Population-imbalance instability in a Bose-Hubbard ladder in the presence of a magnetic flux

Abstract

We consider a two-leg Bose-Hubbard ladder in the presence of a magnetic flux. We make use of Gross-Pitaevskii, Bogoliubov, bosonization, and renormalization group approaches to reveal a structure of ground-state phase diagrams in a weak-coupling regime relevant to cold atom experiments. It is found that, except for a certain flux $\ensuremath{\phi}=\ensuremath{\pi}$, the system shows different properties as changing hoppings, which also leads to a quantum phase transition similar to the ferromagnetic $XXZ$ model. This implies that population-imbalance instability occurs for certain parameter regimes. On the other hand, for $\ensuremath{\phi}=\ensuremath{\pi}$, it is shown that an umklapp process caused by commensurability of a magnetic flux stabilizes a superfluid with chirality and the system does not experience such a phase transition.