Atom-atom correlations in time-of-flight imaging of ultracold bosons in optical lattices

Abstract

We study the spatial correlations of strongly interacting bosons in a ground state, confined in a two-dimensional square and a three-dimensional cubic lattice. Using the combined Bogoliubov method and the quantum rotor approach, we map the Hamiltonian of strongly interacting bosons onto U(1) phase action in order to calculate the atom-atom correlations' decay along the principal axis and a diagonal of the lattice-plane direction as a function of distance. Lower tunneling rates lead to quicker decays of the correlations, whose character becomes exponential. Finally, correlation functions allow us to calculate quantities that are directly bound to experimental outcomes, namely time-of-flight absorption images and resulting visibility. Our results contain all the characteristic features present in experimental data (transition from Mott insulating blob to superfluid peaks, etc.), emphasizing the usability of the proposed approach.

Ultracold bosons with short-range interaction in regular optical lattices

“…In Refs. [80,362] it was also shown that the correlations along the lattice diagonals are weaker than those parallel to the lattice axes in agreement with Eqs. (261)- (263) and numerical data in Fig.…”

“…In higher dimensions, no exact results have been reported in the literature for the MI at T = 0. Nevertheless, high-order SCE [80] as well as the quantum rotor approach supplemented by the Bogoliubov theory [362] reveal exponential decay of F a for small J/U in two and three dimensions. In Refs.…”

Phase coherence and fragmentation of two-component Bose-Einstein condensates loaded in state-dependent optical lattices

“…Instead, some studies have developed novel analytic methods [34][35][36][37]. On the other hand, for BECs in shallow optical lattices, theoretical analysis of phase decoherence in 1D has been extensively performed via an extended Gross-Pitaevskii equation (GPE) approach [38], or via the Truncated Wigner Approximation (TWA) approach [31].…”

Optical Conductivity of Ultra-Cold Bosons in Optical Lattices

“…The exact derivation of the quantum rotor approach can be found in [8][9][10][11]. Here we present the general idea behind the method and the final outcome.…”