Dimensional crossover of a Rabi-coupled two-component Bose-Einstein condensate in an optical lattice

Dimensionality is a central concept in developing the theory of low-dimensional physics. However, previous research on dimensional crossover in the context of a Bose-Einstein condensate (BEC) has focused on the single-component BEC. To our best knowledge, further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking. In this work, we are motivated to investigate the dimensional crossover in a three-dimensional (3D) Rabi-coupled two-component BEC. The spin degrees of freedom consist of the Rabi-like and inter- and intra- interaction coupling constants. The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively. Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations, with an emphasis on the separated effects of Rabi-like and inter- and intra- interaction coupling constants on the quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.