Quantum synchronization between two strongly driven YIG spheres mediated via a microwave cavity

TL;DR

The paper addresses how two driven magnon modes embedded in separate YIG spheres can synchronize through indirect coupling via a single-mode microwave cavity. It develops a theoretical framework using a rotating-frame Hamiltonian with Kerr nonlinearities, derives Langevin equations, and applies mean-field linearization to obtain a covariance-based measure of quantum synchronization, $S_q^\phi$. The results show both classical and quantum synchronization can emerge, with $S_q^\phi$ approaching unity under appropriate drive, detuning, and coupling, while increasing thermal occupancy degrades quantum synchronization. This work demonstrates a tunable, cavity-mediated nonlinear mechanism for synchronization in magnonic systems, with potential implications for quantum information processing and hybrid quantum technologies, particularly under low-temperature conditions where quantum effects are more robust.

Abstract

We present a theoretical study of synchronization between two strongly driven magnon modes indirectly coupled via a single-mode microwave cavity. Each magnon mode, hosted in separate Yttrium Iron Garnet spheres, interacts coherently with the cavity field, leading to cavity-mediated nonlinear coupling. We show, by using input-output formalism, that both classical and quantum synchronization emerge for appropriate choices of coupling, detuning, and driving. We find that thermal noise reduces quantum synchronization, highlighting the importance of low-temperature conditions. This study provides useful insights into tunable magnonic interactions in cavity systems, with possible applications in quantum information processing and hybrid quantum technologies.

Figures (4)

• Figure 1: Schematic representation of two YIG (Yttrium Iron Garnet) spheres, ${m}_1$ and ${m}_2$, coupled via a common microwave cavity mode, ${a}$.
• Figure 2: Limit-cycle trajectories in the $q_{1} \leftrightharpoons p_{1}$ (red) and $q_{2} \leftrightharpoons p_{2}$ (blue) spaces (a, d, g), and variation of the mean values $\bar{q}_{1}$ (red) and $\bar{q}_{2}$ (blue) (b, e, h), along with mean values $\bar{p}_{1}$ (red) and $\bar{p}_{2}$ (blue) (c, f, i). The chosen parameters are: (a--c) $\Omega_{1} = 1$, $\Omega_{2} = 1.00001$, $g_{1} = g_{2} = 0.1$. (d--f) $\Omega_{1} = 1$, $\Omega_{2} = 1.1$, $g_{1} = g_{2} = 0.1$. (g--i) $\Omega_{1} = 1$, $\Omega_{2} = 1.00001$, $g_{1} = 0.2$, $g_{2} = 0.1$. All other parameters are identical across cases: $\Omega_{c} = 1$, $\Delta_{1} = \Delta_{2} = 0.001$, $\Delta_{c} = -0.2$, $K_{1} = K_{2} = 10^{-10}$, and $\gamma_{1} = \gamma_{2} = \gamma_{c} = 0.1$. All parameters are normalized with respect to $\Omega_{1}$ with the initial conditions $(\bar{q}_1,\bar{p}_1)=(1,0) =(\bar{q}_2,\bar{p}_2)$. The limit cycle trajectories are shown till $\Omega_1t =10^5$.
• Figure 3: Limit-cycle trajectories in the $q_{1} \leftrightharpoons p_{1}$ (red) and $q_{2} \leftrightharpoons p_{2}$ (blue) spaces (a, d, g); variation of the mean values $\bar{q}_{1}$ (red), $\bar{q}_{2}$ (blue) (b, e, h); and $\bar{p}_{1}$ (red), $\bar{p}_{2}$ (blue) (c, f, i). The parameters for each case are: (a--c) $\Omega_{1} = 1$, $\Omega_{2} = 1.00001$,$\Delta_{1} = \Delta_{2} = 0.001$. (d--f) $\Omega_{1} = 1$, $\Omega_{2} = 1.1$, $\Delta_{1} = \Delta_{2} = 0.001$. (g--i) $\Omega_{1} = 1$, $\Omega_{2} = 1.00001$, $\Delta_{1} = 0.001$, $\Delta_{2} = 0.0025$. Other parameters (common to all cases): $\Omega_{c} = 1$, $\Delta_{c} = -0.2$, $g_{1} = g_{2} = 0.5$, $K_{1} = K_{2} = 10^{-10}$, and $\gamma_{1} = \gamma_{2} = \gamma_{c} = 0.1$. All parameters are normalized with respect to $\Omega_{1}$ with the initial conditions $(\bar{q}_1,\bar{p}_1)=(1,0)$ and $(\bar{q}_2,\bar{p}_2)=(2,0)$. The limit cycle trajectories are shown till $\Omega_1t=10^5$.
• Figure 4: (a) Variation of $S_{q}^{\phi}$, with respect to time $t$ , (b) variation of $\bar{S}_{q}^{\phi}$, with respect to the mean phonon number $\bar{n}_{m}$ of the environment. The other parameters are $g_1=g_2=0.1$, $K_1=K_2=10^{-10}$, $\Omega_{1}=1$, $\Omega_{2}=1.1$, $\Omega_{c}=1$, $\Delta_1 = \Delta_2 =0.001$, $\Delta_c =-0.2$, $\gamma_1=\gamma_2=\gamma_c=0.1$, and $\phi= 0.1320$ radian. We have chosen an initial condition $(\bar{q}_1,\bar{p}_1) = (1,1)=(\bar{q}_2,\bar{p}_2)$.