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arXiv:2407.14307 · Physical Review A

Time-dependent condensate formation in ultracold atoms with energy-dependent transport coefficients

M. Larsson, Georg Wolschin

Published Aug 6, 2024• 1 citation
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Abstract

Time-dependent Bose-Einstein condensate formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coefficients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coefficients, and with recent deep-quench data for $^{39}\mathrm{K}$ at various scattering lengths. Some nonphysical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion.

DOI
10.1103/physreva.110.023305

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Time-dependent Bose-Einstein condensate formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coefficients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coefficients, and with recent deep-quench data for 39K^{39}\mathrm{K}39K at various scattering lengths. Some nonphysical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion.
Abstract We calculate the time-dependent formation of Bose–Einstein condensates (BECs) in potassium vapours based on a previously derived exactly solvable nonlinear boson diffusion equation (NBDE). Thermalization following a sudden energy quench from an initial temperature TiT_\mathrm {i}Ti​ T i to a final temperature TfT_\mathrm {f}Tf​ T f below the critical value and BEC formation are accounted for using closed-form analytical solutions of the NBDE. The time-dependent condensate fraction is compared with available 39^{39}39 39 K data for various scattering lengths. Graphic Abstract
A variational technique is applied to solve the time-dependent nonlinear Schr\"odinger equation (Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schr\"odinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable when the shape of the condensate is sufficiently simple.