Quantum entanglement of anharmonic oscillators

TL;DR

This paper explores how anharmonic nonlinear oscillators exhibit complex quantum entanglement dynamics, influenced by nonlinearity and dissipation, with applications to optomechanical systems showing non-classical states and quadrature squeezing.

Contribution

It provides a detailed analysis of entanglement in anharmonic oscillators, including an analytical treatment of cavity optomechanics with nonlinear mirrors, revealing non-classical states without conditional measurements.

Findings

Time-varying entanglement influenced by nonlinearity

Steady state dynamics affected by dissipation and nonlinearity

Generation of non-classical states and quadrature squeezing in optomechanical systems

Abstract

We investigate the quantum entanglement dynamics of undriven anharmonic (nonlinear) oscillators with quartic potentials. We first consider the indirect interaction between two such nonlinear oscillators mediated by a third, linear oscillator and show that it leads to a time-varying entanglement of the oscillators, the entanglement being strongly influenced by the nonlinear oscillator dynamics. In the presence of dissipation, the role of nonlinearity is strongly manifested in the steady state dynamics of the indirectly coupled anharmonic oscillators. We further illustrate the effect of nonlinearities by studying the coupling between an electromagnetic field in a cavity with one movable mirror which is modeled as a nonlinear oscillator. For this case we present a full analytical treatment, which is valid in a regime where both the nonlinearity and the coupling due to radiation pressure is weak. We show that, without the need of any conditional measurements on the cavity field, the state of the movable mirror is non-classical as a result of the combined effect of the intrinsic nonlinearity and the radiation pressure coupling. This interaction is also shown to be responsible for squeezing the movable mirror's position quadrature beyond the minimum uncertainty state even when the mirror is initially prepared in its ground state.