Quantum noise spectra for periodically driven cavity optomechanics

Abstract

A growing number of experimental setups in cavity optomechanics exploit periodically driven fields. However, such setups are not amenable to analysis by using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators, (ii) Floquet [Phys. Rev. A 94, 023803 (2016)], and (iii) iterative analysis [New J. Phys. 18, 113021 (2016)]. We prove that (i) and (ii) yield equivalent noise spectra and find that (iii) is an analytical approximation to (i) for weak modulations. We calculate the noise spectra of a doubly modulated system describing experiments of levitated particles in hybrid electro-optical traps. We show excellent agreement with Langevin stochastic simulations in the thermal regime and predict squeezing in the quantum regime. Finally, we reveal how otherwise-inaccessible spectral components of a modulated system can be measured in heterodyne detection through an appropriate choice of modulation frequencies.

Quantum Motional Sideband Asymmetry in the Presence of Kerr-Type Nonlinearities

“…Langevin equations with periodic time-dependence can be analyzed with a recently developed method [49]. Note that closely related models have been studied in the context of levitated optomechanics [50,51], where instead of the cavity, the mechanical resonator frequency is modulated.…”

Quantum sensing and cooling in three-dimensional levitated cavity optomechanics

“…In this Appendix we briefly review the framework of quantum linear theory (QLT) of optomechanics. Optically levitated systems [26,27] generally involve multiple optical and mechanical modes. Such multimode systems (N optical and M mechanical degrees of freedom) are typically described by the well-studied linearized Hamiltonian [1]…”

Two-timescale stochastic Langevin propagation for classical and quantum optomechanics

“…The trapping potential introduces a temporal modulation which introduces non-stationary components in the PSD calculations and makes even the QLT much more complicated. The QLT theory was developed in [30,31] but there was only compared with stochastics in thermal regimes. Further details are also also in the Supplementary Information.…”