Phase diagram of trapped bosons in a kagome lattice-application of inhomogeneous mean field theory

Motivated by the possibility of obtaining a trimerized optical lattice, such as a kagome lattice experimentally by employing counter propagating laser beams, we investigate the phase diagram of correlated bosons in a kagome lattice in the presence of a harmonic confinement. To study the phase diagram, we compute the order parameters of an extended Bose-Hubbard model which is solved via the standard mean field technique in the presence of a trapping potential. It is emphasized that such trapping effects (together with the density exchange term) lead to the necessity of considering the detailed geometry of the lattice, and thus the measured quantities appeal to a particular geometry, kagome lattice being the case here. The phase diagram thus obtained yields co-existence of different compressible and incompressible phases. There are distinct signatures of superfluid, insulating, density ordered and supersolid phases as one moves towards the edge of the lattice starting from the centre of the confining potential. A comparison of the results obtained for the order parameters corresponding to other geometries, such as square and honeycomb lattices are presented. Relevant to the time-of-flight experiments, the order parameters have been computed in the momentum space, which corroborate the existence of different phases for a kagome lattice.