Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

TL;DR

This paper models a nonlinear nanomechanical resonator coupled to a microwave cavity, revealing bifurcation structures and entanglement phenomena in both semi-classical and quantum regimes, with potential implications for quantum information processing.

Contribution

It introduces a theoretical framework showing how bifurcations in a coupled nanomechanical-microwave system lead to entanglement and quantum signatures of classical limit-cycles.

Findings

Bifurcation from fixed points to limit cycles in semi-classical dynamics.

Maximum entanglement occurs near the bifurcation point.

Quantum signatures of classical limit-cycles are observed.

Abstract

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.