Abstract
Layla Hormozi (Joint Quantum Institute, NIST and University of Maryland)
Quantum Hall Effect for Lattice Bosons
We study the ground state of a 2D system of interacting bosonic atoms, trapped in the periodic potential of an optical lattice, under the influence of a strong synthetic magnetic field. When the number of flux quanta per lattice plaquette is close to 1/2, we use the notion of "pseudospin" and map the system to a two-species model in the continuum limit. We find that the interaction potential in the lowest Landau level single particle basis involves terms that do not conserve pseudospin. These terms, which correspond to the umklapp process in the momentum space, promote BCS-type pairings between particles with the same pseudospin. For the incompressible state at filling fraction $\nu = 1$ we propose a trial wavefunction which includes two pfaffian pairing terms and carry out numerical tests that confirm the paired nature of the ground state. Furthermore, these pairing terms seem to play a prime role in stabilizing the underlying incompressible state.