Controlling atomic spin mixing via multiphoton transitions in a cavity

We propose to control spin-mixing dynamics in a gas of spinor atoms, via the combination of two off-resonant Raman transition pathways, enabled by a common cavity mode and a bichromatic pump laser. The mixing rate, which is proportional to the synthesized spin-exchange interaction strength, and the effective atomic quadratic Zeeman shift (QZS), can both be tuned by changing the pump laser parameters. Quench and driving dynamics of the atomic collective spin are shown to be controllable on a faster timescale than in existing experiments based on inherent spin-exchange collision interactions. The results we present open a promising avenue for exploring spin-mixing physics of atomic ensembles accessible in current experiments.