Superradiant phase transition in cavity magnonics via Floquet engineering

Abstract

We propose a scheme to engineer the superradiant phase transition (SPT) in cavity magnonics by periodically modulating the frequency of the magnon mode. The studied system is composed of a yttrium iron garnet (YIG) sphere positioned inside a microwave cavity, where magnons in the YIG sphere are strongly coupled to microwave photons. Under the Floquet drive, the effective frequencies of both the cavity and magnon modes can be readily controlled via the frequency and strength of Floquet field. This tunability allows the cavity magnonic system to support a rich steady-state phase diagram, featuring parity-symmetric, parity-symmetry-broken, bistable, and unstable phases. With the increase of Floquet-field strength, the system exhibit a discontinuous phase transition from the parity-symmetric phase to the parity-symmetry-broken phase at a critical threshold, accompanied by an abrupt jump of the magnon occupation from zero to a finite value. Upon further increase of Floquet-field strength, the magnon occupation declines continuously from a nonzero value back to zero, corresponding to a second-order phase transition that restores the parity-symmetric phase. Additionally, fluctuations in magnon number during the SPT process are examined. Our work establishes an alternative route to engineer the cavity-magnon SPT without relying on microwave parametric drive.

Figures (5)

• Figure 1: Schematic diagram of the Floquet-driven cavity magnonic system. The system is composed of a microwave cavity and a YIG sphere driven by a Floquet field, where the magnon mode is strongly coupled to the cavity mode.
• Figure 2: The effective frequencies $\{\omega_c,\omega_m\}$ and coupling strengths $\{\lambda _r,\lambda _{\rm cr}\}$ versus the reduced drive strength $\Omega/\omega_D$, where $n_2 = -4$, $g_m/\kappa = 50$ in panel (a) and $n_2 = -5$, $g_m/\kappa = 110$ in panel (b). Other parameters are $\tilde{\omega}_c=\tilde{\omega}_m$, $\tilde{\omega}_c + \tilde{\omega}_m + n_2 \omega_D = 16\kappa$, $\kappa=\gamma=1$, and $n_1 = 0$Xu20Pishehvar25Wang18.
• Figure 3: Steady-state phase diagram for the cavity magnonic system. Gray, red, yellow and blue regions represent the parity-symmetric phase (PSP), parity-symmetry-broken phase (PSBP), bistable phase (BP), and unstable phase (UP), respectively. The solid curves of different colors denote phase boundaries, with white asterisks marking the tricritical points and purple triangles indicating the specific positions chosen for the numerical simulations in Fig. \ref{['fig4']}. The used parameters are the same as in Fig. \ref{['fig2']}.
• Figure 4: (a)-(d) Temporal evolution of the scaled magnon number $\langle b^\dag b\rangle/(\gamma/K)$ at the points marked by purple triangles in Fig. \ref{['fig3']}: (a) the parity-symmetric phase ($\lambda_{r}/\kappa=\lambda_{\text{cr}}/\kappa=2$), (b) the parity-symmetry-broken phase ($\lambda_{r}/\kappa=\lambda_{\text{cr}}/\kappa=10$), (c) the bistable phase ($\lambda_{r}/\kappa=20$, $\lambda_{\text{cr}}/\kappa=4$), and (d) the unstable phase ($\lambda_{r}/\kappa=-1$, $\lambda_{\text{cr}}/\kappa=-25$). The inset in (d) displays an enlarged view of the temporal evolution of $\langle b^\dag b\rangle/(\gamma/K)$ for the time interval $6 \leq \kappa t \leq 7$. In (a)-(d), the solid blue curves correspond to initial conditions $\langle a\rangle_{t=0}/\sqrt{\gamma/K}=-7.8-5.7i$ and $\langle b\rangle_{t=0}/\sqrt{\gamma/K}=3.1+2.9i$, while the dashed red curves represent $\langle a\rangle_{t=0}/\sqrt{\gamma/K}=-0.1-0.1i$ and $\langle b\rangle_{t=0}/\sqrt{\gamma/K}=0.1+0.1i$. Other parameters are the same as in Fig. \ref{['fig2']}.
• Figure 5: (a) The scaled magnon number $\langle b^{\dag}b\rangle /(\gamma / K)$ and (b) the magnon number fluctuation $\lg(\langle \delta b^{\dag}\delta b\rangle + 1)$ versus the reduced drive amplitude $\Omega/\omega_{D}$, with $n_a=n_b=0$. The abbreviations PSP and PSBP denote the parity-symmetric phase and parity-symmetry-broken phase, respectively. Other parameters are the same as in Fig. \ref{['fig2']}(b).