Multiphonon quantum dynamics in cavity optomechanical systems

The multiphonon quantum dynamics in laser-pumped cavity optomechanical samples containing a vibrating mirror is investigated. Especially, we focus on dispersive interaction regimes where the externally applied coherent field frequency detuning from the optical resonator frequency is not equal to the mirror's oscillating frequency or to its multiples. As a result, for moderately strong couplings among the involved subsystems, the quantum dynamics of this complex system is described by multiphonon absorption or emission processes, respectively. Particularly, we demonstrate efficient ways to monitor the phonon quantum dynamics via photon detection. The possibility to extract the relevant sample parameters, for instance, the coupling strength between the mechanical mirror and the electromagnetic field, is also discussed.

Figure 1

(a) The steady-state optical cavity mean photon number $\langle n\rangle \equiv \langle a^{†}a\rangle$ as well as (b) the corresponding mechanical resonator mean phonon number $\langle m\rangle \equiv \langle b^{†}b\rangle$ as a function of $\mathrm{\Delta }/\omega$. Here, $\chi =0.1, \epsilon /\omega =0.02, {\kappa }_a/\omega =2\times {10}^{-3}$, and ${\kappa }_b/\omega =2\times {10}^{-5}$, and only single-phonon processes were included. Also, $\overline{n}=1$ for solid lines, while $\overline{n}=0$ for short-dashed lines, respectively.

Figure 2

The steady-state second-order correlation function for (a) photons, $g_a^{\left(2\right)}\left(0\right)$, and (b) for phonons, $g_b^{\left(2\right)}\left(0\right)$, as a function of $\mathrm{\Delta }/\omega$. The solid lines are for $\overline{n}=1$, while the short-dashed one for $\overline{n}=0$, respectively. Other parameters are as in Fig. 1.

Figure 3

The steady-state behaviors of (a) the mean phonon number $\langle m\rangle$ as well as (b) the second-order phonon-phonon correlation function $g_b^{\left(2\right)}\left(0\right)$ as a function of $\chi =g/\omega$. The dashed blue line is plotted for a single-phonon process whereas the green solid one is for three-phonon processes, respectively. Here, $\mathrm{\Delta }/\omega =0.09$ and $\overline{n}=1$ while other parameters are as in Fig. 1.