Interaction induced topology in a Bose-Hubbard chain under non-Hermitian Drive

Exotic topological phases with no analogue in traditional static Hermitian systems have been observed in Floquet and non-Hermitian systems. We propose a model that combines non-Hermiticity and Floquet engineering to realize topological energy spectrum in a 1D bosonic system. Our Hamiltonian is a 1D Bose gas with an asymmetric density dependent non-Hermitian gauge field. The single particle spectrum is topologically trivial while the spectrum with multiple particles has a non-trivial winding number, suggesting the topology arises from interactions. We calculate a non-trivial winding number of 2 under periodic boundary conditions if there are two particles in the system. Equivalently, we observe a skin effect in the open boundary geometry, only if there are multiple particles in the system. We further find that the spectrum can be separated into two sectors: one where the particles cluster and one where the particles avoid each other. We derive an effective theory that accurately describes the properties of the clustering sector as a non-Hermitian SSH model. Finally, we propose that our model can be realized in bosons trapped in optical lattices or in coupled optical waveguide arrays.