Quantum Speed Limit and Optimal Control of Many-Boson Dynamics

TL;DR

This paper explores the quantum speed limit in complex many-boson systems, demonstrating how optimal control can enhance transfer speed and counteract interaction effects in a bosonic Josephson junction.

Contribution

It extends quantum speed limit concepts to many-body systems and introduces control protocols that improve transfer efficiency near the quantum speed limit.

Findings

Control pulses can eliminate interaction effects

Transfer speed can be enhanced beyond self-trapping limits

Numerical optimization approaches improve transfer efficiency

Abstract

We extend the concept of quantum speed limit -- the minimal time needed to perform a driven evolution -- to complex interacting many-body systems. We investigate a prototypical many-body system, a bosonic Josephson junction, at increasing levels of complexity: (a) within the two-mode approximation {corresponding to} a nonlinear two-level system, (b) at the mean-field level by solving the nonlinear Gross-Pitaevskii equation in a double well potential, and (c) at an exact many-body level by solving the time-dependent many-body Schr\"odinger equation. We propose a control protocol to transfer atoms from the ground state of a well to the ground state of the neighbouring well. Furthermore, we show that the detrimental effects of the inter-particle repulsion can be eliminated by means of a compensating control pulse, yielding, quite surprisingly, an enhancement of the transfer speed because of the particle interaction -- in contrast to the self-trapping scenario. Finally, we perform numerical optimisations of both the nonlinear and the (exact) many-body quantum dynamics in order to further enhance the transfer efficiency close to the quantum speed limit.