Nonlinear speed-ups in ultracold quantum gases

TL;DR

This paper investigates how effective nonlinearities in many-body quantum systems can be exploited to accelerate quantum evolution, analyzing quantum speed limits through numerical and analytical models.

Contribution

It provides a detailed analysis of the relationship between nonlinearity strength and quantum speed limits in ultracold quantum gases, combining numerical and analytical approaches.

Findings

Quantum speed limit increases with nonlinearity strength.

Scaling of speed limit with nonlinearity degree is non-trivial.

Numerical and analytical models confirm the effects of nonlinearity on evolution speed.

Abstract

Quantum mechanics is an inherently linear theory. However, collective effects in many body quantum systems can give rise to effectively nonlinear dynamics. In the present work, we analyze whether and to what extent such nonlinear effects can be exploited to enhance the rate of quantum evolution. To this end, we compute a suitable version of the quantum speed limit for numerical and analytical examples. We find that the quantum speed limit grows with the strength of the nonlinearity, yet it does not trivially scale with the ``degree'' of nonlinearity. This is numerically demonstrated for the parametric harmonic oscillator obeying Gross-Piteavskii and Kolomeisky dynamics, and analytically for expanding boxes under Gross-Pitaevskii dynamics.