Maximizing optomechanical entanglement with optimal control

TL;DR

This paper formulates the generation of optomechanical entanglement as an optimal control problem in hyperbolic space and uses numerical methods to find pulse sequences that maximize entanglement, achieving significant results in the strong coupling regime.

Contribution

It introduces a novel optimal control framework in hyperbolic space for maximizing optomechanical entanglement and derives exact optimal pulse sequences.

Findings

Maximal entanglement achieved within a fraction of an oscillator period.

Optimal control in hyperbolic space effectively enhances entanglement generation.

Strong coupling regime allows for substantial entanglement within short times.

Abstract

In this article, we formulate the generation of optomechanical entanglement between the linearly coupled cavity field and the mechanical resonator as an optimal control problem in hyperbolic space $H^3$, with control input the coupling rate of the two oscillators. Next, we use optimal control theory to find the allowed optimal values of the coupling which maximize the amount of generated entanglement for a fixed duration of the interaction. Finally, we employ a numerical optimization method to obtain the exact optimal pulse sequences for several illustrative examples. In the strong coupling regime, where the coupling rate is comparable or larger than the frequency of the mechanical resonator, a substantial amount of entanglement can be generated within a fraction of a single oscillator period.