Thermal and quantum noncondensate particles near the superfluid to Mott insulator transition

Abstract

We investigate the finite temperature momentum distribution of bosonic noncondensate particles inside a 3D optical lattice near the superfluid to Mott insulator transition point, treating the quantum fluctuation and thermal fluctuation effects on equal footing. We explicitly address the different momentum (\(q\)) dependence of quasi-particles excitations resulted from thermal and quantum origin: the former scales as \(|\bfq|^{-2}\) and hence is dominant in the small momentum region, while the later scales as \(|\bfq|^{-1}\) and hence dominant in the large momentum limit. Analytic and semi-analytic results are derived, providing a unique method to determine the temperature, condensate density, coherent length and/or single particle gap etc. inside the optical lattice. Our results also agree with the scaling theory of a quantum \(XY\) model near the transition point. Experimental implication of the TOF measurement is also discussed.