Infinite Lattices of Vortex Molecules in Rabi-Coupled Condensates

Vortex molecules can form in a two component superfluid when a Rabi field drives transitions between the two components. We study the ground state of an infinite system of vortex molecules in 2D, using a numerical scheme which makes no use of the lowest Landau level approximation. We find the ground state lattice geometry for different values of inter-component interactions and strength of the Rabi field. In the limit of large field when molecules are tightly bound, we develop a complimentary analytical description. The energy governing the alignment of molecules on a triangular lattice is found to correspond to that of an infinite system of 2D quadrupoles, which may be written in terms of an elliptic function $\mathcal{Q}(z_{ij};\omega_1 , \omega_2 )$. This allows for a numerical evaluation of the energy which enables us to find the ground state configuration of the molecules.