Strong thermomechanical squeezing in a far-detuned membrane-in-the-middle system

We demonstrate 8.5 dB thermal squeezing of a membrane oscillator using the dynamical backaction effect and electrostatic feedback in an optomechanical membrane-in-the-middle setup. We show that strong squeezing can be obtained even in the far-detuning regime of a sideband-resolved system. By using the dielectrophoretic force of a metallic needle kept in close proximity to the membrane, we implement the one-quadrature active feedback scheme to prevent the divergence of the amplified quadrature and surpass the 3 dB limit of mechanical squeezing. We also discuss different regions of the sideband spectrum where strong squeezing can be obtained. Although the demonstration here is classical, this technique is equally applicable to prepare the mechanical oscillator in a quantum squeezed state.

Figure 1

Experimental membrane-in-the-middle setup. The probe laser is locked to the optical cavity resonance frequency with the Pound-Drever-Hall (PDH) technique and used to record the motion of the membrane, the pump laser applies the parametric force, and the needle generates the parametric electrophoretic force. EOM: electro-optical modulator; OI: optical isolator; PID: proportional-integral differential feedback controller; PBS: polarizing beam splitter; CCD: charge coupled device.

Figure 2

Measurement of the effective damping ${\mathrm{\Gamma }}_{\text{eff}}$ (red) and mechanical frequency shift $\delta {\mathrm{\Omega }}_m$ (blue) depending on the pump laser detuning from the cavity resonance (at $\mathrm{\Delta }=0$). Regions I–III show potential regions to perform spring constant modulation by frequency modulation of the laser. The solid lines represent theoretical fits to the experimental data.

Figure 3

(a) Phase-space trajectory of the mechanical oscillator with an effective temperature $T_{\text{eff}}=120$ K. (b) Squeezed trajectory with gain parameter $g=0.96$ after aligning the squeezing direction with $X_2$ quadrature. (c),(d) Bistability in the $X_1$ quadrature and squeezed distribution in the $X_2$ quadrature for $g>1$, (c) as a function of time and (d) in phase space.

Figure 4

Normalized variances in the $X_1$ and $X_2$ quadratures as a function of the gain parameter $g$. The shaded area highlights the allowed parameter space without any feedback. Diamonds: $h=0$; circles: $h=2.9$ and a maximum of 7.03 dB squeezing; squares: $h=21.5$ and a maximum of 8.5 dB squeezing. $T_{\text{eff}}$ is 120 K for $h=0$ and 2.9, respectively, and 182 K for $h=21.5$. Solid lines represent theoretical fits based on Eq. (4).