Resonant Multiphoton Conversion Mediated by a Shared Vibration in Cavity QED

arXiv:2610.34249v1 Announce Type: new Abstract: We show that a vibration shared by two emitter subensembles can jointly establish multiphoton resonance and constructive interference among the virtual exchange pathways responsible for coherent conversion. For opposite displacements with an integer magnitude ratio $r\geq2$, the displacements induced by $r$ excitations in the less displaced subensemble and one in the other cancel exactly, a condition we call displacement neutrality. When the emitter and cavity frequencies match, the resulting composite is resonant with $r+1$ cavity photons, while the vibration-mediated cross interaction makes the conversion pathways add constructively, establishing a direct relation between the displacement ratio and the conversion order.