Quantum-geometric contribution to the Bogoliubov modes in a two-band Bose-Einstein condensate

We consider a weakly interacting Bose-Einstein condensate that is loaded into an optical lattice with a two -point basis and described by a two-band Bose-Hubbard model with generic one-body and two-body terms. By first projecting the system onto the lower Bloch band and then applying the Bogoliubov approximation to the resultant Hamiltonian, we show that the inverse effective-mass tensor of the superfluid carriers in the Bogoliubov spectrum has two physically distinct contributions. In addition to the usual inverse band-mass tensor that is originating from the intraband processes within the lower Bloch band, there is also a quantum-geometric contribution that is induced by the two-body interactions through the interband processes. We also discuss the conditions under which the latter contribution is expressed in terms of the quantum-metric tensor of the Bloch states, i.e., the natural Fubini-Study metric on the Bloch sphere.

Automated summary

We investigate a weakly interacting Bose-Einstein condensate in an optical lattice using a two-band Bose-Hubbard model. By considering both one-body and two-body terms, we analyze the contributions to the inverse effective-mass tensor of the superfluid carriers in the Bogoliubov spectrum. We find that, in addition to the usual inverse band-mass tensor, quantum-geometric contribution induced by two-body interactions also plays a significant role.