Quantum fluctuations and condensate fraction during the time-of-flight expansion

TL;DR

This paper investigates quantum fluctuations in time-of-flight experiments for condensates released from optical lattices, revealing a universal decay of condensate fraction and proposing methods to measure it.

Contribution

It introduces a semi-quantitative analysis of quantum depletion during TOF expansion and demonstrates a universal algebraic decay of the condensate fraction.

Findings

Condensate fraction decreases monotonically during TOF expansion.

Universal algebraic decay law for the condensate fraction.

Good agreement between analytical analysis and numerical simulations.

Abstract

The quantum fluctuation effects in the time-of-flight (TOF) experiment for a condensate released from an optical lattice potential is studied within the truncated Wigner approximation. By investigating both the spatial and momentum density distributions, we find that the condensate fraction decreases monotonically in time and hence cannot be measured in the standard TOF image. We then propose a semi-quantitative analysis for such dynamical quantum depletion process. Our study shows a universal algebraic decay of the true condensate fraction, and have a very good agreement with numerical results. We also discuss possible methods to determine the condensate fraction inside the optical lattice, and its implication to the TOF experiments in higher dimensional systems.