Scaling theory for the collapse of a trapped Bose gas in a synthetic magnetic field: a critical study at the condensation point

TL;DR

This paper develops a scaling theory for the collapse of a trapped Bose gas under synthetic magnetic fields, analyzing how anisotropy, temperature, and magnetic effects influence critical particle numbers and phase transition behavior.

Contribution

It provides the first analytical study of collapse dynamics in a Bose gas with synthetic magnetic fields, including temperature effects and critical exponents.

Findings

Critical particle number depends on anisotropy, magnetic field, and temperature.

A dramatic change in the specific heat critical exponent occurs near collapse.

Results are experimentally testable with current ultracold atomic systems.

Abstract

We have analytically explored both the zero temperature and the finite temperature scaling theory for the collapse of an attractively interacting 3-D harmonically trapped Bose gas in a synthetic magnetic field. We have considered short-ranged (contact) attractive inter-particle interactions and Hartree-Fock approximation for the same. We have separately studied the collapse of both the condensate and the thermal cloud below and above the condensation point, respectively. We have obtained an anisotropy, artificial magnetic field, and temperature-dependent critical number of particles for the collapse of the condensate. We have found a dramatic change in the critical exponent (from $\alpha=1$ to $0$) of the specific heat ($C_v\propto|T-T_c|^{\alpha}$) when the thermal cloud is about to collapse with the critical number of particles ($N=N_c$) just below and above the condensation point. All the results obtained by us below and around the condensation point are experimentally testable within the present-day experimental set-up for the ultracold systems in the magneto-optical traps.