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arXiv:0804.2915 · Physical Review A

Preparing a highly degenerate Fermi gas in an optical lattice

Jason Williams, J. H. Huckans, R.W. Stites, E.L. Hazlett, Kenneth M. O’Hara

Published Jul 30, 2010• 7 citations
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Abstract

We propose a method to prepare fermionic atoms in a three-dimensional optical lattice at unprecedentedly low temperatures and uniform filling factors. The process involves adiabatic loading of degenerate atoms into multiple energy bands of an optical lattice followed by a filtering stage whereby atoms from all but the lowest band are removed. Of critical importance is the use of a nonharmonic trapping potential to provide external confinement for the atoms. For realistic experimental parameters, this procedure will produce a Fermi gas in a lattice with a reduced temperature $T/{T}_{F}~0.003$ and an entropy per particle of $s~0.02 {k}_{B}$.

DOI
10.1103/physreva.82.011610

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We propose a method to prepare fermionic atoms in a three-dimensional optical lattice at unprecedentedly low temperatures and uniform filling factors. The process involves adiabatic loading of degenerate atoms into multiple energy bands of an optical lattice followed by a filtering stage whereby atoms from all but the lowest band are removed. Of critical importance is the use of a nonharmonic trapping potential to provide external confinement for the atoms. For realistic experimental parameters, this procedure will produce a Fermi gas in a lattice with a reduced temperature T/TF 0.003T/{T}_{F}~0.003T/TF​ 0.003 and an entropy per particle of s 0.02kBs~0.02 {k}_{B}s 0.02kB​.
We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.
The entropy-temperature curves are calculated for noninteracting fermions in a three-dimensional optical lattice. These curves facilitate understanding of how adiabatic changes in the lattice depth affect the temperature, and we demonstrate regimes in which the atomic sample can be significantly heated or cooled. When the Fermi energy of the system is near the location of a band gap, the cooling regimes disappear for all temperatures and the system can be heated by only lattice loading. For samples with greater than one fermion per site, we find that lattice loading can lead to a large increase in the degeneracy of the system. We study the scaling properties of the system in the degenerate regimes and assess the effects of nonadiabatic loading.
Abstract. We report on the realization of a strongly interacting quantum degenerate gas of fermionic atoms in a three-dimensional optical lattice. We prepare a bandinsulating state for a two-component Fermi gas with one atom per spin state per lattice site. Using a Feshbach resonance, we induce strong interactions between the atoms. When sweeping the magnetic field from the repulsive side towards the attractive side of the Feshbach resonance we induce a coupling between Bloch bands leading to a transfer of atoms from the lowest band into higher bands. Sweeping the magnetic field across the Feshbach resonance from the attractive towards the repulsive side leads to two-particle bound states and ultimately to the formation of molecules. From the fraction of formed molecules we determine the temperature of the atoms in the lattice.
We report on the realization of a strongly interacting quantum degenerate gas of fermionic atoms in a three-dimensional optical lattice. We prepare a band-insulating state for a two-component Fermi gas with one atom per spin state per lattice site. Using a Feshbach resonance, we induce strong interactions between the atoms. When sweeping the magnetic field from the repulsive side towards the attractive side of the Feshbach resonance we induce a coupling between Bloch bands leading to a transfer of atoms from the lowest band into higher bands. Sweeping the magnetic field across the Feshbach resonance from the attractive towards the repulsive side leads to two-particle bound states and ultimately to the formation of molecules. From the fraction of formed molecules we determine the temperature of the atoms in the lattice.
We propose an experimental procedure to cool fermionic atoms loaded into an optical lattice. The central idea is to spatially divide the system into entropy-rich and -poor regions by shaping the confining potential profile. Atoms in regions of high entropy per particle are subsequently isolated from the system. We discuss how to experimentally carry out this proposal and perform a quantitative study of its efficiency. We find that the entropy per particle, sss, can typically be reduced by a factor of 10 such that entropies lower than $s/{k}_{B}\ensuremath{\sim}0.2$ can be reached. Cooling into highly sought-after quantum phases (such as an antiferromagnet) can thus be achieved. We show that this procedure is robust against variations of the experimental conditions.
In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas, we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favorable conditions for realizing degenerate Fermi gases in optical lattices.