Quantum correlations in molecular cavity optomechanics

TL;DR

This work develops a comprehensive theoretical framework for generating and controlling quantum correlations in a double-cavity molecular optomechanical system, leveraging collective molecular vibrations to mediate inter-cavity entanglement, steering, and Gaussian discord. Through linearized quantum Langevin dynamics and covariance-matrix formalism, it quantifies entanglement via logarithmic negativity, steering via directional determinants, and discord via Gaussian formulations, under detuning, coupling, and phase conditions. A key finding is that phase control with $ heta = m\pi$ enhances all three correlations, while the molecular mode enables robust, room-temperature-like operation by effectively cooling the vibrational mode and enabling mediated quantum connectivity; entanglement persists up to temperatures near $1000\,\mathrm{K}$. The results also reveal distinct detuning regimes for maximal correlations, a hierarchy of discord and entanglement distributions, and a notable resilience to cavity loss, underscoring McOM as a promising platform for scalable quantum information processing and networks.

Abstract

Quantum correlations are interesting resources for modern quantum technologies such as quantum information processing, quantum communication, quantum teleportation, and quantum computation tasks. However, engineering these quantum states turns to be not an easy task. Here, we unveil a theoretical framework for generating and controlling quantum correlations within a double-cavity molecular optomechanical (McOM) system. Our approach leverages strong interactions between confined optical fields and collective molecular vibrations, creating a versatile environment for exploring robust quantum correlations. Our findings reveal that by judiciously optimizing the coupling strength between the cavity field and the molecular collective mode leads to significant enhancement of entanglement, quantum steering, and quantum discord. We demonstrate that cavity-cavity quantum correlations can be effectively mediated by the molecular collective mode, enabling a unique pathway for inter-cavity quantum connectivity. Moreover, the quantum entanglement generated in our McOM system exhibits robustness against thermal noise, persisting up to temperatures approaching $1000 K$. This strong resilience, qualifies molecular optomechanics as a compelling architecture for scalable, room-temperature quantum information processing and the practical realization of quantum networks. Additionally, the phase-dependent behaviour of quantum discord provides a fundamental basis for developing ultra-sensitive gas sensors, with potential applications in environmental monitoring, medical diagnostics, and industrial safety.

Figures (11)

