Pump-controlled multilevel phase jump in dissipative cavity magnonics

Dissipative coupling enables loss- and interference-based control of non-Hermitian microwave scattering, but the conventional two-mode cavity–Walker mode response supports only one 2π phase jump at a constrained frequency. Here, we introduce a pump-induced magnon mode coherently coupled to the Walker mode, with a pump-tunable coupling strength g that reshapes the complex transmission S21. Phase jumps are identified with transverse negative-real-axis crossings of S21, and four critical coupling strengths governing the creation, disappearance, and folding of the crossing roots are obtained analytically. At zero detuning, tuning g produces successive multiplicities of one, three, five, four, and zero. Varying the cavity radiative decay rate changes the threshold ordering and the accessible counts, while Walker mode–cavity detuning breaks the symmetry of phase jumps and allows their frequencies to be tuned jointly by g and the detuning. These results establish phase-jump multiplicity as a reconfigurable scattering property of dissipative cavity magnonics and could support pump-programmable phase-encoded microwave responses.