Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice

A two-dimensional Fock-state lattice (FSL) is constructed from the many-body states of two interacting two-mode quantum gases. By periodically driving interspecies interactions and pulsing tunneling between modes each gas, a synthetic gauge field generated. We derive an effective Hamiltonian in short pulse limit which resembles Harper-Hofstadter where magnetic flux per plaquette controlled by ratio interaction energy frequency. The quasispectrum Floquet operator sequence shows celebrated Hofstadter's butterfly pattern as well existence edge states. From calculation local Chern marker, we establish that FSL has nontrivial topology simulating dynamics states, show they exhibit chirality. Finally, inclusion intraspecies creates overall harmonic trap introduces nonlinear effect macroscopic self-trapping, shown to hinder movement along edges lattice. This work avenue explore fields link condensed matter systems