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arXiv:1405.0543 · Physical Review A

Effective orbital ordering in multiwell optical lattices with fermionic atoms

A. M. Belemuk, N. M. Chtchelkatchev, Andrey V. Mikheyenkov

Published Aug 19, 2014• 5 citations
arXivHTMLPDF

Abstract

We consider the behavior of Fermi atoms on optical superlattices with two-well structure for each node. Fermions on such lattices serve as an analog simulator of the Fermi-type Hamiltonian. We derive a mapping between fermion quantum ordering in the optical superlattices and the spin-orbital physics developed for degenerate $d$-electron compounds. The appropriate effective spin-orbital model appears to be a modification of the Kugel-Khomskii Hamiltonian. We show how different ground states of this Hamiltonian correspond to particular spin-pseudospin arrangement patterns of fermions on the lattice. The dependence of the fermion arrangement on phases of complex hopping amplitudes is illustrated.

DOI
10.1103/physreva.90.023625

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We consider the behavior of Fermi atoms on optical superlattices with two-well structure for each node. Fermions on such lattices serve as an analog simulator of the Fermi-type Hamiltonian. We derive a mapping between fermion quantum ordering in the optical superlattices and the spin-orbital physics developed for degenerate ddd-electron compounds. The appropriate effective spin-orbital model appears to be a modification of the Kugel-Khomskii Hamiltonian. We show how different ground states of this Hamiltonian correspond to particular spin-pseudospin arrangement patterns of fermions on the lattice. The dependence of the fermion arrangement on phases of complex hopping amplitudes is illustrated.
Orbital degrees of freedom play an important role in understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we consider spinless fermionic atoms loaded into ppp-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Due to the interplay of anisotropic hoppings and geometrical frustration, a rich phase diagram is found, including stripe-orbital, paraorbital, and ferro-orbital phases, in contrast to its bosonic analog with orbital-skyrmion ordering in the identical lattice. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.
We explore the superfluid phases of a two-component Fermi mixture with hybridized orbitals in optical lattices. We show that there exists a general mapping of this system to the Lieb lattice. By using simple multiband models with hopping between sss- and ppp-orbital states, we show that superfluid order parameters can have a $\ensuremath{\pi}$-phase difference between lattice sites, which is distinct from the case with hopping between sss orbitals. If the population imbalance between the two spin species is tuned, the superfluid phase may evolve through various phases due to the interplay between hopping, interactions, and imbalance. We show that the rich behavior is observable in experimentally realizable systems.
Fermionic atoms in an optical superlattice can realize a very peculiar Anderson lattice model in which impurities interact with each other through a discretized set of delocalized levels. We show that under these finite-size features strongly correlated phases appear. By tuning the parameters of the superlattice two different phases could be observed: a Kondo-singlet phase in which each impurity forms a singlet with the Fermi level of its neighboring conducting islands, and a magnetic phase in which long range magnetic order is established between the impurities mediated by the intermediate islands. The interplay between these two phenomena depends on the parity of the number of particles per discretized set. We show how Kondo-induced resonances of measurable size can be observed through the atomic interference pattern.
Orbital phases of ppp-band ultracold fermions in the frustrated triangular lattice
Orbital degrees of freedom play an important role for understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we consider spinless fermionic atoms loaded into ppp-orbital bands of a two-dimensional frustrated triangular lattice. The system can be described by an extended Fermi-Hubbard model, which is numerically solved by using the orbital version of real-space dynamical mean-field theory. Low-temperature phase diagrams are obtained, which contain stripe-, ferro- and para-orbital ordered quantum phases, due to the interplay of anisotropic hoppings and geometrical frustration. In order to understand the underlying mechanics of competing orbital orders, we derive an effective orbital-exchange model, which yields consistent explanation with our main numerical results.
Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-dimensional square optical lattice. We find that laser-assisted spin-dependent hopping, specifically tuned to the (2s+1)(2s+1)(2s+1)-dimensional representations of the su\mathfrak{su}su(2) Lie algebra, directly leads to a regime where the emerging massless excitations correspond to Dirac-Weyl fermions with arbitrary pseudospin sss. We show that this platform hosts two different phases: a semimetallic phase that occurs for half-integer sss, and a metallic phase that contains a flat zero-energy band at integer sss. These phases host a variety of interesting effects, such as a very rich anomalous quantum Hall effect and a remarkable multirefringent Klein tunneling. In addition, we show that these effects are directly related to the number of underlying Dirac-Weyl species and zero modes.
A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.