Beyond-Mean-Field Effects in Rabi-Coupled Two-Component Bose-Einstein Condensate

We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi-coupling frequency Omega, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang scaling proportional to n(5/2) to an expansion in integer powers of density, where, in addition to a two-body BMF term proportional to n(3)/root Omega, there emerges a repulsive three-body contribution proportional to n(3)/root Omega. We experimentally evidence these two contributions, thanks to their different scaling with Omega, in the expansion of a Rabi-coupled twocomponent K-39 condensate in a waveguide. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of the vanishing mean field.