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arXiv:0812.0815 · Physical Review A

Loss of superfluidity by fermions in the boson Hubbard model on an optical lattice

Roman M. Lutchyn, Sumanta Tewari, S. Das Sarma

Published Jan 30, 2009• 24 citations
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Abstract

The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of bosons to higher Bloch bands, coupled with contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss the implications for cold-atom experiments where expansion of the Mott lobes by fermions has been conclusively established.

DOI
10.1103/physreva.79.011606

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The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of bosons to higher Bloch bands, coupled with contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discuss the implications for cold-atom experiments where expansion of the Mott lobes by fermions has been conclusively established.
We study the phase diagram of a degenerate gas of bosons in an optical lattice, described by the boson Hubbard Hamiltonian, interacting with spin-polarized fermions. Virtual transitions of the bosons to the higher Bloch bands, coupled with the contact interspecies interactions of either sign, result in an effective increase of the bosonic on-site repulsion. If this renormalization of the on-site potential is dominant over the fermionic screening of the boson interactions, superfluid coherence of the Bose-Hubbard system will be reduced by the fermions. We discuss experimental implications for cold atomic systems.
Building on the work of Fisher et al. [Phys. Rev. B 40, 546 (1989)], we develop the perturbation theory for the Bose-Hubbard model and apply it to calculate the effects of a degenerate gas of spin-polarized fermions interacting by contact interactions with the constituent bosons. For the single-band Bose-Hubbard model, we find that the net effect of the screening of the boson on-site interaction by the fermions is to suppress the Mott-insulating lobes in the Bose-Hubbard phase diagram. For the more general multiband model, we find that, in addition to the fermion screening effects, the virtual excitations of the bosons to the higher Bloch bands, coupled with the contact interactions with the fermions, result in an effective increase (decrease) of the boson on-site repulsion (hopping parameter). If the higher-band renormalization of the boson parameters is dominant over the fermion screening of the interaction, the Mott-insulating lobes in the Bose-Hubbard phase diagram are enhanced for either sign of the Bose-Fermi interactions, consistent with the recent experiments.
The extended effective multiorbital Bose–Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid–Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.
We theoretically investigate the enhanced localization of bosonic atoms by fermionic atoms in three-dimensional optical lattices and find a self-trapping of the bosons for attractive boson-fermion interaction. Because of this mutual interaction, the fermion orbitals are substantially squeezed, which results in a strong deformation of the effective potential for bosons. This effect is enhanced by an increasing bosonic filling factor leading to a large shift of the transition between the superfluid and the Mott-insulator phase. We find a nonlinear dependency of the critical potential depth on the boson-fermion interaction strength. The results, in general, demonstrate the important role of higher Bloch bands for the physics of attractively interacting quantum gas mixtures in optical lattices and are of direct relevance to recent experiments with 87Rb-40K mixtures, where a large shift of the critical point has been found.
In this paper, the quantum phase transition between the superfluid state and the Mott-insulator state is studied based on an extended Bose-Hubbard model with two- and three-body on-site interactions. By employing the mean-field approximation we find the extension of the insulating ``lobes'' and the existence of a fixed point in three-dimensional phase space. We investigate the link between experimental parameters and theoretical variables. The possibility to observe our results through some experimental effects in optically trapped Bose-Einstein condensates is also discussed.
The Mott-insulator--superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.