Gauge potentials and vortices in the Fock space of a pair of periodically driven Bose-Einstein condensates

We perform a theoretical study of the coupled dynamics of two species of Bose-Einstein condensates (BECs) in a double-well potential where both the tunneling and the interatomic interactions are driven periodically in time. The population difference between the wells of each species gives rise to a two-dimensional lattice in Fock space with dimensions given by the number of atoms in each BEC. We use a Floquet analysis to derive an effective Hamiltonian that acts in this Fock space and find that it contains an artificial gauge field. This system simulates noninteracting particles in a tight-binding lattice subject to an additional harmonic potential and vector potential. When the intraspecies interactions are attractive there is a critical value at which the ground state undergoes a transition from a Gaussian state to a quantized vortex state in Fock space. The transition can be quantified in terms of the angular momentum and the entanglement entropy of the ground state with both showing sudden jumps as the intraspecies interactions become stronger. The stability of the vortex state vanishes in the thermodynamic limit.