Three-body interactions in Rabi-coupled Bose gases: A perturbative approach

In ultracold atomic gases, radio-frequency coupling between two spin states can lead to atoms being in a stable coherent superposition of the two states (dressed states). When the two-body interactions (scattering lengths) are different between the two states, it offers the possibility not only to control the interatomic interaction but also to modify the equation of states with emerging three-body terms with different signs and scalings with the parameters. We derive these terms in a unified perturbation framework and show that they correspond to genuine three-body processes found at different orders in perturbation theory. Our work justifies the introduction of contact three-body interactions in dressed-state systems when the spin degree of freedom is integrated out.