Dynamics of Quantum Entanglement Between Photon and Phonon Modes in a Coulomb-coupled Optomechanical Cavity Magnonic Systems

TL;DR

This work analyzes entanglement dynamics in a hybrid Coulomb-enabled cavity magnon optomechanical (COMM) system comprising a microwave cavity, a YIG-based magnon mode, and two electrostatically coupled mechanical resonators. By deriving a frame-rotated Hamiltonian and linearized quantum Langevin equations, the authors obtain an 8×8 drift matrix and diffusion, solve the Lyapunov equation to obtain a steady-state covariance $V$, and quantify bipartite entanglement using the logarithmic negativity $E_N$ from reduced 4×4 blocks. They demonstrate that magnon Kerr nonlinearity $K_s$ and Coulomb coupling $G_c$ act as key tunable knobs to enhance and stabilize entanglement, increasing resilience to temperature and enabling robust photon–phonon and phonon–phonon correlations. The results identify parameter regimes that support robust continuous-variable entanglement, with implications for quantum memories and hybrid quantum networks in which disparate quantum platforms are coherently interfaced.

Abstract

Quantum entanglement is a fundamental phenomenon in quantum information science and a crucial resource for quantum technologies such as precision sensing, secure communication, and computation. In hybrid cavity magno-optomechanical systems, entanglement among cavity photons, magnons, and phonons enables manipulation of quantum states across different modes via radiation pressure-based light-matter interaction. We propose a hybrid optomechanical cavity-magnonic setup with Yttrium iron garnet (YIG) sphere allowing magnons to couple with photons via magnetic-dipole interaction. The system also uses optomechanical and electrostatic interactions to entangle cavity photons and mechanical resonators. We focus on how the magnon nonlinear Kerr effect and varying coupling strengths influence entanglement dynamics. By analysing nonlinear effects alongside other coupling parameters, we identify optimal conditions for initiating and sustaining robust entanglement between the motional modes (phonons) of two Coulomb-coupled mechanical resonators. Our model predicts that adding Coulomb interaction and magnon coupling enhances the degree and tunability of entanglement, making it more resilient to thermal baths at 3 K. This study addresses how to optimize and sustain phonon-phonon entanglement in complex hybrid quantum systems. These findings offer insights relevant to developing quantum memories for continuous variable quantum information processing and other quantum technologies.

Figures (9)

• Figure 1: The conceptual foundation of the Coulomb-enabled optomechanical cavity magnonic system under study involves a single optomechanical cavity featuring a fixed mirror on the left and a perfectly reflecting mechanical resonator M$_1$ on the right resonating around its equilibrium position, with a Yttrium Iron Garnet (YIG) sphere enclosed between them. The microwave cavity photons, denoted as $c$, couple to the magnon $m$ of the YIG sphere through a magnetic-dipole interaction characterized by coupling strength $g_m$, and to the mechanical resonator M$_1$ via optomechanical coupling with strength $G_0$. The YIG sphere is subjected to an external magnetic drive field $B_0$ with strength $\Omega_B$ to generate an appropriate number of magnons within the YIG sphere. A third mechanical resonator, M$_2$, on the right interacts with M$_1$ through electrostatic interactions, characterized by coupling strength $G_c$, as both resonators are capacitively charged with opposite polarities via a DC bias voltage. The physical separation between the two resonators is denoted as $d$, while $x_1$ and $x_2$ represent their small displacements from equilibrium positions.
• Figure 2: (Color online) Steady-state quantum entanglement $E_N$ between two charged mechanical resonators plotted against scaled cavity detuning $\Delta_c$ and magneto-optical coupling strength under different values of Coulomb coupling (a) $G_c = 0$, (b) $G_c = 0.1 \omega_1$, (c) $G_c = 0.3 \omega_1$, and (d) $G_c = 0.7 \omega_1$. The general system parameters are: $\omega_1/2\pi = \omega_2/2\pi = 10~ \text{MHz}$, $\omega_m /2\pi = 10 ~\text{GHz}$, $\gamma_m/2\pi = 0.1 ~\text{MHz}$, $\kappa /2\pi = 5.5 ~\text{MHz}$, $\gamma_1 /2\pi = \gamma_2/2\pi = 200 ~\text{Hz}$, $G_{\text{eff}} = 0.55 \kappa$, $\Delta_m = \omega_1$, $\Delta K = 0.65 \omega_1$, $\hbar = 1.0546 \times 10^{-34} ~\text{J}\cdot\text{s}$, and the bath temperature $T = 10~ \text{mK}$.
• Figure 3: (Color online) Entanglement ($E_N$) between two charged mechanical resonators plotted against bath temperature $T$, (a) and (b) under different values of optomechanical coupling $G_{\rm eff}$ and Coulomb coulomb coupling $G_c$ when $g_m /2\pi = 11.3$ MHz, (c) and (d) under different values of $G_{\rm eff}$ and $G_c$, respectively, when $g_m /2\pi = 13.2$ MHz. The general parameters used are: (a), (c) $G_c = 0.5\omega_1$, and (b), (d) $G_{\rm{eff}} = 0.95\kappa$. Other parameters used here are the same as in Fig. \ref{['GcControlledEN']}.
• Figure 4: (Color online) Contour plot of Entanglement ($E_N$) between two motional modes plotted against scaled cavity detuning and Coulomb coupling interaction under different values of photon loss rate parameter: (a) $\kappa /2\pi = 2$ MHz, (b) $\kappa /2\pi = 6$ MHz, and (c) $\kappa /2\pi = 9$ MHz. The general parameters used are: $G_{\rm{eff}}/2\pi = 1.5$ MHz, $g_m /2\pi = 10$ MHz, and $T = 15$ mK. Other parameters used here are the same as in Fig. \ref{['GcControlledEN']}.
• Figure 5: (Color online) Contour plot for the quantum Entanglement between two charged mechanical resonators plotted against the scaled cavity detuning $\Delta_c$ and the magnon loss rate $\gamma_m$. (a) when the Coulomb coupling strength is $G_c = 0.4\omega_1$, and (b) the Coulomb coupling strength is tuned to $G_c = 0.8\omega_1$. The general parameters used are: $g_m /2\pi = 15.5$ MHz. The other parameters used in this figure have the same values as depicted in Fig. \ref{['GcControlledEN']}.