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.