Quantum phase synchronisation enhanced via Coulomb interaction in an optomechanical system

TL;DR

The paper tackles how Coulomb coupling between two mechanical resonators influences synchronization in a four-mode optomechanical system. It develops full quantum Langevin dynamics, linearizes around a steady state, and analyzes three synchronization regimes using a covariance-matrix framework. The key finding is that Coulomb coupling significantly enhances quantum phase synchronization, while complete synchronization and φ-synchronization remain largely governed by optical driving. This work provides a practical route to engineer synchronized quantum networks in hybrid optomechanical platforms.

Abstract

In this work, we investigate the dynamics of quantum synchronization in a four-mode optomechanical system, focusing on the influence of the Coulomb interaction between two mechanical resonators. We analyze the effect of the Coulomb coupling on three distinct synchronization regimes, i.e., complete quantum synchronization, $φ$-synchronization, and quantum phase synchronization. Our results show that while the Coulomb interaction plays a pivotal role in significantly enhancing quantum phase synchronization by facilitating energy exchange and phase coherence, it has little impact on complete and $φ$-synchronization. This indicates that amplitude and frequency locking are primarily determined by the optical driving, whereas phase alignment depends critically on inter-resonator coupling. We also demonstrate that the oscillations of the two optical cavities, which are indirectly coupled via the mechanical resonators, can become aligned over time, resulting in classical synchronization. These findings provide a robust mechanism for controlling collective quantum dynamics and offer a foundation for applications in quantum communication, precision sensing, and the development of synchronized quantum networks.

Figures (8)

• Figure 1: A schematic diagram of two cavities coupled via radiation pressure with strength J and driven by the coupling fields of amplitudes $\mathcal{E}_1$ and $\mathcal{E}_2$ respectively. Mechanical resonators situated inside the cavities are coupled via Coulomb interaction.
• Figure 2: Variation of the mean values of the mechanical resonators for different Coulomb coupling strengths. (a) $q_{1s}$ (red solid line) and $q_{2s}$ (blue dashed line) for $\chi_c/\omega_{1}=0.4$, (b) $p_{1s}$ (red solid line) and $p_{2s}$ (blue dashed line) for $\chi_c/\omega_{1}=0.4$, (c) $q_{1s}$ (red solid line) and $q_{2s}$ (blue dashed line) for $\chi_c/\omega_{1}=0.0$, and (d) $p_{1s}$ (red solid line) and $p_{2s}$ (blue dashed line) for $\chi_c/\omega_{1}=0.0$. Parameters are chosen as: $\omega_2/\omega_1=1.005$, $\Delta_1=-\omega_1$, $\Delta_2=-\omega_2$, $g_1/\omega_1=1\times 10^{-3}$, $g_2=g_1$, $\gamma_{mj}/\omega_{1}=1\times 10^{-3}$, $\kappa_1/\omega_1=0.15$, $\kappa_2=\kappa_1$, $J/\omega_{1}=0.02$, $\mathcal{E}_1/\omega_{1}=150$, $\mathcal{E}_2=\mathcal{E}_1$.
• Figure 3: (a) The limit cycle trajectories in $q_{1s}(t)\rightleftharpoons p_{1s}(t)$ and $q_{2s}(t)\rightleftharpoons p_{2s}(t)$ spaces for $\chi_c/\omega_{1}=0.4$. (b) The limit cycle trajectories in $q_{1s}(t)\rightleftharpoons p_{1s}(t)$ and $q_{2s}(t)\rightleftharpoons p_{2s}(t)$ spaces for $\chi_c/\omega_{1}=0.0$. The parameters are as in Fig. \ref{['fig:2']}.
• Figure 4: (a) The time evolution of position and momentum of the two cavities (a) $x_{1}$ (red solid line), $x_{2}$ (blue dashed line). (b) $y_{1}$ (red solid line), $y_{2}$ (blue dashed line). The parameters are as in Fig. \ref{['fig:2']} except for $J/\omega_1=0$ and $\chi_c/\omega_{1}=0.6$.
• Figure 5: (a) The time evolution of position and momentum of the two cavities (a) $x_{1}$ (red solid line), $x_{2}$ (blue dashed line). (b) $y_{1}$ (red solid line), $y_{2}$ (blue dashed line). The parameters are as in Figu. \ref{['fig:2']} except for $J/\omega_1=0.02$ and $\chi_c/\omega_{1}=0.6$.