Robust stationary mechanical squeezing in a kicked quadratic optomechanical system

We propose a scheme for the generation of a robust stationary squeezed state of a mechanical resonator in a quadratically coupled optomechanical system, driven by a pulsed laser. The intracavity photon number presents periodic intense peaks suddenly stiffening the effective harmonic potential felt by the mechanical resonator. These “optical spring kicks” tend to squeeze the resonator position, and due to the interplay with fluctuation-dissipation processes one can generate a stationary state with more than 10 dB of squeezing in a realistic scenario, even starting from moderately “precooled” initial thermal states.

Figure 1

(a) The minimum quadrature variance ${\sigma }_{\min }$ [in dB with respect to the vacuum level, i.e., $10{log}_{10}\left(2{\sigma }_{\text{min}}\right)$] versus $n\tau$ for $\overline{n}=10$. The insets show a fine-grained view of the stroboscopic dynamics at different times. (b) Purity (and in the insets, von Neumann entropy $S$ and effective occupancy $n_{\mathrm{eff}}$) of the MR state versus $n\tau$. The other parameters are ${\omega }_m=0.5\times {10}^6$ s${}^{-1}$, ${\gamma }_m={10}^2$ s${}^{-1}$, $\tau ={10}^{-7}$ s, and $\theta =10$.

Figure 2

The same as in Fig. 1, except that $\overline{n}=200$. One still gets squeezing, but the steady state is far from being pure.

Figure 3

The minimum quadrature variance ${\sigma }_{\min }$ (in dB as in Fig. 1), and the purity $P$ (in the inset) versus $n\tau$ in the case when $\theta$ randomly fluctuates from kick to kick according to a Gaussian distribution centered around $\theta =10$ and with variance 0.001. The other parameters are as in Fig. 1. The blue solid line refers to a single experimental run, while the red dotted line refers to the average over 100 trajectories.