  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
intra-species interactions are attractive there is a critical value at which
the ground state of the Floquet operator 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 as well as the entanglement entropy
of the ground state with both showing sudden jumps as the intra-species
interactions become stronger. The stability of the vortex state vanishes in the
thermodynamic limit.
