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arXiv:1009.4737 · Physical Review Letters

Interaction-Dependent Temperature Effects in Bose-Fermi Mixtures in Optical Lattices

M. Cramer

Published May 26, 2011• 11 citations
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Abstract

We present a quantitative finite temperature analysis of a recent experiment with Bose-Fermi mixtures in optical lattices, in which the dependence of the coherence of bosons on the interspecies interaction was analyzed. Our theory reproduces the characteristics of this dependence and suggests that intrinsic temperature effects play an important role in these systems. Namely, under the assumption that the ramping up of the optical lattice is an isentropic process, adiabatic temperature changes of the mixture occur that depend on the interaction between bosons and fermions. Matching the entropy of two regimes-no lattice on the one hand and deep lattices on the other-allows us to compute the temperature in the lattice and the visibility of the quasimomentum distribution of the bosonic atoms, which we compare to the experiment.

DOI
10.1103/physrevlett.106.215302

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We present a quantitative finite temperature analysis of a recent experiment with Bose-Fermi mixtures in optical lattices, in which the dependence of the coherence of bosons on the interspecies interaction was analyzed. Our theory reproduces the characteristics of this dependence and suggests that intrinsic temperature effects play an important role in these systems. Namely, under the assumption that the ramping up of the optical lattice is an isentropic process, adiabatic temperature changes of the mixture occur that depend on the interaction between bosons and fermions. Matching the entropy of two regimes-no lattice on the one hand and deep lattices on the other-allows us to compute the temperature in the lattice and the visibility of the quasimomentum distribution of the bosonic atoms, which we compare to the experiment.
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When atoms are loaded into an optical lattice, the process of gradually turning on the lattice is almost adiabatic. In this paper, we investigate how the temperature changes when going from the gapless superfluid phase to the gapped Mott phase along isentropic lines. To do so we calculate the entropy in the single-band Bose–Hubbard model for various densities, interaction strengths and temperatures in one and two dimensions for homogeneous and trapped systems. Our theory is able to reproduce the experimentally observed visibilities and therefore strongly supports the view that current experiments remain in the quantum regime for the considered lattice depths with low temperatures and minimal heating.
We analyze the effects of adiabatic ramping of optical lattices on the temperature of spin-1 bosons in a homogeneous lattice. Using mean-field theory, we present the isentropes in the temperature-interaction strength (T,U0T,{U}_{0}T,U0​) plane for ferromagnetic, antiferromagnetic, and zero spin couplings. Following the isentropic lines, temperature changes can be determined during adiabatic loading of current experiments. We show that the heating-cooling separatrix lies on the superfluid-Mott phase boundary with cooling occurring within the superfluid and heating in the Mott insulator and quantify the effects of spin coupling on the heating rate. We find that the mean-field isentropes for low initial entropy terminate at the superfluid--Mott-insulator phase boundary.
We investigate a bosonic quantum gas consisting of two interacting species in an optical lattice at zero and finite temperature. The equilibrium properties and dynamics of this system are obtained by means of the Gutzwiller mean-field method. In particular we model recent experiments where the ramp-up of the optical lattice occurs on a time scale comparable to the tunneling time of the bosons. We demonstrate the violation of adiabaticity of this process with respect to the many-body quantum states, and we reproduce and explain the oscillations of the visibility as a function of ramp-up time, as seen in experiments.
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.
We investigate a Bose-Fermi mixture in a three-dimensional optical lattice, trapped in a harmonic potential. Using generalized dynamical mean-field theory, which treats the Bose-Bose and Bose-Fermi interaction in a fully nonperturbative way, we show that for experimentally relevant parameters a peak in the condensate fraction close to the point of vanishing Bose-Fermi interaction is reproduced within a single-band framework. We identify two physical mechanisms contributing to this effect: the spatial redistribution of particles when the interspecies interaction is changed and the reduced phase space for strong interactions, which results in a higher temperature at fixed entropy.