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arXiv:cond-mat/0311012 · New Journal of Physics

Interaction broadening of Wannier functions and Mott transitions in atomic BEC

Jinbin Li, Yue Yu, Artem M. Dudarev, Qian Niu

Published Aug 30, 2006• 39 citations
arXivHTMLPDF

Abstract

Superfluid to Mott-insulator transitions in atomic Bose–Einstein condensates (BEC) in optical lattices are investigated for the case of number of atoms per site larger than one. To account for mean field repulsion between the atoms in each well, we construct an orthogonal set of Wannier functions. The resulting hopping amplitude and on-site interaction may be substantially different from those calculated with single-atom Wannier functions. As illustrations of the approach, we consider lattices of various dimensionality and different mean occupations. We find that in three-dimensional optical lattices the correction to the critical lattice depth is significant enough to be measured experimentally even for a small number of atoms. Finally, we discuss the validity of the single-band model.

DOI
10.1088/1367-2630/8/8/154

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Superfluid to Mott-insulator transitions in atomic Bose–Einstein condensates (BEC) in optical lattices are investigated for the case of number of atoms per site larger than one. To account for mean field repulsion between the atoms in each well, we construct an orthogonal set of Wannier functions. The resulting hopping amplitude and on-site interaction may be substantially different from those calculated with single-atom Wannier functions. As illustrations of the approach, we consider lattices of various dimensionality and different mean occupations. We find that in three-dimensional optical lattices the correction to the critical lattice depth is significant enough to be measured experimentally even for a small number of atoms. Finally, we discuss the validity of the single-band model.
We show that one can properly take into account of the interaction effects and construct a set of orthonormal Wannier functions for a Bose-Einstein condensate in an optical lattice. These interaction-dependent Wannier functions are used to compute the tunneling rate JJJ and the on-site repulsion UUU in the Bose-Hubbard model. Both parameters are found to be substantially different from ones calculated with the single-particle Wannier functions. Our numerical results of UUU are found in good agreement with the measured on-site energy in a recent experiment [Campbell {\it et al.} Science {\bf 314}, 281 (2006)].
Recent experiments revealed the importance of higher-band effects for the Mott-insulator(MI)--superfluid transition(SF) of ultracold bosonic atoms or mixtures of bosons and fermions in deep optical lattices [Best et al., Phys. Rev. Lett. 102, 030408 (2009); Will et al., Nature (London) 465, 197 (2010)]. In the present work we derive an effective lowest-band Hamiltonian in three dimensions that generalizes the standard Bose-Fermi-Hubbard model taking these effects as well as nonlinear corrections of the tunneling amplitudes mediated by interspecies interactions into account. It is shown that a correct description of the lattice states in terms of the bare-lattice Wannier functions, rather than approximations such as harmonic-oscillator states, is essential. In contrast to self-consistent approaches based on effective Wannier functions, our approach captures the observed reduction of the superfluid phase for repulsive interspecies interactions.
87Rb Bose Einstein Condensate in 3D optical lattice was studied in the regime of weak interaction(the superfluid phase) and strong interaction(the Mott insulating phase). The stability of superfluid currents was studied using a moving optical lattice. The critical momentum for stable superfluid current varies from 0.5 recoil momentum (shallow lattice) to 0 (the Mott insulator) as the system reaches the Mott insulator transition. The phase diagram for the disappearance of superfluidity was studied as a function of momentum and lattice depth. Our phase diagram boundary ex-trapolates to the critical lattice depth for the superfluid-to-MI transition. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed. A new auxiliary vacuum chamber, which is called the science chamber, was de-signed and installed to improve optical lattice experimental performance and imaging resolution power. Atoms are transported from the main chamber to the science cham-ber. By further evaporation cooling, BECs with N- 2-3 x 104 atoms are produced
We have numerically calculated the single-band Wannier functions for interacting Bose gases in optical lattices with a self-consistent approach. We find that the Wannier functions are broadened by repulsive interaction. The tunneling parameter JJJ and the on-site interaction UUU computed with the broadened Wannier functions are found to change significantly with the number of atoms per site. Our theory can explain the nonuniform atomic clock shift observed in Campbell et al., Science 313, 649 (2006).
We study the effects of repulsive on-site interactions on the broadening of the localized Wannier functions used for calculating the parameters to describe ultracold atoms in optical lattices. For this, we replace the common single-particle Wannier functions, which do not contain any information about the interactions, by two-particle Wannier functions obtained from an exact solution which takes the interactions into account. We then use these interaction-dependent basis functions to calculate the Bose-Hubbard model parameters, showing that they are substantially different both at low and high lattice depths from the ones calculated using single-particle Wannier functions. Our results suggest that density effects are not negligible for many parameter ranges and need to be taken into account in metrology experiments.
We study the short-range coherence of ultracold lattice Bose gases in the Mott insulating phase. We calculate the visibility of the interference pattern and the results agree quantitatively with the recent experimental measurement [Phys. Rev. Lett. 95, 050404 (2005)]. The visibility deviation from the inversely linear dependence on the bare on-site interaction U_0 is explained both in smaller and larger U_0. For a smaller U_0, it comes from a second order correction. For a larger U_0, except the breakdown of adiabaticity as analyzed by Gerbier et al, there might be another source to cause this deviation, which is the diversity between U0U_0U0​ determined by the single atom Wannier function and the effective on site interaction U_eff for a multi-occupation per site.