Scaling dynamics of the ultracold Bose gas

TL;DR

This paper introduces an exact, scalable reformulation of the Gross-Pitaevskii equation for ultracold Bose gases, enabling long-time simulations of large-scale expansion dynamics without hydrodynamic approximations.

Contribution

It presents a novel adaptive coordinate frame approach that allows precise simulation of Bose gas expansion, overcoming previous limitations related to system size and evolution time.

Findings

Recovered known scaling laws for ideal and Thomas-Fermi gases

Identified a linear aspect-ratio preserving expansion regime

Showed that exact aspect-ratio invariant free expansion is impossible for nonlinear evolution

Abstract

The large-scale expansion dynamics of quantum gases is a central tool for ultracold gas experiments and poses a significant challenge for theory. In this work we provide an exact reformulation of the Gross-Pitaevskii equation for the ultracold Bose gas in a coordinate frame that adaptively scales with the system size during evolution, enabling simulations of long evolution times during expansion or similar large-scale manipulation. Our approach makes no hydrodynamic approximations, is not restricted to a scaling ansatz, harmonic potentials, or energy eigenstates, and can be generalized readily to non-contact interactions via the appropriate stress tensor of the quantum fluid. As applications, we simulate the expansion of the ideal gas, a cigar-shaped condensate in the Thomas-Fermi regime, and a linear superposition of counter propagating Gaussian wavepackets. We recover known scaling for the ideal gas and Thomas-Fermi regimes, and identify a linear regime of aspect-ratio preserving free expansion; analysis of the scaling dynamics equations shows that an exact, aspect-ratio invariant, free expansion does not exist for nonlinear evolution. Our treatment enables exploration of nonlinear effects in matter-wave dynamics over large scale-changing evolution.