Multistability and Self-Trapping in Cavity-Magnonic Dimer

Abstract

We show that a driven-dissipative cavity-magnonic dimer supports multistability with coexisting symmetric and symmetry-broken steady states. The interplay between magnon Kerr nonlinearity and photon tunneling induces magnon self-trapping, leading to a persistent population imbalance between the two resonators. In the vicinity of saddle-node bifurcations, the system exhibits critical slowing down, with relaxation times far exceeding the intrinsic dissipation scale. Focusing on quan- tum correlations, we analyze the quantum fidelity and mutual information between the intercavity magnon modes. We find that both the infidelity and the mutual information increase sharply near the phase boundaries, providing clear quantum signatures of the multistable and symmetry-broken phases. Our results establish cavity magnonic dimers as a versatile platform for exploring nonlinear nonequilibrium physics in hybrid quantum systems.

Figures (4)

• Figure 1: (a) Schematic diagram of the driven cavity--magnon dimer. (b) Steady-state magnon occupation for different dynamical classes. (c)--(f) Semiclassical dynamics of the cavity--magnon dimer reaching different steady states. Symmetric initial conditions evolve toward symmetric steady states with either both high or both low magnon populations, whereas asymmetric initial conditions converge to symmetry-broken steady states characterized by high--low or low--high populations in the respective modes. The parameters used in the simulation are $\omega_{a}/2\pi = 10$ GHz, $\kappa_{a}/2\pi = \kappa_{m}/2\pi = 1$ MHz, $\Delta_{a}/2\pi = \Delta_{m}/2\pi = -11$ MHz, $K/2\pi = 9$ nHz, $g/2\pi = 7$ MHz, $J=0.8\kappa_{a}$, $P_d=30$ mW.
• Figure 2: (a) Steady-state magnon numbers $n_{m_L}$ and $n_{m_R}$ versus drive power $P_d$(mW). Red markers denote symmetric saddle-node bifurcation points, and green markers denote asymmetric ones. (b) Phase diagram of the symmetry-broken steady states in the $P_d$–$J/\kappa_a$ plane. 1S: monostable symmetric phase; 2S: bistable symmetric phase; 2S–2AS: multistable phase supporting four coexisting steady states (two symmetric and two asymmetric). The corresponding steady-state population imbalance $\vert Z\vert$ is also shown. The $\triangleleft$ symbol marks the emergence of the Hopf-bifurcation phase.
• Figure 3: Quench dynamics of the magnon numbers $n_{m_L}$ (solid red) and $n_{m_R}$ (dashed blue) for different drive powers near the saddle-node bifurcation points marked in Fig. \ref{['fig:stability']}: (a) $S_{\mathrm{up}}$, (b) $S_{\mathrm{down}}$, (c) $AS_{\mathrm{up}}$, and (d) $AS_{\mathrm{down}}$. In all panels, the transient time increases from the lighter to darker curves, with the darkest curve corresponding to the point closest to the bifurcation.
• Figure 4: Variation of (a) maximum infidelity and (b) mutual information between the magnon modes in the left and right cavities as a function of the drive power $P_d$ (mW). Panel (b) includes all combinations of low- and high-occupation states.