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arXiv:cond-mat/0301544 · Physical Review A

Three-fluid description of the sympathetic cooling of a boson-fermion mixture

Michiel Wouters, Jacques Tempere, J. T. Devreese

Published Oct 23, 2002• 14 citations
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Abstract

We present a model for sympathetic cooling of a mixture of fermionic and bosonic atomic gases in harmonic traps, based on a three-fluid description. The model confirms the experimentally observed cooling limit of about ${0.2T}_{F}$ when only bosons are pumped. We propose sequential cooling---pumping first of bosons and afterward fermions---as a way to obtain lower temperatures. For this scheme, our model predicts that temperatures less than ${0.1T}_{F}$ can be reached.

DOI
10.1103/physreva.66.043414

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We present a model for sympathetic cooling of a mixture of fermionic and bosonic atomic gases in harmonic traps, based on a three-fluid description. The model confirms the experimentally observed cooling limit of about 0.2TF{0.2T}_{F}0.2TF​ when only bosons are pumped. We propose sequential cooling---pumping first of bosons and afterward fermions---as a way to obtain lower temperatures. For this scheme, our model predicts that temperatures less than 0.1TF{0.1T}_{F}0.1TF​ can be reached.
The study of low density, ultracold atomic Fermi gases is a promising avenue to understand fermion superfluidity from first principles. One technique currently used to bring Fermi gases in the degenerate regime is sympathetic cooling through a reservoir made of an ultracold Bose gas. We discuss a proposal for trapping and cooling of two-species Fermi-Bose mixtures into optical dipole traps made from combinations of laser beams having two different wavelengths. In these bichromatic traps it is possible, by a proper choice of the relative laser powers, to selectively trap the two species in such a way that fermions experience a stronger confinement than bosons. As a consequence, a deep Fermi degeneracy can be reached having at the same time a softer degenerate regime for the Bose gas. This leads to an increase in the sympathetic cooling efficiency and allows for higher precision thermometry of the Fermi - Bose mixture.
We study the sympathetic cooling of a trapped Fermi gas interacting with an ideal Bose gas below the critical temperature of the Bose-Einstein condensation. We derive the quantum master equation, which describes the dynamics of the fermionic component, and postulating the thermal distribution for both gases we calculate analytically the rate at which fermions are cooled by the bosonic atoms. The particle losses constitute an important source of heating of the degenerate Fermi gas. We evaluate the rate of loss-induced heating and derive analytical results for the final temperature of fermions, which is limited in the presence of particle losses.
We discuss a sympathetic cooling strategy that can successfully mitigate fermion-hole heating in a dilute atomic Fermi-Bose mixture and access the temperature regime in which the fermions behave as a Fermi liquid. We introduce an energy-based formalism to describe the temperature dynamics with which we study a specific and promising mixture, composed of 6Li^{6}\mathrm{Li}6Li and 87Rb^{87}\mathrm{Rb}87Rb. Analyzing the harmonically trapped mixture, we find that the favorable features of this mixture are further enhanced by using different trapping frequencies for the two species.
Sympathetic cooling of two atomic isotopes is experimentally investigated. Using forced evaporation of a bosonic 7Li{}^{7}\mathrm{Li}7Li gas in a magnetic trap, a sample of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ 6Li{}^{6}\mathrm{Li}6Li fermions has been sympathetically cooled to $9(3) \ensuremath{\mu}\mathrm{K},$ corresponding to 2.2(0.8)2.2(0.8)2.2(0.8) times the Fermi temperature. The measured rate constant for two-body inelastic collisions of the 7Li{}^{7}\mathrm{Li}7Li ∣2,2〉|2,2〉∣2,2〉 state at low magnetic field is ${1.0}_{\ensuremath{-}0.5}^{+0.8}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14} {\mathrm{cm}}^{3}{\mathrm{s}}^{\ensuremath{-}1}.$
The standard approach for generating deeply degenerate quantum gases is evaporative or sympathetic cooling in a harmonic trap, after which the gas has reached its minimum entropy. All subsequent state transformations rely on adiabatic changes of a closed system, and coupling to the environment or non-adiabatic processes monotonically increase the entropy. Here, we demonstrate that this experimental paradigm can be bypassed by utilizing species-selective trapping with a low-dissipation optical tune-out trap in a dual-species mixture. We successfully reduce the entropy of a two-component fermionic quantum gas via isothermal compression within a bosonic bath, reaching deep quantum degeneracy of T/TF=0.024+0.007T/T_F = 0.024^{+0.007}T/TF​=0.024+0.007, with TFT_FTF​ the Fermi temperature. By characterizing the cross-dimensional relaxation and thermalization, we demonstrate that cooling light fermions with heavy bosons remains efficient and fast, even deep in the degenerate regime, where the thermalization time is found to be independent of T/TFT/T_FT/TF​. Our results pave the way for direct cooling within optical lattices, box traps, or other complex potentials, thereby eliminating the reliance on adiabatic state transformations to reach strongly interacting many-body regimes.
We discuss the cooling efficiency of ultracold Fermi-Bose mixtures in species-selective traps using a thermodynamical approach. The dynamics of evaporative cooling trajectories is analyzed in the specific case of bichromatic optical dipole traps also taking into account the effect of partial spatial overlap between the Fermi gas and the thermal component of the Bose gas. We show that large trapping frequency ratios between the Fermi and the Bose species allow for the achievement of a deeper Fermi degeneracy, consolidating in a thermodynamic setting earlier arguments based on more restrictive assumptions. In particular, we confirm that the minimum temperature of the mixture is obtained at the crossover between boson and fermion heat capacities, and that below such a temperature sympathetic cooling vanishes. When the effect of partial overlap is taken into account, optimal sympathetic cooling of the Fermi species may be achieved by properly tuning the relative trapping strength of the two species in a time-dependent fashion. Alternatively, the dimensionality of the trap in the final stage of cooling can be changed by increasing the confinement strength, which also results in a crossover of the heat capacities at deeper Fermi degeneracies. This technique may be extended to Fermi-Bose degenerate mixtures in optical lattices.