The superradiant phase transition (SPT) has been widely studied in cavity quantum electrodynamics (CQED). However, this SPT is still subject to ongoing debates due to the no-go theorem induced by the so-called ${\mathbf{A}}^2$ term (AT). We propose a hybrid quantum system, consisting of a single-mode cavity simultaneously coupled to both a two-level system and yttrium-iron-garnet sphere supporting magnons with Kerr nonlinearity, to restore the SPT against the AT. The Kerr magnons here can effectively introduce an additional AT tunable and strong enough to counteract the intrinsic AT, via adiabatically eliminating the degrees of freedom of the magnons. We show that the Kerr-magnon-induced SPT can exist in both cases of ignoring and including the intrinsic AT. Without the intrinsic AT, the critical coupling strength can be dramatically reduced by introducing the Kerr magnons, which greatly relaxes the experimental conditions for observing the SPT. With the intrinsic AT, the forbidden SPT can be recovered with the Kerr magnons in a reversed way. Our work paves a potential way to manipulate the SPT against the AT in hybrid systems combining CQED and nonlinear magnonics.

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• Hybrid quantum systems
• Magnons
• Quantum phase transitions
• Rabi model