Ultra-Fast Converging Path-Integral Approach for Rotating Ideal Bose-Einstein Condensates

TL;DR

This paper introduces a highly efficient recursive method to analyze the thermodynamical and dynamical properties of rotating ideal Bose gases, providing more accurate results especially for small particle numbers and critical rotation regimes.

Contribution

The paper applies a new recursive approach to compute the one-particle propagator, enabling precise analysis of rotating Bose-Einstein condensates with improved accuracy over previous semiclassical methods.

Findings

Enhanced accuracy for small particle numbers.

Increased time scales for free expansion near critical rotation.

Better agreement with experimental observations.

Abstract

A recently developed efficient recursive approach for analytically calculating the short-time evolution of the one-particle propagator to extremely high orders is applied here for numerically studying the thermodynamical and dynamical properties of a rotating ideal Bose gas of $^{87}$Rb atoms in an anharmonic trap. At first, the one-particle energy spectrum of the system is obtained by diagonalizing the discretized short-time propagator. Using this, many-boson properties such as the condensation temperature, the ground-state occupancy, density profiles, and time-of-flight absorption pictures are calculated for varying rotation frequencies. The obtained results improve previous semiclassical calculations, in particular for smaller particle numbers. Furthermore, we find that typical time scales for a free expansion are increased by an order of magnitude for the delicate regime of both critical and overcritical rotation.