Nonreciprocal magnon blockade via combining Barnett and Sagnac effects in a nonlinear system

We propose a scheme to achieve nonreciprocal unconventional magnon blockade (NUMB) based on the Barnett and Sagnac effects in a hybrid nonlinear system, in which a microwave cavity with two modes and a yttrium iron garnet (YIG) sphere are included. Two cavity modes with the fundamental and the second-harmonic frequencies are coupled by virtue of the χ⁽²⁾ nonlinear materials, and meanwhile, the fundamental mode interacts with the magnon mode via the magnetic dipole interaction. Under weak driving and coupling conditions, the magnon blockade is obtained, where the second-order correlation function has been used to analyze the magnon antibunching based on the numerical simulations and analytical calculations. The underlying mechanism is that quantum destructive interference occurs between different transition paths. In addition, the combination of the Barnett and Sagnac effects, which leads to the simultaneous frequency shifts of the magnon and two microwave modes, could induce the nonreciprocity of magnon antibunching due to the positive and negative detunings via changing the direction of the external fields. The scheme we present is based on the weak near-resonant coupling between quantum modes and the weak driving of magnon and photon modes, which may demonstrate the potential for achieving the single-magnon resource in a hybrid cavity magnonic system and provide valuable guidance for the design of nonreciprocal magnon devices.