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Fermion induced superfluid decoherence in the boson Hubbard model on an optical lattice

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

Published Dec 3, 2008• 0 citations
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Abstract

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.

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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.
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.
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 mixture of the scalar bosonic and the spinless or polarized fermionic cold atoms in the one-dimensional optical lattice is studied. The system is modeled by the Bose-Fermi-Hubbard Hamiltonian, which shows different behavior from that of the Bose-Hubbard or the Fermi-Hubbard models. Because the $\text{SU}(1\ensuremath{\mid}1)$-supersymmetric Bethe ansatz solution gives an excellent approximation to this kind of mixed cold atomic systems, the ground-state properties of the system such as the densities of state in the momentum space are obtained based on the Bethe ansatz. If the number of bosons is equal to that of fermions and the filling factor is 1, it is found that there exists a critical on-site interaction Uc{U}_{c}Uc​. If U<UcU<{U}_{c}U<Uc​, the ground state of the system is in the superfluid phase, while if U>UcU>{U}_{c}U>Uc​, the ground state is in the insulating phase. The superfluid-insulator transition occurs at Uc{U}_{c}Uc​. From the analysis of the superfluid density, the value of the critical point is determined as Uc=2.79256{U}_{c}=2.79256Uc​=2.79256, which is larger than the Uc=0{U}_{c}=0Uc​=0 for the Fermi-Hubbard model and smaller than the Uc=3.28{U}_{c}=3.28Uc​=3.28 for the Bose-Hubbard model. The elementary excitations and effective Hamiltonian in the strong-coupling limit are also discussed.
We analyze the finite-temperature phase diagram of the boson-fermion-Hubbard model with Feshbach converting interaction, using the coherent-state path-integral method. We show that depending on the position of the bosonic band, this type of interaction, even if weak, can drive the system into the resonant superfluid phase in the strong bosonic interaction limit. It turns out that this phase can exist for an arbitrary number of fermions (i.e., fermionic concentration between 0 and 2), but with the bosonic particle number very close to an integer value. We point out that the standard time-of-flight method in optical lattice experiments can be an adequate technique to confirm the existence of this resonant phase. Moreover, in the nonresonant regime, the enhancement of the critical temperature of the superfluid phase due to Feshbach interaction is also observed. We account for this interesting phenomena for a hole- or particlelike pairing mechanism depending on the system density and mutual location of the fermionic and bosonic bands.
We study the ground-state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive and has similarities with electron-phonon coupling in crystals. We investigate behavior of the mixtures in the limit, where the Bogoliubov sound velocity that dictates bosonic dynamics is comparable to the Fermi velocity, hence the retardation effects are an important part of the physics. The dynamic Lindhard response function of the fermionic density to changes in the bosonic number of particles above some critical frequency can alter the sign, and consequently the interspecies interaction between particles becomes repulsive in contrast to the static limit (instantaneous and always attractive). Considering the above, we show that the structure of the phase diagrams crucially depends on the difference in masses of the bosons and fermions. We discuss the situations where integrating out the fermionic field provides an additional interaction that can decrease or increase bosonic coherence.
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.