Time-dependent condensation of bosonic potassium

TL;DR

This paper presents an analytical study of the time-dependent formation of Bose--Einstein condensates in potassium vapors, using a solvable nonlinear diffusion equation to model thermalization and condensate growth after a sudden temperature change.

Contribution

It introduces a novel analytical approach to model BEC formation dynamics in potassium, providing explicit solutions that match experimental data.

Findings

Analytical solutions describe BEC formation after a temperature quench.

Model results agree with experimental data for different scattering lengths.

The approach offers insights into thermalization and condensate growth processes.

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 $T_\mathrm{i}$ to a final temperature $T_\mathrm{f}$ 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 $^{39}$K data for various scattering lengths.