Fig. 5: Steady-state solutions of one-atom optomechanical microlaser.
From: Active optomechanics
a Steady-state number \({N}_{{{{{{\rm{photon}}}}}},{{{{{\rm{ss}}}}}}}\) of intracavity photons as a function of the atom–cavity detuning \(\Delta\). For comparison, \({N}_{{{{{{\rm{photon}}}}}},{{{{{\rm{ss}}}}}}}\) of the corresponding one-atom microlaser in the absence of the optomechanical coupling (i.e. zero optomechanical constant \(\xi =0\)) is also plotted. The mechanical oscillation frequency \(\Omega\) is chosen as the frequency unit. The corresponding steady-state number \({N}_{{{{{{\rm{phonon}}}}}},{{{{{\rm{ss}}}}}}}\) of phonons is shown in b. The blue shade denotes the heating regime with \({N}_{{{{{{\rm{phonon}}}}}},{{{{{\rm{ss}}}}}}} \, > \, {n}_{{{{{{\rm{thrm}}}}}}}\) while the pink shade corresponds to the cooling regime with \({N}_{{{{{{\rm{phonon}}}}}},{{{{{\rm{ss}}}}}}} \, < \, {n}_{{{{{{\rm{thrm}}}}}}}\). Here, \({n}_{{{{{{\rm{thrm}}}}}}}\) denotes the average number of thermal quanta. c Distributions of photon and phonon numbers with \(\Delta =\pm \Omega\). d Dependence of the second-order correlation function \({g}_{{{{{{\rm{photon}}}}}}}^{(2)}(\tau )\) of photons at the zero-time delay \(\tau =0\) on the detuning \(\Delta\). The second-order correlation function of the common one-atom microlaser with fixed cavity mirrors (\(\xi =0\)) is also plotted for comparison. e Second-order correlation function \({g}_{{{{{{\rm{phonon}}}}}}}^{(2)}(\tau =0)\) of phonons relative to the second-order correlation function \({g}_{{{{{{\rm{thrm}}}}}}}^{(2)}(\tau =0)\) of the thermal state. f Ratio\(\,{{{{{\rm{\chi }}}}}}\equiv {[{g}_{{{{{{\rm{photon}}}}}}-{{{{{\rm{phonon}}}}}}}^{(2)}(0)]}^{2}/{g}_{{{{{{\rm{photon}}}}}}}^{(1)}(0){g}_{{{{{{\rm{phonon}}}}}}}^{(1)}(0)\) vs. the atom–cavity detuning \(\Delta\). Here, \({g}_{{{{{{\rm{photon}}}}}}-{{{{{\rm{phonon}}}}}}}^{(2)}(0)\) denotes the cross-correlation function between photons and phonons. For all curves, the cavity \(Q\) factor is \({10}^{7}\) and the pump rate is set at \(R \sim 2\pi \times 0.35\) MHz.
