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arXiv:0903.0108

Accessing the Neel phase of ultracold fermionic atoms in a simple-cubic optical lattice

Charles Mathy, David A. Huse

Published Feb 28, 2009• 0 citations
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Abstract

We examine the phase diagram of a simple-cubic optical lattice half-filled by two species of fermionic atoms with a repulsive s-wave contact interaction. We use the Hartree approximation in the regime of weaker interactions, and a Hubbard model approximation in the Mott insulating phase. The regime where the Neel phase of this system is likely to be most accessible to experiments is at intermediate lattice strengths and interactions, and our two approximations agree fairly well in this regime. We discuss the various issues that may determine where in this phase diagram the Neel phase is first produced and detected experimentally, and analyze the quantum phases that occur in the intermediate lattice strength regime.

DOI
10.48550/arxiv.0903.0108

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We examine the phase diagram of a simple-cubic optical lattice half-filled by two species of fermionic atoms with a repulsive s-wave contact interaction. We use the Hartree approximation in the regime of weaker interactions, and a Hubbard model approximation in the Mott insulating phase. The regime where the Neel phase of this system is likely to be most accessible to experiments is at intermediate lattice strengths and interactions, and our two approximations agree fairly well in this regime. We discuss the various issues that may determine where in this phase diagram the Neel phase is first produced and detected experimentally, and analyze the quantum phases that occur in the intermediate lattice strength regime.
We examine the phase diagram of a simple-cubic optical lattice half filled by two species of fermionic atoms with a repulsive sss-wave contact interaction. We use the Hartree approximation in the regime of weaker interactions and a Hubbard model approximation in the Mott insulating phase. The regime where the N\'eel phase of this system is likely to be most accessible to experiments is at intermediate lattice strengths and interactions, and our two approximations agree fairly well in this regime. We discuss the various issues that may determine where in this phase diagram the N\'eel phase is first produced and detected experimentally, and analyze the quantum phases that occur in the intermediate lattice strength regime.
We review our theoretical analysis of repulsively interacting three-component fermionic atoms in optical lattices. We discuss quantum phase transitions at around half filling with a balanced population by focusing on Mott transitions, staggered ordering, and superfluidity. At half filling (with 3/2 atoms per site), characteristic Mott transitions are induced by the anisotropic interactions, where two-particle repulsions between any two of the three colors have different strengths. At half filling, two types of staggered ordered states appear at low temperatures depending on the anisotropy of the interactions. As the temperature increases, phase transitions occur from the staggered ordered states to the unordered Mott states. Deviating from half filling, an exotic superfluid state appears close to a regime in which the Mott transition occurs. We explain the origin of these phase transitions and present the finite-temperature phase diagrams.
We study Fermi gases in a three-dimensional cubic optical lattice with five fermions per site, i.e., the sss band is completely filled and the ppp band with threefold degeneracy is half filled. We show that for repulsive interaction between fermions, the system will exhibit spin-3/2 antiferromagnetic order at low temperature. This conclusion is obtained both in strong interaction regime by strong coupling expansion and in weak interaction regime by the Hartree--Fock mean-field theory with analysis of the Fermi surface nesting. We also show that in the strongly correlated regime the N\'eel temperature for ppp band antiferromagnetism is 2 to 3 orders of magnitudes higher than that of sss band, which is much more promising to be attained in cold atom experiments.
We study the possibility of realizing strong coupled many-body quantum phases in ultracold atomic systems. Motivated by recent experiments, we first analyze the phase diagram of a Bose-Fermi mixture across a Feshbach resonance, and offer an explanation for the collapse of the system observed close to the Feshbach resonance: we find that phase separation leads to a high density phase which causes the collapse. We then focus on the recent attempts to realize the three-dimensional fermionic Hubbard model in an optical lattice. One milestone on the experimentalists' agenda is to access the antiferromagnetic ordered Neél phase, which has so far been hindered by the low ordering temperature. We ask which experimental parameters maximize the antiferromagnetic interactions, which set the scale for the ordering temperature. We find that the maximum is obtained in a regime where the effective Hamiltonian describing the system no longer corresponds to a simple one-band Hubbard model, and we characterize the physics of the system in this regime. The final system we consider is mass imbalanced polarized two-component Fermi gases interacting via a Feshbach resonance. By going to the strongly polarized limit, we use a recently developed method to obtain results which have been shown to be accurate in the mass balanced case, and we find an intriguing set of competing phases in this limit. We discuss what these results imply for the full phase diagram.
We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in situ imaging to extract the central density of the gas and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interactions reveal that the temperature of the gas is of the order of, or below, the tunneling energy scale. Our results hold great promise for the exploration of many-body phenomena with ultracold atoms, where the local compressibility can be a useful tool to detect signatures of different phases or phase boundaries at specific values of the filling.
We study a two-species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with onsite interspecies repulsive interaction. Such a model can be realized in a cold-atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable interspecies interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities for the minority species, we find that several correlated phases emerge as the ground state, including a spin density wave state, a charge density wave state with stripe structure, and various ppp-wave BCS pairing states for both species. We study this system using a functional renormalization group method, determine its phase diagram at weak coupling, discuss the origin and characteristics of each phase, and provide estimates for the critical temperatures.