Nonreciprocal superradiant quantum phase transition induced by magnon Kerr effect

TL;DR

This work addresses realizing a nonreciprocal superradiant quantum phase transition (SQPT) by exploiting the magnon Kerr effect (MKE) in a cavity magnonic system consisting of a YIG sphere coupled to a microwave cavity under parametric driving. The authors derive a non-Hermitian effective Hamiltonian incorporating Kerr nonlinearity $K$, detunings $\Delta_a,\Delta_m$, drive strength $\Omega$, and coupling $g_m$, and obtain steady-state magnon numbers $|M|^2$ with three branches, whose stability yields a phase diagram featuring normal, superradiant, and bistable regions. Crucially, the sign of $K$ (controlled by bias-field orientation along [100] vs [110]) leads to distinct critical thresholds $\Omega_1$ and $\Omega_2$, making the SQPT nonreciprocal between $K>0$ and $K<0$; this nonreciprocity is quantified by a bidirectional contrast ratio $\mathcal{I}$ that peaks in an intermediate drive window. The results demonstrate a practical, tunable mechanism for nonreciprocal SQPT in cavity magnonics with realistic experimental parameters, offering a pathway to directional quantum devices and advanced photonic-magnonic systems.

Abstract

Recently, proposals for realizing a nonreciprocal superradiant quantum phase transition (SQPT) have been put forward, based on either nonreciprocal interactions between two spin ensembles or the Sagnac-Fizeau shift in a spinning cavity. However, experimental implementation of such a nonreciprocal SQPT remains challenging. This motivates the search for new mechanisms capable of producing a nonreciprocal SQPT. Here, we propose an alternative approach to realize a nonreciprocal SQPT, induced by the magnon Kerr effect (MKE), in a cavity magnonic system, where magnons in a yttrium iron garnet (YIG) sphere are coupled to cavity photons. The MKE coefficient is positive ($K>0$) when the bias magnetic field is aligned along the crystallographic axis [100], but negative ($K<0$) when aligned along the axis [110]. We show that the steady-state phase diagram for $K > 0$ differs markedly from that for $K < 0$. This contrast is the origin of the nonreciprocal SQPT. By further studying the steady-state magnon occupation and its fluctuations versus the parametric drive strength, we demonstrate that the SQPT becomes nonreciprocal, characterized by distinct critical thresholds for $K > 0$ and $K < 0$. Moreover, we introduce a bidirectional contrast ratio to quantify this nonreciprocal behavior. Our work provides a new mechanism for realizing the nonreciprocal SQPT, with potential applications in designing nonreciprocal quantum devices.

Figures (4)

• Figure 1: Schematic diagram of the proposed cavity magnonic system. The system comprises a parametrically driven microwave cavity and a YIG sphere magnetized to saturation by a bias magnetic field $B_0$. The magnetic field is aligned along either the crystallographic axis [100] or [110] (see the red-arrowed lines) of the YIG sphere.
• Figure 2: Steady-state phase diagram of the cavity magnonic system versus the normalized drive strength $\Omega/\kappa_a$ and the detuning ratio $\Delta_m/\Delta_a$, where (a) $K > 0$ and (b) $K < 0$. NP, SP, and BP represent the normal phase, superradiant phase, and bistable phase, respectively. The white background in the upper-right corner of panel (b) indicates the unstable region. The vertical blue solid line marks the critical drive strength $\Omega=\Omega_1$, while the green dashed-dotted curve indicates the critical drive strength $\Omega=\Omega_2$. Other parameters are chosen to be $\Delta_{a}/\kappa_a=3$, $g_m/\kappa_a=2.4$, and $\gamma_m/\kappa_a=1$.
• Figure 3: (a),(b) Scaled steady-state magnon numbers $|M|^2/|(\gamma_m/K)|$ and (c),(d) magnon number fluctuations $\lg(\langle\delta m^\dagger \delta m \rangle + 1)$ versus the normalized drive strength $\Omega/\kappa_a$, where $T=0$. Yellow shaded regions mark the nonreciprocal domains of SQPT, where $|M|^2(K>0) \neq |M|^2(K<0)$. The red solid curves correspond to $K > 0$, and the blue dashed curves correspond to $K < 0$. The detuning ratios are $\Delta_m/\Delta_a = 1.3$ and $\Delta_m/\Delta_a = 0.8$ in panels (a),(c) and (b),(d), respectively. Other parameters are the same as those in Fig. \ref{['fig2']}.
• Figure 4: Bidirectional contrast ratio $\mathcal{I}$ as a function of the normalized drive strength $\Omega/\kappa_a$ and the detuning ratio $\Delta_m/\Delta_a$. The white background in the upper-right corner corresponds to the unstable region in Fig. \ref{['fig2']}(b). The vertical white solid line marks the critical drive $\Omega = \Omega_1$, and the black dashed curve indicates $\Omega = \Omega_2$. Other parameters are the same as those in Fig. \ref{['fig2']}.