Fig. 4: Frequency stability of the optomechanical laser.
From: Active optomechanics
a Numerically simulated spectrum \({S}_{y}(\omega )\) of the signal \(y(t)={\omega }_{{{\rm{L}}}}(t)/{\omega }_{{{\rm{A}}}}\) with the perturbed laser frequency \({\omega }_{{{\rm{L}}}}(t)\) and the atomic transition frequency \({\omega }_{{{\rm{A}}}}\). The optical cavity has a low \(Q\) factor of \({10}^{5}\). For the optomechanical laser, the optical cavity has a movable mirror. For the corresponding conventional laser, the positions of both cavity mirrors are fixed. In addition to the photon radiation pressure, an extra environmental noise force \({F}_{{{{{{\rm{xtra}}}}}}}(t)\) is exerted upon the mechanical oscillator whose oscillation frequency \(\Omega\) is chosen as the frequency unit. The pink-colored noise force \({F}_{{{{{{\rm{xtra}}}}}}}(t)\) is chosen as \({F}_{{{{{{\rm{xtra}}}}}}}(t)=200\hslash \xi \cdot F(t)\) with the frequency pull parameter \(\xi\). The spectral density of the noise function \(F(t)\) is given by \(1/\omega\). The pump rate \(R\) is set at \({10}^{3}{R}_{0}\) with the minimum pump threshold \({R}_{0}\) and the atom–cavity detuning is chosen as \(\Delta =-\kappa\) with the cavity loss rate \(\kappa\). The spectra \({S}_{y}(\omega )\) under different conditions are plotted. Two spectral peaks are presented in \({S}_{y}(\omega )\) at around \(\omega =2\mu\) and \(\omega =\Omega\) with the atom–cavity coupling strength \(\mu\) and the mechanical oscillation frequency \(\Omega\). The corresponding Allan deviations \({\sigma }_{y}(\tau )\) are shown in b. c, d Spectra \({S}_{y}(\omega )\) and Allan deviations \({\sigma }_{y}(\tau )\) with a high \(Q\) factor of \({10}^{7}\) under different conditions. For comparison, the shot-noise-limited spectra and Allan deviations have been inserted.
