Dissipative versus dispersive coupling in quantum optomechanics: Squeezing ability and stability

The generation of squeezed light and the optomechanical instability of a dissipative type of opto-mechanical coupling are theoretically addressed for a cavity with the input mirror serving as a mechanical oscillator or for an equivalent system. The problem is treated analytically for the case of resonance excitation or small detunings, mainly focusing on the bad-cavity limit. A qualitative difference between the dissipative and purely dispersive coupling is reported. In particular, it is shown that, for the purely dissipative coupling in the bad-cavity regime, the backaction is strongly reduced and the squeezing ability of the system is strongly suppressed, in contrast to the case of purely dispersive coupling. It is also shown that, for small detunings, stability diagrams for the cases of the purely dispersive and dissipative couplings are qualitatively identical to within the change of the sign of detuning. The results obtained are compared with those from the recent theoretical publications.

Figure 1

Stability diagram for a one-sided cavity with the input mirror serving as the mechanical oscillator, or an equivalent system, according to Kilda and Nunnenkamp [7]. Dark areas show instability intervals in terms of the normalized detuning $\mathrm{\Delta }/{\omega }_m$ ($\mathrm{\Delta }={\omega }_L-{\omega }_c$ - detuning, ${\omega }_m$- mechanical frequency). (a) Purely dissipative coupling. (b) Purely dispersive coupling. In the notations of our paper, the model settings are $G_{\omega }=1.2\gamma$, $G_{\gamma }=-0.3\gamma$, ${\gamma }_m/{\omega }_m={10}^{-5}$, and $\gamma /{\omega }_m=0.3$; $\gamma$, decay rate of the cavity; ${\gamma }_m$, mechanical decay rate.