Quantum entanglement enhanced via dark mode control in molecular optomechanics

Abstract

Quantum entanglement is an interesting resource for modern quantum technologies, where generating multiple quantum entanglement is highly required. However, entanglement engineering between multiple modes is strongly suppressed by dark mode effect. Here, we proposed a scheme based on molecular cavity optomechanical structure that enhances quantum bipartite and tripartite entanglement via dark mode breaking. Our proposal consists of an optical cavity that hosts two molecular ensembles which are coupled through an intermolecular coupling. A vibrational hopping rate $J_m$ captures the intermolecular coupling that is phase modulated via the synthetic gauge field method. The breaking of the dark mode is controlled by tuning both the intermolecular coupling and its modulation phase. By adjusting these parameters in our proposal, we can flexibly switch between the Dark Mode Unbroken (DMU) and the Dark Mode Broken (DMB) regimes. We find that in the dark-mode-unbroken regime, the amount of the generated bipartite and tripartite entanglement is significantly low or is suppressed. In contrast, in the dark-mode-broken regime, the entanglement is greatly enhanced,i.e., up to twofold enhancement. Moreover, the generated entanglement is more resilient against thermal noise in the dark-mode-broken regime compared to the thermal robustness in the unbroken regime. Therefore, our proposed scheme serves as a benckmark system to improve quantum correlations engineering, and to generate noise-tolerant quantum resources for applications in numerous modern quantum technologies.

Figures (10)

• Figure 1: Sketch of our benckmark system. (a) A molecular cavity optomechanical system, illustrating the interaction between the intracavity mode and the ensemble of $N$ identical molecules with a vibrational frequency $\omega_{m}$. The vibrational mode is depicted as two masses connected by a spring, emphasizing the coupling between molecular vibrations. (b) Diagram illustrating the interactions between the subsystems, the collective vibrational modes of the molecules and the intracavity mode.
• Figure 2: (a) Coupling strength $G_-$ versus the coupling ratio $G_1/G_2$ and the vibration frequency ratio $\omega_1/\omega_2$ for $J_m=0$. (b) Polar representation for both $\tilde{G}_\pm$ for $G_1=G_2=0.1\omega_m$, and $J_m=0.1\omega_m$. The other used parameters are $\omega_1/2\pi=\omega_2/2\pi= 30THz$, $\omega_1=\omega_2= 30THz=\omega_m$, $\kappa=1/3\omega_m$, $\gamma=10^{-4}\omega_m$, $g_v=10^{-4}\omega_m$, and $T=312 K$.
• Figure 3: Logarithmic negativity (a) $E^N_{aB_2}$ vs the optomechanical coupling strength $G_j/\omega_m$ and the scaled detuning $\tilde{\Delta}_a/\omega_m$, when $J_m/\omega_m=0$ and $\theta=0$, and (b) $E^N_{aB_2}$ vs the optomechanical coupling strength $G_j/\omega_m$ and the coupling constant $J_m/\omega_m$, when $\tilde{\Delta}_a/\omega_m=0.7$ and $\theta=\pi/2$. The other used parameters are $\omega_1/2\pi=\omega_2/2\pi= 30THz$, $\omega_1=\omega_2= 30THz=\omega_m$, $\kappa=1/3\omega_m$, $\gamma=10^{-4}\omega_m$, $g_v=10^{-3}\omega_m$, $T=312 K$, M=0 and N=100.
• Figure 4: (a) Density plot of bipartite $E_{B_1B_2}^N$ vs the scaled detuning $\tilde{\Delta}_a/\omega_m$ and the optomechanical coupling strength $G_j/\omega_m$ when $J_m/\omega_m=0.0$, N=100, $\kappa/\omega_m=1/3$, and $\theta=0$. (b) Density plot of bipartite, $E_{B_1B_2}^N$ vs the scaled detuning $\tilde{\Delta}_a/\omega_m$ and the optomechanical coupling strength $G_j/\omega_m$ when $J_m/\omega_m=0.02$, N=100, $\kappa/\omega_m=1/3$, and $\theta=\pi/2$. (c) Density plot of bipartite entanglement $E_{B_1B_2}^N$ vs the optomechanical coupling strength $G_j/\omega_m$ and couplng constant $J_m/\omega_m$, when $\tilde{\Delta}_a/\omega_m=1.5$, N=100, $\kappa/\omega_m=1/3$, and $\theta=\pi/2$. (d) Bipartite entanglement $E_{B_1B_2}^N$ vs the optomechanical coupling strength $G_j/\omega_m$ for different values of $J_m/\omega_m$, when $\tilde{\Delta}_a/\omega_m=1.5$, N=100, $\kappa/\omega_m=1/3$, and $\theta=\pi/2$. Here, $\gamma_m/\omega_m$=0.3, M=N/2, and $n_{th}=0.001$.
• Figure 5: (a) Density plot of bipartite entanglement, $E_{B_1B_2}^N$ vs the distribution number of collective mode, M and the scaled decay rate $\kappa/\omega_m$ when $J_m/\omega_m=0$ and $\theta=0$. (b) Density plot of bipartite entanglement, $E_{B_1B_2}^N$ vs the total number of molecules, N, and scaled decay rate, $\kappa/\omega_m$ when M=N/2, $J_m/\omega_m=0$ and $\theta=0$. (c) Density plot of bipartite entanglement, $E_{B_1B_2}^N$ vs the distribution number of collective mode, M and the scaled decay rate $\kappa/\omega_m$ when $J_m/\omega_m=0.02$ and $\theta=\pi/2$. (d) Density plot of bipartite entanglement, $E_{B_1B_2}^N$ vs the total number of molecules, N, and the scaled decay rate, $\kappa/\omega_m$ when M=N/2, $J_m/\omega_m=0.02$, $G_j/\omega_m$=0.2 and $\theta=\pi/2$. Common parameters are chosen as, $\gamma_m/\omega_m$=0.3, $\tilde{\Delta}_a/\omega_m$=1.5, N=100; M=50, and $T= 210$ K.