Two-membrane cavity optomechanics: non-linear dynamics

Abstract

We study the non-linear dynamics of a multimode optomechanical system constituted of a driven high-finesse Fabry–Pérot cavity containing two vibrating dielectric membranes. The analytical study allows to derive a full and consistent description of the displacement detection by a probe beam in the non-linear regime, enabling the faithful detection of membrane displacements well above the usual sensing limit corresponding to the cavity linewidth. In the weak driving regime where the system is in a pre-synchronized situation, the unexcited oscillator has a small, synchronized component at the frequency of the excited one; both large and small amplitude resonator motions are transduced in a nontrivial way by the non-linear response of the optical probe beam. We find perfect agreement between the experimental results, the numerical simulations, and an analytical approach based on slowly-varying amplitude equations.

Two-Membrane Cavity Optomechanics: Linear and Non-Linear Dynamics

“…For ξ 1, the sideband output field has a spectral amplitude linear with ξ, and it is possible to perform a direct measurement of the position coordinate q 1 ; for ξ ≥ 1 we should consider a correction factor because linearity is no more valid. In our case, the theoretical correction factor is N 1 0.70, which corresponds to an expected observable stationary limit cycle amplitude of q ob 1 183 pm (see Figure 7) [23]. Because of the oscillating behaviour of the Bessel functions, Equation ( 47) considering sufficiently large pump power, may have more than one solution [oblique black-dashed line in Figure 6b], which corresponds to the multistability phenomenon theoretically analysed, and then verified in references [30,32].…”

“…The equation is not satisfied because the pump power is below the threshold for finding a root. (b) The intersection of left and right side of Equation (47) for the parameters of reference [23], are reported dashed-orange and solid-blue curves, respectively, determines the steady-state value of ξ st 1 . We find ξ st 1 = 1.054, and an effective steady-state amplitude q st 1 = 2|A 1 |x zpf = 263.0 pm.…”

“…However, 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]. A fixed amplitude limit cycle is established, with a free running oscillation phase, which may lock to external forces or to other optomechanical oscillators [35], leading to synchronization (see references [12,15,16,22,[36][37][38][39][40][41][42] for theoretical characterizations, and references [17][18][19][20][21]24,[43][44][45][46] for experimental demonstrations in optomechanical and electromechanical devices).…”

“…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]. 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 [8,10,23].…”

“…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]. 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 [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].…”