Bogoliubov theory of quantum correlations in the time-dependent Bose-Hubbard model

TL;DR

This paper develops a Bogoliubov theoretical framework to analyze quantum fluctuations in a time-dependent Bose-Hubbard model, providing analytical insights into the evolution of correlations during the superfluid to Mott insulator transition.

Contribution

It introduces an adapted mean-field expansion for large fillings to study quantum correlations dynamically, connecting theoretical predictions with experimental observability.

Findings

Analytical expressions for number and phase fluctuations over time.

Conditions for observing correlation dynamics in experiments.

Estimation of quantum depletion growth and order decay.

Abstract

By means of an adapted mean-field expansion for large fillings $n\gg1$, we study the evolution of quantum fluctuations in the time-dependent Bose-Hubbard model, starting in the superfluid state and approaching the Mott phase by decreasing the tunneling rate or increasing the interaction strength in time. For experimentally relevant cases, we derive analytical results for the temporal behavior of the number and phase fluctuations, respectively. This allows us to calculate the growth of the quantum depletion and the decay of off-diagonal long-range order. We estimate the conditions for the observability of the time dependence in the correlation functions in the experimental setups with external trapping present. Finally, we discuss the analogy to quantum effects in the early universe during the inflationary epoch.