Optical Entanglement Facilitated by Opto-Mechanical Cooling

TL;DR

This work tackles the challenge of generating continuous-variable entanglement between two optical sidebands in a cavity optomechanical system amidst thermal noise. It introduces a three-mode, resolved-sideband cavity with a driven central mode, derives a full quantum Langevin model, and shows that entanglement between $\omega_\pm=\omega_0\pm\omega_m$ can be sustained when optical cooling reduces the mechanical thermal occupation and a sufficient asymmetry $G_+-G_-$ is achieved. The entanglement is detected via optimized quadrature combinations and, in practice, through synodyne detection; the bandwidth is governed by the optical decay $\gamma_0$ and can be broad while maintaining significant entanglement. The results point to robust, ambient-condition CV entanglement with potential applications in quantum communication, sensing, and hybrid quantum networks leveraging mechanical interfaces.

Abstract

Optomechanical generation of entangled optical beams is usually hindered by thermal noise. We present a theoretical study of low frequency entanglement generation between two optical harmonics emitted from a cavity optomechanical system operating in the resolved-sideband regime. The system comprises three nearly equidistant optical modes in a high-finesse cavity, with the central mode coherently driven. This configuration enables radiation-pressure interactions that generate strong quantum correlations between the two sideband modes. Remarkably, these correlations persist even at large numbers of thermal quanta if one properly engineers the optical cooling rate of the mechanical mode. Our findings demonstrate the feasibility of robust entanglement under ambient conditions, opening new avenues for hybrid quantum technologies based on mechanical interfaces and continuous-variable quantum information processing.

Figures (4)

• Figure 1: Spectral density $S_{\beta_{a+}}$\ref{['SE']} as function of spectral frequency $\Omega$. Solid black line stands for SQL. Dashed blue line stands for the input power $P_{in}$ and other parameters from Table \ref{['table1']}, dotted red line corresponds to five time larger ($\times 5$) $P_{in}$. Parameters $z_\pm$ are selected in the optimal way, parameter $G=(G_++G_-)/2=2\times 10^6\, \gamma_m$. $S_{\beta_{a+}}$ barely depends on opto-mechanical damping since $|G_+-G_-|< 0.05\,G$.
• Figure 2: Optimal angles $\theta(\Omega)$ and $\phi(\Omega)$ defined in \ref{['phi']} as functions of spectral frequency $\Omega$. The curve correspond to parameters $G=(G_++G_-)/2=2\times 10^6\, \gamma_m$ and $G_+-G_- = 10^3\gamma_m$ (black solid line), $G_+-G_- = 10^4\gamma_m$ (blue dashed line), $G_+-G_- = 10^5\gamma_m$ (red dotted line). Other parameters are taken from Table \ref{['table1']}.
• Figure 3: Spectral density $S_{\beta_{a+}}$ for the parameters listed in Table \ref{['table1']}. Black line represents SQL. Dashed blue line stands for the optimal detection procedure (c.f. Fig. \ref{['fig1']}) at $G/\gamma_m = 2\times 10^6,\ (G_+-G_-)/\gamma_m=10^4$. The spectral density of the noise measured with the synodyne technique, $S_\text{syno}$, given by Eq. \ref{['Ssyno']}, is shown by the dashed-dotted magenta line at the same parameters and the dashed-dotted-dotted green line at $G/\gamma_m = 2\times 10^6,\ (G_+-G_-)/\gamma_m= \gamma_0/\gamma_m =3 \times 10^5$.
• Figure 4: Parameters $G$, $G_+-G_-$, and expectation value of the mechanical phonon number $n_d$ found numerically for various values of the frequency detuning $\Delta_0$ of the pump light from the corresponding optical mode. The system is stable when $|\Delta_0|/\gamma_0< 2\times 10^{-2}$.