Time-resolved density correlations as probe of squeezing in toroidal Bose-Einstein condensates

TL;DR

This paper investigates how time-resolved density correlations in a toroidal Bose-Einstein condensate can reveal the squeezing of quantum modes caused by a sudden change in interaction strength, providing a potential method for measuring quantum excitations.

Contribution

It introduces a method to analyze time-resolved density correlations to quantify quantum squeezing in Bose-Einstein condensates after a quench.

Findings

Density-density correlation functions exhibit oscillations at twice the excitation frequencies.

Time-resolved measurements can determine the Bogoliubov coefficients.

The approach links density correlations to quantum squeezing in condensates.

Abstract

I study the evolution of mean field and linear quantum fluctuations in a toroidal Bose-Einstein condensate, whose interaction strength is quenched from a finite (repulsive) value to zero. The azimuthal equal-time density-density correlation function is calculated and shows temporal oscillations with twice the (final) excitation frequencies after the transition. These oscillations are a direct consequence of positive and negative frequency mixing during non-adiabatic evolution. I will argue that a time-resolved measurement of the equal-time density correlator might be used to calculate the moduli of the Bogoliubov coefficients and thus the amount of squeezing imposed on a mode, i.e., the number of atoms excited out of the condensate.