Photon Blockade Effect in Optomechanical Systems

We analyze the photon statistics of a weakly driven optomechanical system and discuss the effect of photon blockade under single-photon strong coupling conditions. We present an intuitive interpretation of this effect in terms of displaced oscillator states and derive analytic expressions for the cavity excitation spectrum and the two-photon correlation function $g^{(2)}(0)$. Our results predict the appearance of nonclassical photon correlations in the combined strong coupling and sideband resolved regime and provide a first detailed understanding of photon-photon interactions in strong coupling optomechanics.

Figure 1

Setup for the detection of photon blockade effects in OMS. The OMS is weakly excited by a coherent laser field, and the statistics of the output field is inferred from photon coincidence measurements.

Figure 2

Level diagram of the isolated, single-mode OMS where $\eta =g_0/{\omega }_m$ and ${\Delta }_g=g_0^2/{\omega }_m$. For a photon number state $|n_c⟩$, the radiation pressure displaces the resonator equilibrium $\sim n_c\times \eta$. As a result, the energy of the photon states is lowered by $n_c^2\times {\Delta }_g$ and leads to different resonance conditions for the first and the second laser photons exciting the cavity.

Figure 3

Cavity excitation spectrum $S({\Delta }_0)$ for different values of the coupling parameter $\eta =g_0/{\omega }_m$ and (a) $\kappa /{\omega }_m=4$ and (b) $\kappa /{\omega }_m=0.1$. In (b) the ZPL indicates the position of the phonon number conserving transition. In both plots, $T=0$ and $Q=150$.

Figure 4

(a) Dependence of $g^{(2)}(0)$ on the bare laser detuning ${\Delta }_0$ for $g_0/{\omega }_m=0.5$ and $\kappa /{\omega }_m=0.15$. The dashed line indicates the approximate result given in Eq. (13). (b) The minimum of $g^{(2)}(0)$ with respect to ${\Delta }_0$ is plotted for different values of $\kappa$ and $g_0$. In both plots, $T=0$ and $Q\to \infty$.