Mechanical cooling in the single-photon quadratical optomechanics

TL;DR

This paper investigates nonlinear mechanical cooling in quadratically coupled optomechanical systems without linearization, revealing unique even-phonon transition processes and nonclassical steady states through scattering theory and quantum simulations.

Contribution

It introduces a scattering theory approach to analyze nonlinear cooling in quadratic optomechanics, highlighting forbidden odd-phonon transitions and nonclassical state properties.

Findings

Only even-phonon transitions occur, odd-phonon transitions are forbidden.

The steady-state phonon number matches quantum master equation results.

Nonclassical mechanical states are achievable with suppressed phonon fluctuations.

Abstract

In the paper we study the nonlinear mechanical cooling processes in the intrinsic quadratically optomechanical coupling system without linearizing the optomechanical interaction. We apply the scattering theory to calculate the transition rates between different mechanical Fock states with the use of the resolvent of Hamiltonian, which allows for a direct identification of the underlying physical processes, where only even-phonon transitions are permitted and odd-phonon transitions are forbidden. We verify the feasibility of the approach by comparing the steady-state mean phonon number obtained from transition rates with the simulation of the full quantum master equation, and also discuss the analytical results in the weak coupling limit that coincide with two-phonon mechanical cooling processes. Furthermore, to evaluate the statistical properties of steady mechanical state, we respectively apply the Mandel Q parameter to show that the oscillator can be in a nonclassical mechanical states, and the phonon number uctuations F to display that the even-phonon transitions favor to suppress the phonon number uctuations compared to the linear coupling optomechanical system.