Double occupancies in confined attractive fermions on optical lattices

Abstract

We perform a numerical study of a one-dimensional Fermion-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The ρ − U/t phase diagram is shown for the systems of attractive interactions (ρ is the characteristic density and U/t the interaction strength scaled in units of the hopping parameter.). We study the double occupancy, the local central density and their derivatives. Their roles are discussed in details in detecting the composite phases induced by the trapping potential.PACS numbers: 05.30. Fk,03.75.Ss,71.10.Pm,71.15.Pd The recent remarkable experimental progress in cooling and manipulating ultracold atomic gases in optical lattices provides us an alternative way to investigate the many-body effects in condensed matter system [1]. For the optical lattices loaded with atomic gases, the on-site interaction between different species can be tuned to be very strong by means of a technique named Feshbach resonance [2] or by increasing the lattice depth to decrease the hopping between neighbor sites. Thus the outstanding controllability offers the possibility to use these systems to "quantum simulate" quantum manybody physics in a well-controlled way. An example is the experimentally realized Tonks-Girardeau gas in a onedimensional (1D) optical lattice [3].In the experiments, the trapping potential used to confine atoms induces inhomogeneity and complexity in characterizing the quantum phases. Though a few techniques exist in experiments observing the new quantum phases and probing various properties in ultracold gases in optical lattices, such as the time-of-flight imaging of the momentum distribution, noise correlations and Bragg spectroscopy [1], there are difficulties in observing the composite phases induced by the inherent trapping potential, for example, the incompressible bulk Mott-and band-insulating phases surrounded by the compressible fluid phases at the edges in the 1D Fermi-Hubbard model under harmonic confinement. Scarola et al. proposed to use the core compressibility by filtering out the edge effects, which offers a direct probe of incompressible phases independent of inhomogeneity [4]. Duan et al. suggested to use the Fourier sampling of time-of-flight images to reveal new correlation functions [5]. Kollath et al. used the double occupancy (DO) induced by periodic lattice modulations via the creation of molecules to identify the pairbinding energy and the spin-ordering in a Fermi gas in an optical lattice [6], which was recently measured in the experiments by molecule formation and used to identify an incompressible Mott-insulator phase of two hyperfine states of strongly repulsive fermionic 40 K atoms [7]. The * Electronic address: gaoxl@zjnu.edu.cn compressibility of the quantum gas in the trap was used recently in identifying the incompressible Mott-insulating phase at strong interactions by independent control of external confinement and lattice depth [8]. Here in this paper we discuss how to characterize the different composit...

Boson core compressibility

“…Comparisons between hightemperature series expansions, dynamical mean-field theory, and experiment were also useful in using double occupancy to measure the temperature of fermions in optical lattices [25]. More recent calculations have shown that the fermion core compressibility can be very useful in one-dimensional optical lattices as well [26,27].…”

Compressibility and entropy of cold fermions in one-dimensional optical lattices

“…Parallel to the experimental progress of manipulating fermions in optical lattices, recently there have been theoretical studies on the role of an external harmonic potential and its effect on compressibility and double occupancies [11][12][13][14][15][16]. The underlying harmonic trapping potential present in all cold-gas experiments causes density to vary across the lattice.…”

“…At zero temperature and high temperatures, our work is complementary to some of the work presented in Refs. [11][12][13][14][15][16][17]. However, we go beyond these studies by systematically extending zero-temperature calculations to any finite temperature.…”