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arXiv:1005.3576 · Physical Review A

Thermodynamic properties of two-component fermionic atoms trapped in a two-dimensional optical lattice

Kensuke Inaba, Makoto Yamashita

Published Jun 9, 2010• 1 citation
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Abstract

We study the finite-temperature properties of two-component fermionic atoms trapped in a two-dimensional (2D) optical lattice. We apply the self-energy functional approach to the 2D Hubbard model with a harmonic-trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott-insulating and the metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusplike anomaly at lower temperatures, suggesting a second- or higher-order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition.

DOI
10.1103/physreva.81.063615

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We study the finite-temperature properties of two-component fermionic atoms trapped in a two-dimensional (2D) optical lattice. We apply the self-energy functional approach to the 2D Hubbard model with a harmonic-trapping potential, and systematically investigate the thermodynamic properties of this system. We find that entropy and grand potential provide evidence of a crossover between the Mott-insulating and the metallic phases at certain temperatures. In addition, we find that entropy exhibits a cusplike anomaly at lower temperatures, suggesting a second- or higher-order antiferromagnetic transition. We estimate the antiferromagnetic transition temperatures, and clarify how the trapping potential affects this magnetic transition.
We calculate several thermodynamic quantities for repulsively interacting one-dimensional fermions. We solve the Hubbard model at both zero and finite temperatures using the Bethe-ansatz method. For arbitrary values of the chemical potential, we calculate the particle number density, the double occupancy, various compressibilities, and the entropy as a function of temperature and interaction. We find that these thermodynamic quantities show a characteristic behavior so that measurements of these quantities can be used as a detection of temperature, the metal-insulator transition, and metallic and insulating phases in the trap environment. Further, we discuss an experimental scheme to extract these thermodynamic quantities from the column density profiles. The entropy and the compressibility of the entire trapped atomic cloud also reveal characteristic features indicating whether insulating and/or metallic phases coexist in the trap.
We investigate finite-temperature properties of three-component (color) repulsive fermionic atoms in optical lattices at half filling using a self-energy functional approach. For a certain anisotropy of the interactions, we find a color density-wave (DW) state at low temperatures. In the weakly interacting region, the second-order phase transition from the color DW state to the Fermi-liquid state occurs with increasing temperature. In the strongly interacting region, by contrast, the first-order transition from the color DW state to a color selective Mott transition (CSMT) state or a Mott insulating state occurs. As the interaction increases above the critical temperatures, we observe a crossover from the CSMT state to the Mott insulating state.
We experimentally study the emergence of antiferromagnetic correlations between ultracold fermionic atoms in a two-dimensional optical lattice with decreasing temperature. We determine the uniform magnetic susceptibility of the two-dimensional Hubbard model from simultaneous measurements of the in situ density distribution of both spin components. At half filling and strong interactions our data approach the Heisenberg model of localized spins with antiferromagnetic correlations. Moreover, we observe a fast decay of magnetic correlations when doping the system away from half filling.
We calculate experimentally relevant properties of trapped fermionic alkaline-earth-metal atoms in an optical lattice, modeled by the SU(N)(N)(N) Hubbard model. We employ a high-temperature expansion that is accurate when the temperature is larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a noninteracting gas, as a function of initial gas temperature. Of particular experimental interest, we find that increasing NNN for fixed particle numbers and initial temperatures gives substantially colder Mott insulators after the adiabatic ramping, up to more than a factor of 5 for relevant parameters. This cooling happens for all NNN, fixing the initial entropy, or for all $N\ensuremath{\lesssim}20$ (the exact value depends on dimensionality), at fixed, experimentally relevant initial temperatures.
We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.
One of the major challenges in realizing antiferromagnetic and superfluid phases in optical lattices is the ability to cool fermions. We determine constraints on the entropy for observing these phases in two-dimensional Hubbard models using determinantal quantum Monte Carlo simulations. We find that an entropy per particle approximately = ln2 is sufficient to observe the insulating gap in the repulsive Hubbard model at half-filling, or the pairing pseudogap in the attractive case. Observing antiferromagnetic correlations or superfluidity in 2D systems requires a further reduction in entropy by a factor of 3 or more. In contrast with higher dimensions, we find that adiabatic cooling is not useful to achieve the required low temperatures. We also show that double-occupancy measurements are useful for thermometry for temperatures greater than the nearest-neighbor hopping energy.