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Physical Review A

Superfluid properties of ultracold fermionic atoms in two-dimensional optical lattices

Yusuke Fujihara, Akihisa Koga, Norio Kawakami

Published Jun 23, 2010• 5 citations
Publisher

Abstract

We investigate two-component ultracold fermionic atoms with attractive interactions trapped in a two-dimensional optical lattice at zero temperature. By introducing a superfluid trial state with spatially modulated order parameters, we perform the variational Monte Carlo simulations to treat the correlation effects beyond mean-field treatments. It is shown that there appears a strong tendency to the formation of a density wave state in the regions with specific values of local atom density. We then analyze two kinds of perturbations to the superfluid state and show that a coexisting state of superfluid and density wave ordering, a sort of supersolid state, can be stabilized. It is discussed how the trap potential and the resulting spatial modulation of the superfluid state affect the momentum distributions and the noise correlation functions.

DOI
10.1103/physreva.81.063627

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We investigate two-component ultracold fermionic atoms with attractive interactions trapped in a two-dimensional optical lattice at zero temperature. By introducing a superfluid trial state with spatially modulated order parameters, we perform the variational Monte Carlo simulations to treat the correlation effects beyond mean-field treatments. It is shown that there appears a strong tendency to the formation of a density wave state in the regions with specific values of local atom density. We then analyze two kinds of perturbations to the superfluid state and show that a coexisting state of superfluid and density wave ordering, a sort of supersolid state, can be stabilized. It is discussed how the trap potential and the resulting spatial modulation of the superfluid state affect the momentum distributions and the noise correlation functions.
We investigate two-component ultracold fermionic atoms with repulsive interactions trapped in an optical lattice with ladder structure. By applying the Bogoliubov--de Gennes equations to an effective $t\text{\ensuremath{-}}J$ model in the strong correlation limit, we discuss how the spatially modulated spin-singlet pairs with ddd-wave-like symmetry are formed in the systems with trapping potentials. Furthermore, a close examination of the condensation energy as well as the local average of potential, kinetic, and exchange energies by means of the variational Monte Carlo method elucidates that local particle correlations enhance the stability of the superfluid state via a substantial energy gain due to singlet pairing in the high particle density region.
We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by means of the dynamical mean-field approximation. It is demonstrated that a supersolid state, where an s-wave superfluid coexists with a density-wave state with a checkerboard pattern, is stabilized by attractive onsite interactions on a square lattice. Our new finding here is that a confining potential plays an invaluable role in stabilizing the supersolid state. We establish a rich phase diagram at low temperatures, which clearly shows how the insulator, the density wave and the superfluid compete with each other to produce an intriguing domain structure. Our results shed light on the possibility of the supersolid state in fermionic optical lattice systems.
We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by combining the real-space dynamical mean-field theory with a two-site impurity solver. By calculating the local particle density and the pair potential in the systems with different clusters, we discuss the stability of a supersolid state, where an sss-wave superfluid coexists with a density-wave state of checkerboard pattern. It is clarified that a confining potential plays an essential role in stabilizing the supersolid state. The phase diagrams are obtained for several effective particle densities.
We study properties of ultracold quantum gases trapped in 1D and under the influence of an underlying optical lattice. We analyze both fermionic and bosonic systems following different numerically exact approaches, like quantum Monte Carlo for soft-core bosons and two-species fermions, and a recently developed exact approach for HCB. The exposition is organized as follows. In Chap. 2, we study single species degenerated fermions on 1D lattices. We show that a splitting of the system takes place in a region of the spectrum with eigenstates that have a non-vanishing weight only in a fraction of the system. We also show that if on top of the lattice an alternating potential is introduced, doubling the original periodicity, an additional slicing' of the system can be achieved. The width and number of such regions can be controlled in a given energy range by the amplitude of the new modulation. By filling these systems the ground state may exhibit insulating regions due to the presence of local gaps, which can be observed in the local density of states. As a complement to these 1D results we present in Appendix A results obtained in 2D lattices. In Chap. 3 we review in some detail the two quantum Monte Carlo (QMC) techniques that are relevant to our study of confined soft-core bosons and two-species fermions on optical lattices, the worldline QMC and the zero temperature projector QMC, respectively. The basis of the classical Monte Carlo method are also presented, included a proof of the Central Limit theorem (Appendix B) that establishes its foundations. Properties of soft-core bosons confined on optical lattices are presented in Chap. 4. QMC simulations show that due to the presence of the slowly varying confining potential the concept of commensurability, typical for periodic systems, loses its meaning. Mott domains appears for a continuous range of fillings and always coexist with superfluid phases, as it was mentioned before. The latter feature is reflected by the behavior of the global compressibility, which never vanishes. A local compressibility, proportional to the variance of the local density, is defined in order to characterize the local Mott-insulating phases. Finally, a phase diagram for trapped systems is also presented. In Chap. 5 we study the ground state properties of two-components fermions confined on optical lattices. Like for the bosonic case, Mott domains also appear for a continuous range of fillings and always coexist with compressible phases. We define a local order parameter (that we denominate local compressibility), which characterizes the Mott insulating phases in an unambiguous way. By means of this local compressibility, we study in detail the interphase between the metallic and insulating region finding that critical behavior sets in revealing a new critical exponent. Furthermore, the behavior of the local compressibility and the variance of the density are found to be universal in this case, independently of the confining potential and the strength of the interaction, as usual in critical phenomena. We present in Chap. 6 a recently developed exact numerical approach that allows to study ground state properties of HCB confined on 1-D lattices. This exact treatment is applied to study the off-diagonal behavior of the one-particle density matrix (OPDM) and related quantities in the equilibrium case. We find that the OPDM decays as a power-law x^-1/2 for large-x, irrespective of the confining potential chosen. The power-law above is shown to determine the scaling of the occupation of the lowest natural orbital in the thermodynamic limit. This scaling and its finite size corrections are also studied for arbitrary powers of the confining potential. In addition, we find a power-law decay of the NO occupations at low densities, and show that its exponent is also universal. The low density limit in the lattice, equivalent to continuous systems, is also analyzed in detail. The approach above is generalized in Chap. 7 to study the non-equilibrium dynamics of HCB in 1-D configurations with an underlying lattice. The presence of the lattice enables the creation of pure Fock states of HCB (a HCB per lattice site) where there is no coherence in the system. We show that quasi-long range correlations develop in the equal-time-one-particle density matrix when such states are allowed to evolve freely, and that they lead to the formation of quasi-condensates of HCB at finite momentum. In addition,we obtain an universal power-law describing the population of the quasi-condensate as a function of time. Finally, we discuss how such systems can be used to create atom lasers with a wave-length that can be controlled through the lattice parameter.
The presence of attractive interaction between fermions can lead to pairing and superfluidity in an optical lattice. The temperature needed to observe superfluidity is about a tenth of the tunneling energy in the optical lattice, and currently beyond experimental reach. However, at strong coupling the precursors to global superfluidity should be visible at achievable temperatures, in terms of fluctuating domains with strong pairing correlations. We explore this regime of the attractive two dimensional fermion Hubbard model, in the presence of a confining potential, using a new Monte Carlo technique. We capture the low temperature inhomogeneous superfluid state with its unusual spectral signatures but mainly focus on the experimentally accessible intermediate temperature state. In this regime, and for the trap center density we consider, there is a large pairing amplitude at the center, spatially correlated into domains extending over several lattice spacings. We map out the thermal evolution of the local density, the double occupancy, the pairing correlations, and the momentum distribution function across this phase fluctuation window.