-Xi 成蹊 Li 李, Wu-Ming 伍明 Liu 刘

Published May 26, 2023• 3 citations
Publisher

Abstract

We investigated the dynamic evolution and interference phenomena of bubble-shaped Bose–Einstein condensates achievable in a micro-gravity environment. Using numerical solutions of the Gross–Pitaevskii equation describing the dynamic evolution of the bubble-shaped Bose–Einstein condensates, we plotted the evolution of the wave function density distribution on its two-dimensional (2D) cross-section and analysed the resulting patterns. We found that changes in the strength of atomic interactions and initial momentum can affect the dynamic evolution of the bubble-shaped Bose–Einstein condensates and their interference fringes. Notably, we have observed that when the initial momentum is sufficiently high, the thickness of the bubble-shaped Bose–Einstein condensate undergoes a counterintuitive thinning, which is a counterintuitive result that requires further investigation. Our findings are poised to advance our comprehension of the physical essence of bubble-shaped Bose–Einstein condensates and to facilitate the development of relevant experiments in micro-gravity environments.

DOI
10.1088/1674-1056/acd922

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We investigate the interference of two-dimensional Bose-Einstein condensates in micro-gravity, which influenced by the interaction strength, initial momentum, gravitational potential and phase difference. We demonstrate that the gravitational potential from the Earth can change the density distribution and phase distribution of the condensate's wave function. As time evolves, a portion of the gravitational potential energy of the microscopic particles can be converted into kinetic energy, which changes the motion of the microscopic particles, and leads to the varying of the density and phase distribution of the wave function. Nevertheless, the influences of the Earth's gravity on the wave function can be eliminated by the micro-gravity environment, which confirmed by many micro-gravity cold atom experiments. Our results present the influences of gravity and other parameters on interference of Bose-Einstein condensates, which help us to reveal the intrinsic natures of the related theoretical predictions and experimental phenomena. Furthermore, our work builds a bridge between the related physical phenomena and our physical intuition about the Bose-Einstein condensates in micro-gravity environment.
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Bose-Einstein condensate has become a highly tunable physical system, which is proven to mimic a number of interesting physical phenomena in condensed matter physics. We study the dynamics of a two-dimensional Bose Einstein condensate (BEC) in the presence of a flat harmonic confinement and time-dependent sharp potential peak. Condensate density can be meticulously controlled with time by tuning the physically relevant parameters: frequency of the harmonic trap, width of the peaks, frequency of their oscillations, initial density etc. By engineering various trap profile, we solve the system, numerically, and explore the resulting spatial interference patters.
Abstract The soliton solutions of the two-dimensional homogeneous Bose–Einstein Condensates Model that is related to the atomic interactions strength and the initial momentum have been discussed through this article to explain the vision when the initial momentum is sufficiently high; the thickness of the bubble-shaped BEC undergoes a counterintuitive thinning. In quantum statistics, the suggested model indicates to two available ways in which a group of noninteracting similar particles may occupy a collection of obtainable possible discrete energy states at thermodynamic equilibrium has been investigated. Many new types of soliton solutions that weren’t achieved before can be constructed, and its descriptions have been documented in the conclusion. In order to derive these new soliton perceptions of the perturbed dynamics of rotating as well as the norm square of the obtaining solution that physically denote to the envelop of these dynamics, we will apply five various schemas. The five distinct schemas that are implemented for the first time to this target are the generalized Kudryashov Schema, the Paul-Painleve Approach schema, the (G′/G)-Expansion Schema, the Extended Simple Equation Schema, and the Riccati–Bernoulli Sub Order Schema are implemented individually, independently in consecutive stages. The consistency for all explored analytical solutions are cleared although these schemas have different tools in prepared. The 2-kind and 3-kind graphs simulations as well as the norm square, which denote physically to envelop of these dynamics, have been documented. The configurator figures that detect the Dynamics’s behaviors as well as all mathematical treatment have been defined via Mathematica program.
Inspired by investigations of Bose-Einstein condensates (BECs) produced in the Cold Atom Laboratory (CAL) aboard the International Space Station, we present a study of thermodynamic properties of shell-shaped BECs. Within the context of a spherically symmetric ``bubble trap'' potential, we study the evolution of the system from small filled spheres to hollow, large, thin shells via the tuning of trap parameters. We analyze the bubble trap spectrum and states and track the distinct changes in spectra between radial and angular modes across the evolution. This separation of the excitation spectrum provides a basis for quantifying dimensional crossover to quasi-2D physics at a given temperature. Using the spectral data, for a range of trap parameters, we compute the critical temperature for a fixed number of particles to form a BEC. For a set of initial temperatures, we also evaluate the change in temperature that would occur in adiabatic expansion from small filled sphere to large thin shell were the trap to be dynamically tuned. We show that the system cools during this expansion but that the decrease in critical temperature occurs more rapidly, thus resulting in depletion of any initial condensate. We contrast our spectral methods with standard semiclassical treatments, which we find must be used with caution in the thin-shell limit. With regard to interactions, using energetic considerations and corroborated through Bogoliubov treatments, we demonstrate that they would be less important for thin shells due to reduced density but vortex physics would become more predominant. Finally, we apply our treatments to traps that realistically model CAL experiments and borrow from the thermodynamic insights found in the idealized bubble case during adiabatic expansion.