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.
Highlights
Cavity optomechanics1, that combines the optical degree of freedom with the mechanical degree of freedom via a radiation-pressure force, has experienced considerable achievements in linear optomechanical coupling regime, such as optomechanically induced transparency (OMIT)2–4, sideband cooling of mechanical resonator5–7 and normal-mode splitting8,9
We assume that the amplitude of probe pulse is proportional to that of control field based on the relationship of εp = 0.05εc
We have performed a theoretical analysis for the controllable amplification of two-phonon higher-order sidebands in the quadratically coupled optomechanical system, where the optical cavity mode couples quadratically rather than linearly to the position of a membrane
Summary
Cavity optomechanics1, that combines the optical degree of freedom with the mechanical degree of freedom via a radiation-pressure force, has experienced considerable achievements in linear optomechanical coupling regime, such as optomechanically induced transparency (OMIT)2–4, sideband cooling of mechanical resonator5–7 and normal-mode splitting8,9. The control field is used to excite the cavity field and support the steady-state value, while the probe pulse and mechanical pump participate in the generation of higher-order sidebands.
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