Parametric resonant enhancement of motional entanglement under optimal control: an analytical study

TL;DR

This paper provides an analytical framework for understanding how parametric resonance can enhance motional entanglement in optically trapped particles, incorporating feedback control and revealing conditions for stationary entangled states.

Contribution

It introduces a detailed analytical model for motional entanglement under parametric resonance with feedback control, extending previous numerical studies.

Findings

Analytical expressions for entanglement degree derived.

Stationary entangled states achieved through parametric gain.

Model accurately reproduces numerical results.

Abstract

We study theoretically continuous-variable entanglement between the motional degrees of freedom of optically trapped massive particles coupled via the Coulomb interaction, in the presence of a feedback control scheme. We perform a detailed analysis of the parametric resonance induced by temporal modulation of the coupling strength, based on the system's coupled nonlinear, nonhomogeneous dynamical equations. Our model accurately reproduces the numerical findings and provides closed-form expressions for the entanglement degree. We demonstrate that a stationary nonequilibrium entangled state is realized as a result of the competition between parametric gain and decoherence.