Improving the cooling of a mechanical oscillator in a dissipative optomechanical system with an optical parametric amplifier

The ground-state cooling of a macroscopic mechanical oscillator is a crucial prerequisite for implementing the quantum manipulation of the mechanical oscillator. Here we show that a degenerate optical parametric amplifier (OPA) can significantly improve the cooling of the mechanical membrane in the purely dissipative coupling system in the unresolved sideband regime. In the presence of the OPA with a parametric phase $\pi /2$, the mechanical membrane can be cooled from room temperature 293 K to 10 mK, a factor of 112 lower than that in the absence of the OPA. If the mechanical oscillator is precooled to 0.1 K, the mechanical membrane can be cooled into the microkelvin regime.

Figure 1

Sketch of the Michelson-Sagnac interferometer with a movable membrane located at the middle point between the two mirrors $M_2$ and $M_3$ (from [20]). An OPA is placed between the two mirrors $M_2$ and $M_3$ and the pump of the OPA is not shown. $M_1$, $M_2$, $M_3$ are the fixed perfect reflecting mirrors, BS: the fixed beam splitter, M: the movable membrane.

Figure 2

The normalized effective resonance frequency ${\omega }_{\text{eff}}\left(\omega \right)/{\omega }_m$ and the normalized effective damping rate ${\gamma }_{\text{eff}}\left(\omega \right)/{\gamma }_m$ of the membrane as a function of the normalized frequency $\omega /\kappa$ for different parametric gains $G=0,0.2\kappa ,0.3\kappa ,0.4\kappa$ when the cavity detuning $\mathrm{\Delta }=-0.27\kappa$ and the parametric phase $\theta =0$. The black solid curve, the blue dashed curve, the green dotdashed curve, the red dotted curve correspond to $G=0,0.2\kappa ,0.3\kappa ,0.4\kappa$, respectively.

Figure 3

The normalized effective resonance frequency ${\omega }_{\text{eff}}\left(0\right)/{\omega }_m$ and the normalized effective damping rate ${\gamma }_{\text{eff}}\left(0\right)/{\gamma }_m$ of the membrane as a function of the parametric phase $\theta /\pi$ for different parametric gains $G=0.2\kappa ,0.3\kappa ,0.4\kappa$ when the cavity detuning $\mathrm{\Delta }=-0.27\kappa$. The blue dashed curve, the green dotdashed curve, the red dotted curve correspond to $G=0.2\kappa ,0.3\kappa ,0.4\kappa$, respectively.

Figure 4

The effective temperature $T_{\text{eff}}$ (K) of the membrane as a function of the normalized negative cavity detuning $\mathrm{\Delta }/\kappa$ for different parametric gains $G=0,0.2\kappa ,0.3\kappa ,0.4\kappa$ when the parametric phase $\theta =0$. The black solid curve, the blue dashed curve, the green dotdashed curve, the red dotted curve correspond to $G=0,0.2\kappa ,0.3\kappa ,0.4\kappa$, respectively.

Figure 5

The effective temperature $T_{\text{eff}}$ (K) of the membrane as a function of the parametric phase $\theta /\pi$ for different parametric gains and different negative cavity detunings. The blue dashed curve is for $G=0.2\kappa$ and $\mathrm{\Delta }=-0.35\kappa$, the green dot-dashed curve is for $G=0.3\kappa$ and $\mathrm{\Delta }=-0.33\kappa$, the red dotted curve is for $G=0.4\kappa$ and $\mathrm{\Delta }=-0.27\kappa$.

Figure 6

The effective temperature $T_{\text{eff}}$ (mK) of the membrane as a function of the normalized negative cavity detuning $\mathrm{\Delta }/\kappa$ for different parametric gains $G=0,0.2\kappa ,0.3\kappa ,0.4\kappa$ when the parametric phase $\theta =\pi /2$. The black solid curve, the blue dashed curve, the green dot-dashed curve, the red dotted curve correspond to $G=0,0.2\kappa ,0.3\kappa ,0.4\kappa$, respectively.