Second-quantized Landau-Zener theory for dynamical instabilities

TL;DR

This paper develops a second-quantized Landau-Zener framework to analyze quantum corrections during dynamical instabilities in nonlinear quantum systems, especially Bose-Einstein condensates, where mean field theories fail.

Contribution

It introduces a novel second-quantized Landau-Zener model to describe quantum effects in dynamical instabilities, extending the understanding beyond mean field approximations.

Findings

Provides a general theoretical framework for quantum corrections during dynamical instabilities.

Models the instability as a twisted crossing in a second-quantized Landau-Zener scenario.

Offers insights into quantum control challenges in Bose-Einstein condensates.

Abstract

State engineering in nonlinear quantum dynamics sometimes may demand driving the system through a sequence of dynamically unstable intermediate states. This very general scenario is especially relevant to dilute Bose-Einstein condensates, for which ambitious control schemes have been based on the powerful Gross-Pitaevskii mean field theory. Since this theory breaks down on logarithmically short time scales in the presence of dynamical instabilities, an interval of instabilities introduces quantum corrections, which may possibly derail a control scheme. To provide a widely applicable theory for such quantum corrections, this paper solves a general problem of time-dependent quantum mechanical dynamical instability, by modelling it as a second-quantized analogue of a Landau-Zener avoided crossing: a `twisted crossing'.