• Figure 1: (a) A molecular optomechanical configuration featuring an ensemble of $N$ molecules strategically placed within two coupled cavities, whose modes are labelled $a$ and $c$. The cavity mode $a$ ($c$) is optomechanically (bilinearly) coupled to the molecular ensemble through the driving filed $\mathcal{E}_a (\mathcal{E}_c$). (b) An interaction picture highlighting the optomechanical coupling ($g_a, g_c$) between the cavity modes ($a, c$) and the collective molecular vibrational mode ($B$).
• Figure 2: (a) Density plot of bipartite entanglement for photon-photon modes ($E_{ca}$) for $\kappa_j/\omega_m = 0.003$, and $G_j/\omega_m = 0.004$. (b) Entanglement for vibration-photon modes ($E_{Ba}$) for $\tilde{\Delta}_a/\omega_m = 0.95$, $G_j/\omega_m =0.004$, $\kappa_c/\omega_m = 0.003$, $\kappa_a = \kappa_c$ and ${\Delta}_c/\omega_m = -0.4$. (c) Entanglement for vibration-photon modes ($E_{Bc}$) for $\kappa_j/\omega_m = 0.05$, and $G_j/\omega_m = 0.005$ as a function of phase $\theta/\pi$ and $J/\omega_m$. Common parameters for all subplots: $\mathcal{E}/\omega_m = 16$, $\gamma_m/\omega_m = 0.005$, $g_c/\omega_m = 3.3e-6$, $g_a/\omega_m = 2.66e-6$, $\kappa_c/\omega_m = 0.0166$, $\kappa_a = \kappa_c$, $\tilde{\Delta}_a/\omega_m = 1$ and ${\Delta}_c/\omega_m = -1$, and $T = 210K$.
• Figure 3: (a) Density plot of one-way steering $\mathcal{G}_{c\to a}$ for $\kappa_j/\omega_m = 0.003$, and $G_j/\omega_m = 0.003$. (b) $\mathcal{G}_{B\to a}$ for $\tilde{\Delta}_a/\omega_m = 1.5$, ${\Delta}_c/\omega_m = -0.5$, $\kappa_j/\omega_m = 0.005$, and $G_j/\omega_m = 0.005$. (c) $\mathcal{G}_{B\to c}$ for $\tilde{\Delta}_a/\omega_m = 1.5$, ${\Delta}_c/\omega_m = -0.5$, $\kappa_j/\omega_m = 0.05$, and $G_j/\omega_m = 0.005$. Common parameters for all subplots: $\mathcal{E}/\omega_m = 16$, $\gamma_m/\omega_m = 0.005$, $g_c/\omega_m = 3.3e-6$, $g_a/\omega_m = 2.66e-6$, $N = e6$, $\kappa_c/\omega_m = 0.0166$, $\kappa_a = \kappa_c$, and $T = 210K$.
• Figure 4: (a) Density plot of quantum discord $\mathcal{D}_{ca}$ between cavity modes $a$ and $c$ for $\kappa_j/\omega_m = 0.05$, and $G_j/\omega_m = 0.005$. (b) Quantum discord $\mathcal{D}_{Ba}$ between the molecular collective mode $B$ and cavity mode $a$ for $\kappa_j/\omega_m = 0.05$, and $G_j/\omega_m = 0.005$. (c) Quantum discord $\mathcal{D}_{Bc}$ between the molecular collective mode $B$ and cavity mode $c$ for $\kappa_j/\omega_m = 0.05$, and $G_j/\omega_m = 0.005$, as a function of phase $\theta/\pi$ and $J/\omega_m$. Common parameters for all subplots: $\mathcal{E}/\omega_m = 16$, $\gamma_m/\omega_m = 0.005$, $g_c/\omega_m = 3.3e-6$, $g_a/\omega_m = 2.66e-6$, $N = e6$, $\tilde{\Delta}_a/\omega_m = 1$ and ${\Delta}_c/\omega_m = -1$, $\tilde{\Delta}_a/\omega_m = 1$ and ${\Delta}_c/\omega_m = -1$, and $T = 210K$.
• Figure 5: (a) Density plot of bipartite entanglement for photon-photon modes ($E_{ca}$) with $J/\omega_m = 0.0$, $\kappa_j/\omega_m = 0.003$ and $G_j/\omega_m = 0.003$. (b) Entanglement for vibration-photon modes ($E_{Ba}$) with $J/\omega_m = 0.0$, $\kappa_j/\omega_m = 0.05$ and $G_j/\omega_m = 0.005$. (c) Entanglement for vibration-photon modes ($E_{Bc}$) for $J/\omega_m = 0.0$, as a function of normalized detunings $\tilde{\Delta}_a/\omega_m$ and ${\Delta}_c/\omega_m$. (d) Density plot of bipartite entanglement for photon-photon modes ($E_{ca}$) with $J/\omega_m = 0.1$, $\kappa_j/\omega_m = 0.003$ and $G_j/\omega_m = 0.003$. (e) Entanglement for vibration-photon modes ($E_{Ba}$) with $J/\omega_m = 0.1$, $\kappa_j/\omega_m = 0.05$ and $G_j/\omega_m = 0.005$. (f) Entanglement for vibration-photon modes ($E_{Bc}$) for $J/\omega_m = 0.1$, as a function of normalized detunings $\tilde{\Delta}_a/\omega_m$ and ${\Delta}_c/\omega_m$. Common parameters for all subplots: $\mathcal{E}/\omega_m = 16$, $\gamma_m/\omega_m = 0.005$, $g_c/\omega_m = 3.3e-6$, $g_a/\omega_m = 2.66e-6$, $N = e6$, $\theta=\pi$, and $T = 210K$.