Hannover 2013 – scientific programme

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A: Fachverband Atomphysik

A 24: Ultra-cold atoms, ions and BEC IV (with Q)

A 24.1: Talk

Wednesday, March 20, 2013, 11:00–11:15, F 428

Mott-insulator state of ultracold atoms in optical lattices: comparison of exact numerical results with controlled approximations — •Konstantin Krutitsky, Friedemann Queisser, Patrick Navez, and Ralf Schützhold — Fakultät für Physik, Universität Duisburg-Essen, Duisburg, Germany

A wide class of phenomena for ultra-cold atoms in deep optical lattices is well described by the Bose-Hubbard model. Using exact numerical and approximate analytical methods, we have studied the ground-state energy, probabilities of the occupation numbers of the individual lattice sites, two-point correlation functions, and the excitation spectrum, in the Mott-insulator regime. Exact results are obtained for one-dimensional lattices up to 14 sites and for two-dimensional lattices of 3x3 sites. They are compared with the fourth order expansion in the ratio of the tunneling rate J and the interaction constant U valid in an arbitrary dimensions and the inverse coordination number 1/Z valid for arbitrary interaction strengths. The zeroth order in 1/Z is equivalent to the Gutzwiller mean field [3]. In one dimension, numerical data nearly coincide with perturbation theory in J/U whereas the first-order results in 1/Z deviate a bit for increasing J. In two dimensions, the 1/Z expansion is already superior to the J/U expansion, and should become even better in three and higher dimensions.

[1] J.K.Freericks and H.Monien, Phys.Rev.B 53, 2691 (1996).

[2] F.Queisser, K.V.Krutitsky, P.Navez, R.Schützhold, arXiv:1203.2164.

[3] S.Sachdev, Quantum phase transitions, Cambridge University Press, 2001.