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arXiv:1107.4349 · Physical Review A

Thermal versus quantum fluctuations of optical-lattice fermions

V. L. Campo, Klaus Capelle, C. Hooley, Jorge Quintanilla, V. W. Scarola

Published Mar 29, 2012• 8 citations
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Abstract

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.

DOI
10.1103/physreva.85.033644

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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.
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Motivated by recent experiments with ultracold fermionic atoms in optical lattices, we study finite temperature magnetic correlations, as singlet and triplet correlations, and the double occupancy in the one-dimensional Hubbard model. We point out that for intermediate interaction strengths the double occupancy has an intriguing doubly nonmonotonic temperature dependence due to the competition between spin and charge modes, related to the Pomeranchuk effect. Furthermore, we determine properties of magnetic correlations in the temperature regimes relevant for current cold atom experiments and discuss effects of the trap on spatially integrated observables. We estimate the entropy and the temperature reached in the experiment by Greif, Uehlinger, Jotzu, Tarruell, and Esslinger [Science 340, 1307 (2013)].
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.
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We study the ground state properties of ultracold fermions trapped in a one-dimensional double-well optical lattice by using the density-matrix renormalization group method. The system is described by an extended Hubbard model with alternating hopping integrals and an external harmonic confining potential. We clarify the characteristic features of the metal–insulator phase transition originating from the double-well structure of the lattices. Several different types of insulating regions coexist when the number of atoms at each site is an integer or a half integer. We found that each insulating phase except for a band insulator exhibits rather large local density fluctuations, reflecting the strong dimerization of atoms within the unit cells of double-well lattices. The phase characteristics are elucidated in detail by investigating the profiles of the local density of atoms, the local density (spin) fluctuations, the double-occupancy probability and the spatially extended sp in correlations.