Abstract
In this paper, we review the linear and non-linear dynamics of an optomechanical system made of a two-membrane etalon in a high-finesse Fabry–Pérot cavity. This two-membrane setup has the capacity to modify on demand the single-photon optomechanical coupling, and in the linearized interaction regime to cool simultaneously two mechanical oscillators. It is a promising platform for realizing cavity optomechanics with multiple resonators. In the non-linear regime, an analytical approach based on slowly varying amplitude equations allows us to derive a consistent and full characterization of the non-linear displacement detection, enabling a truthful detection of membrane displacements much above the usual linear sensing limited by the cavity linewidth. Such a high quality system also shows a pre-synchronization regime.
Highlights
We review the linear and non-linear dynamics of an optomechanical system made of a two-membrane etalon in a high-finesse Fabry–Pérot cavity [8,10,23]
When the optical cavity is driven on the red sideband, the linear dynamics of such a system is explored: the optomechanical coupling can be controlled on demand [8,9,25] by a local control of the membrane position along the cavity axis, and multiple oscillators can be simultaneously cooled [8,26], or exploited for photon-mediated coherent interaction and heat transfer between separate resonators [13,14]
We show that when multiple mechanical resonators are detected by the same single probe field simultaneously interacting with all of them, and at least one resonator enters a limit cycle, one has a non-trivial, non-linear dynamics of the system, which has to be properly considered, yielding a highly non-linear calibration of the displacement measurement obtained by means of the output probe readout
Summary
Cooperative effects, enhanced interactions and nontrivial dynamics occur when multiple mechanical resonators are placed within an optical cavity [1,2,3,4,5,6,7,8,9,10]; for example, one can induce and control the coherent exchange of excitations [11,12,13,14], or study self-oscillations and their synchronization in the case of two or more mechanical resonators [12,15,16,17,18,19,20,21,22,23,24]. The radiation pressure interaction is proportional to the photon number and it may have non-linear effects on both the mechanical and optical degrees of freedom which become evident when the mechanical motion is excited [27] by means of laser driving on the blue sideband of the optical cavity Optical backaction in this case counteracts the internal mechanical friction, and when the total effective damping becomes equal to zero, a Hopf bifurcation into a regime of self-induced mechanical oscillations takes place [23,28,29,30,31,32,33,34].
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