Frustrated Bose condensates in optical lattices

Abstract

We study the Bose-condensed ground states of bosons in a two-dimensional optical lattice in the presence of frustration due to an effective vector potential, for example, due to lattice rotation. We use a mapping to a large-$S$ frustrated magnet to study quantum fluctuations in the condensed state. Quantum effects are introduced by considering a $1/S$ expansion around the classical ground state. The large-$S$ regime should be relevant to systems with many particles per site. As the system approaches the Mott insulating state, the hole density becomes small. Our large-$S$ results show that, even when the system is very dilute, the holes remain a (partially) condensed system. Moreover, the superfluid density is comparable to the condensate density. In other words, the large-$S$ regime does not display an instability to noncondensed phases. However, for cases with fewer than 1/3 flux quantum per lattice plaquette, we find that the fractional condensate depletion increases as the system approaches the Mott phase, giving rise to the possibility of a noncondensed state before the Mott phase is reached for systems with smaller $S$.