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

Abstract

We study the spatial correlations of strongly interacting bosons in a ground state, confined in two-dimensional square and three-dimensional cubic lattice. Using 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, which 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.), which emphasizes the usability of the proposed approach.

http://pra.aps.org/abstract/PRA/v84/i5/e053613

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Bose-Fermi Mixtures in a Three-dimensional Optical Lattice
• Localization of bosonic atoms by fermionic impurities in a 3d optical lattice
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Interference pattern and visibility of a Mott insulator
• Spatial correlations of trapped 1d bosons in an optical lattice
• Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results
• Process chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram
• Quantum rotor description of the Mott-insulator transition in the Bose-Hubbard model
• Finite-temperature effects on the superfluid Bose-Einstein condensation of confined ultracold atoms in three-dimensional optical lattices
• Synthetic magnetic field effects on neutral bosonic condensates in quasi three-dimensional anisotropic layered structures

Cited by in corpus (8)

• Ultracold bosons with short-range interaction in regular optical lattices
• Time-of-flight patterns of ultra-cold bosons in optical lattices in various Abelian artificial magnetic field gauges
• Spin-squeezed atomic crystal
• Particle-hole character of the Higgs and Goldstone modes in strongly-interacting lattice bosons
• Temperature-dependent excitation spectra of ultra-cold bosons in optical lattices
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Finite temperature superfluid transition of strongly-correlated lattice bosons in various geometries
• Finite-temperature quantum rotor approach for ultracold bosons in optical lattices