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Acta Physica Polonica A

Low-Temperature Phases in Two-Orbital Hubbard Model Realized with Ultracold Atoms in Optical Lattices

Andrii Sotnikov, Yeimer Zambrano, Agnieszka Cichy

Published Nov 1, 2020• 1 citation
Publisher

Abstract

We study ultracold quantum gases of alkaline-earth-like atoms loaded into three-dimensional statedependent optical lattice.In particular, we focus on the fermionic ytterbium-173 atoms due to their unique properties, in particular, low-lying metastable excited e electronic state, decoupling of the nuclear spin from the electronic degrees of freedom and different AC-polarizabilities of the ground g and e states.This allows to realize the two-band Hubbard model and study its unique critical properties.The theoretical analysis is performed in the region of applicability of the tight-binding approximation at different lattice depths and different fillings by atoms in the g-and e-orbital states.By means of dynamical mean-field theory, we analyze stability regions of the emerging ordered phases.

DOI
10.12693/aphyspola.138.669

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We study ultracold quantum gases of alkaline-earth-like atoms loaded into three-dimensional statedependent optical lattice.In particular, we focus on the fermionic ytterbium-173 atoms due to their unique properties, in particular, low-lying metastable excited e electronic state, decoupling of the nuclear spin from the electronic degrees of freedom and different AC-polarizabilities of the ground g and e states.This allows to realize the two-band Hubbard model and study its unique critical properties.The theoretical analysis is performed in the region of applicability of the tight-binding approximation at different lattice depths and different fillings by atoms in the g-and e-orbital states.By means of dynamical mean-field theory, we analyze stability regions of the emerging ordered phases.
We explore the rich nature of correlations in the ground state of ultracold atoms trapped in state-dependent optical lattices. In particular, we consider interacting fermionic ytterbium or strontium atoms, realizing a two-orbital Hubbard model with two spin components. We analyze the model in one-dimensional setting with the experimentally relevant hierarchy of tunneling and interaction amplitudes by means of exact diagonalization and matrix product states approaches, and study the correlation functions in density, spin, and orbital sectors as functions of variable densities of atoms in the ground and metastable excited states. We show that in certain ranges of densities these atomic systems demonstrate strong density-wave, ferro- and antiferromagnetic, as well as antiferroorbital correlations.
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We report on a dynamical mean-field theoretical analysis of emerging low-temperature phases in multicomponent gases of fermionic alkaline-earth(-like) atoms in state-dependent optical lattices. Using the example of 173^{173}173Yb atoms, we show that a two-orbital mixture with two nuclear spin components is a promising candidate for studies of not only magnetic but also staggered orbital ordering peculiar to certain solid-state materials. We calculate and study the phase diagram of the full Hamiltonian with parameters similar to existing experiments and reveal an antiferroorbital phase. This long-range-ordered phase is inherently stable, and we analyze the change of local and global observables across the corresponding transition lines, paving the way for experimental observations. Furthermore, we suggest a realistic extension of the system to include and probe a Jahn-Teller source field playing one of the key roles in real crystals.
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We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, (3) the realization of a Mott insulator of (173)Yb atoms, (4) the creation of various kinds of Fermi-Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.