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arXiv:cond-mat/0510567 · Physical Review A

Thermometry of fermionic atoms in an optical lattice

Michael Köhl

Published Mar 8, 2006• 49 citations
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Abstract

Low temperatures are necessary for the observation of strongly correlated quantum phases of fermionic atoms in optical lattices. We analyze how the temperature of a Fermi gas is altered when the fermions are loaded into an optical lattice with an underlying harmonic confining potential, and show how the temperature can be measured. The temperature of the atoms in the optical lattice determines the fraction of doubly occupied lattice sites of a two-component Fermi gas. We analytically calculate this quantity and find a strong temperature dependence. This fraction can be measured by studying the production of molecules in the lattice using a Feshbach resonance, which allows for precise thermometry of atoms in an optical lattice.

DOI
10.1103/physreva.73.031601

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Low temperatures are necessary for the observation of strongly correlated quantum phases of fermionic atoms in optical lattices. We analyze how the temperature of a Fermi gas is altered when the fermions are loaded into an optical lattice with an underlying harmonic confining potential, and show how the temperature can be measured. The temperature of the atoms in the optical lattice determines the fraction of doubly occupied lattice sites of a two-component Fermi gas. We analytically calculate this quantity and find a strong temperature dependence. This fraction can be measured by studying the production of molecules in the lattice using a Feshbach resonance, which allows for precise thermometry of atoms in an optical lattice.
A method is proposed to directly measure the temperature of a gas of weakly interacting fermionic atoms loaded into an optical lattice. This technique relies on Raman spectroscopy and is applicable to experimentally relevant temperature regimes. Additionally, a similar spectroscopy scheme can be used to obtain information on the quasiparticle properties and Hubbard bands of the metallic and Mott-insulating states of interacting fermionic spin mixtures. These two methods provide experimentalists with probes to accurately characterize fermionic quantum gases confined to optical lattices.
We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.
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 propose a method of using off-resonant light scattering to measure the temperature of fermionic atoms tightly confined in a two-dimensional optical-lattice potential. We show that fluctuations of the intensity in the far-field diffraction pattern arising from thermal correlations of the atoms can be accurately detected above the shot noise by collecting photons scattered in a forward direction, with the diffraction maxima blocked. The sensitivity of this method of thermometry is enhanced by an additional harmonic trapping potential.
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 show that, for fermionic atoms in a one-dimensional optical lattice, the fraction of atoms in doubly occupied sites is a highly nonmonotonic function of temperature. We demonstrate that this property persists even in the presence of realistic harmonic confinement, and that it leads to a suppression of entropy at intermediate temperatures that offers a route to adiabatic cooling. Our interpretation of the suppression is that such intermediate temperatures are simultaneously too high for quantum coherence and too low for significant thermal excitation of double occupancy thus offering a clear indicator of the onset of quantum fluctuations.