Amplifying Two-Mode Squeezing in Nanomechanical Resonators

TL;DR

The paper presents a scheme to surpass the conventional $3$ dB limit on two-mode squeezing in a nanomechanical system by combining two-tone driving with a nondegenerate optical parametric amplifier inside a doubly resonant optomechanical cavity. Ground-state cooling from red-detuned drives and displacement squeezing from blue-detuned drives, together with intracavity NDOPA squeezing, enable strong two-mode squeezing of mechanical resonators, characterized via a Gaussian steady state analyzed through the covariance matrix and Lyapunov equation. The authors show parameter regimes where squeezing exceeds the standard limit (up to about $5.7$ dB under certain conditions) and discuss robustness against thermal noise, along with experimental feasibility using current optomechanical technologies and homodyne detection. They also explore entanglement transfer and propose symplectic eigenvalues as a robust alternative metric for squeezing, outlining potential quantum sensing and information processing applications and suggesting future extensions to quantum networks and varied environments.

Abstract

Quantum squeezing plays a crucial role in enhancing the precision of quantum metrology and improving the efficiency of quantum information processing protocols. We thus propose a scheme to amplify two-mode squeezing in nanomechanical resonators, harnessing parametric amplification and two-tone laser controls. The red-detuned laser drives facilitate the cooling of the nanomechanical resonators down to their ground state and allow optimal quantum state transfer in the weak-coupling, resolved sideband regime. In particular, the competing blue-detuned lasers in the driving pairs induce displacement squeezing in mechanical resonators. Thus, the quantum state transfer of the squeezing in nanomechanical resonators and the intracavity correlated photons of the parametric amplifier significantly enhance the two-mode mechanical squeezing. Notably, increasing the coupling strength of the red detuned laser and the ratio of blue-to-red detuned laser dramatically amplifies the two-mode mechanical squeezing under realistic experiment parameters of a typical optomechanical system. Our findings reveal that the proposed cooperative mechanism effectively enhances the level of two-mode mechanical squeezing with a considerable improvement and demonstrates exceptional resilience to thermal noise.

Figures (9)

• Figure 1: The schematic model of the system, a doubly resonant hybrid optomechanical cavity, comprises a pumped NDOPA and two pairs of two-tone laser drives. Further details are provided in the main text
• Figure 2: Density plots of the degree of two-mode quadrature squeezing of mechanical modes $S^{2}_m$(dB) as a function of normalized parametric coupling coefficient $(\Lambda/\kappa)$ versus phase $(\phi/\pi)$ of NDOPA for (a) $P_{_+} / P_{_-} =0$, and (b) $P_{_+} / P_{_-} =0.1$ corresponding to quadrature squeezing $<(\delta x_{d})^2>$ when $P_{_-}=10$ nW, and $T=10$ mK. The other parameters are found in the main text.
• Figure 3: Plots of the degree of (a) two-mode optical squeezing $S^{2}_c$(dB) corresponding to quadrature squeezing $<(\delta y_{c})^2>$ and (b) two-mode mechanical squeezing $S^{2}_m$(dB) corresponding to quadrature squeezing $<(\delta x_{d})^2>$ versus the ratio of blue-to-red detuning powers $(P_{_+} / P_{_-})$ for the different parametric phases of NDOPA $\phi$ when the red-detuned laser drive $P_{_-}=3$ nW, and parametric coupling coefficient of NDOPA $\Lambda=0.49\kappa$. The other parameters are the same as Fig. \ref{['fig:2']}
• Figure 4: Plots of the degree of two-mode squeezing in (a) optical modes $S^{2}_c$(dB) and (b) mechanical modes $S^{2}_m$(dB) versus the ratio of blue-to-red detuning powers $(P_{_+} / P_{_-})$ for different parametric coupling coefficient $\Lambda$ of NDOPA when parametric phase of NDOPA $\phi=0$ and the red-detuned laser drive $P_{_-}=3$ nW. The other parameters are the same as Fig. \ref{['fig:2']}.
• Figure 5: Density plots of the degree of two-mode mechanical squeezing $S^{2}_m$(dB) as a function of the the normalized red-tone driving strength $G_{_-}$ versus the blue-tone driving strength $G_{_+}$ (normalized by red-tone driving strength $G_{_-}$) for (a) $\Lambda=0$, and (b) $\Lambda=0.49 \kappa$ when $\phi=0$. The other parameters are the same as Fig. \ref{['fig:2']}.