Title: A cavity-induced artificial gauge field in a Bose-Hubbard ladder,
Abstract: We consider theoretically ultracold interacting bosonic atoms confined to
quasi-one-dimensional ladder structures formed by optical lattices and coupled
to the field of an optical cavity. The atoms can collect a spatial phase
imprint during a cavity-assisted tunneling along a rung via Raman transitions
employing a cavity mode and a transverse running wave pump beam. By adiabatic
elimination of the cavity field we obtain an effective Hamiltonian for the
bosonic atoms, with a self-consistency condition. Using the numerical density
matrix renormalization group method, we obtain a rich steady state diagram of
self-organized steady states. Transitions between superfluid to Mott-insulating
states occur, on top of which we can have Meissner, vortex liquid, and vortex
lattice phases. Also a state that explicitly breaks the symmetry between the
two legs of the ladder, namely the biased-ladder phase is dynamically
stabilized.