Tunable two-phonon higher-order sideband amplification in a quadratically coupled optomechanical system

Abstract

We propose an efficient scheme for the controllable amplification of two-phonon higher-order sidebands in a quadratically coupled optomechanical system. In this scheme, a strong control field and a weak probe pulse are injected into the cavity, and the membrane located at the middle position of the cavity is driven resonantly by a weak coherent mechanical pump. Beyond the conventional linearized approximation, we derive analytical expressions for the output transmission of probe pulse and the amplitude of second-order sideband by adding the nonlinear coefficients into the Heisenberg-Langevin formalism. Using experimentally achievable parameters, we identify the conditions under which the mechanical pump and the frequency detuning of control field allow us to modify the transmission of probe pulse and improve the amplitude of two-phonon higher-order sideband generation beyond what is achievable in absence of the mechanical pump. Furthermore, we also find that the higher-order sideband generation depends sensitively on the phase of mechanical pump when the control field becomes strong. The present proposal offers a practical opportunity to design chip-scale optical communications and optical frequency combs.

Higher-Order Interactions in Quantum Optomechanics: Analysis of Quadratic Terms

“…It is easily seen that in the regime of large optical frequency ω >> Ω, we get β ≈ 0 and the non-standard term vanishes. This is what has actually been probed in nearly all experiments on quadratic optomechanical interactions so far [18][19][20][21][22][23][24]36]. The large mechanical frequency regime of standard quadratic interactions has been however recently probed [25] and it has been suggested that the roles of optical and mechanical parts are expected to interchange without consideration of the non-standard quadratic effect.…”

“…Higher-order operators have been already used in analysis of nonlinear standard optomechanics [35], where its application has uncovered effects known as sideband inequivalence, quantities such as coherent phonon population, as well as corrections to the optomechanical spring effect, zero-point field optomechanical interactions, and a minimal basis with the highest-order which allows exact integration of optomechanical Hamiltonian subject to multiplicative noise input. Also, it has been independently used [36] for investigation of quadratic effects. But this method has not been verified yet for non-standard quadratic optomechanics, which is the central topic of this study.…”

Optomechanically induced transparency, amplification, and Fano resonance in a multimode optomechanical system with quadratic coupling

“…In experiments, mechanical driving field has been exploited to realize electro-optomechanically induced transparency [78], cascaded optical transparency [79], phase-sensitive parametric amplifier [80], injection locking [81], and virtual exceptional points [82]. Recently, optomechanically induced opacity and amplification of two-phonon higher-order sidebands have been studied in a quadratically coupled optomechanical system with mechanical driving [83,84]. It is pointed out that mechanical driving in the quadratically coupled system can be realized by parametrically modulating the spring constant of the membrane at twice the membrane's resonance frequency with an integrated electrical interface [80-83, 85, 86], which generates the mechanical coherence via the two-phonon process.…”

Enhancement of optomechanically induced sum sidebands using parametric interactions

“…If the probe field is much weaker than the control field, one can use the perturbation method to get the prominent feature of optomechanically induced transparency. Recently, nonlinear optomechanical dynamics have emerged as an interesting frontier in cavity optomechanics [27][28][29][30]. This emerging subject leads to a variety of high-order OMIT effects due to the intrinsic nonlinear optomechanical interactions [31,32], such as photon-phonon polariton pairs [33] and sideband generations [27,34,35].…”