  We experimentally demonstrate strong coupling between the ferromagnetic
magnons in a small yttrium-iron-garnet (YIG) sphere and the drive-field-induced
dressed states of a superconducting qubit, which gives rise to the double
dressing of the superconducting qubit. The YIG sphere and the superconducting
qubit are embedded in a microwave cavity and the effective coupling between
them is mediated by the virtual cavity photons. The theoretical results fit the
experimental observations well in a wide region of the drive-field power
resonantly applied to the superconducting qubit and reveal that the driven
qubit-magnon hybrid quantum system can be harnessed to emulate a
particle-hole-symmetric pair coupled to a bosonic mode. This hybrid quantum
system offers a novel platform for quantum simulation of the composite
quasi-particles consisting of fermions and bosons.
