Generation of magnonic squeezed state and its superposition in a hybrid qubit-magnon system

We propose a protocol for generating magnonic squeezed states (MSS) and their superpositions (SMSS) in a hybrid system comprising a superconducting flux qubit magnetically coupled to the Kittel mode of a yttrium iron garnet (YIG) sphere. The flux qubit provides an intrinsic longitudinal interaction with the magnon mode, which, under resonant microwave driving, gives rise to an effective qubit-state-dependent squeezing Hamiltonian. Numerical simulations incorporating realistic dissipation demonstrate that magnon quadrature noise reduction exceeding 8 dB is achievable with experimentally accessible parameters. By preparing the qubit in a superposition state followed by projective measurement, we further obtain symmetric and antisymmetric superpositions of orthogonally squeezed magnon states exhibiting clear phase-space interference fringes. We discuss how the fourfold rotational symmetry of these states supports a bosonic logical encoding with potential for protecting against dominant error channels in magnonic platforms.