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arXiv:0905.4948 · New Journal of Physics

Ultracold gases of ytterbium: ferromagnetism and Mott states in an SU(6) Fermi system

Miguel A. Cazalilla, A. F. Ho, Masahito Ueda

Published Oct 21, 2009• 282 citations
arXivHTMLPDF

Abstract

It is argued that an ultracold quantum degenerate gas of ytterbium 173 Yb atoms having nuclear spin I =5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU( n >2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU( n ) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU( n >2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.

DOI
10.1088/1367-2630/11/10/103033

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It is argued that an ultracold quantum degenerate gas of ytterbium 173 Yb atoms having nuclear spin I =5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU( n >2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU( n ) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU( n >2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.
Abstract At temperatures well below the Fermi temperature T F , the coupling of magnetic fluctuations to particle-hole excitations in a two-component Fermi gas leads to non-analytic corrections in the renormalized free energy and makes the transition to itinerant ferromagnetism first order. On the other hand, despite that larger symmetry often introduces larger degeneracies in the low-lying states, here we show that for a Fermi gas with SU(N > 2)-symmetry in three space dimensions the ferromagnetic phase transition is first order in agreement with the predictions of Landau’s mean-field theory in its minimal formulation, which contains a cubic term in the free-energy (Cazalilla et al 2009 New J. Phys. 11 103033). By performing unrestricted Hartree–Fock calculations for an SU(N > 2)-symmetric Fermi gas with short range interactions, we find the order parameter undergoes a finite jump across the transition. In addition, for SU(N > 2) we do not observe any tri-critical point up to temperatures T ≃ 0.5 T F , for which the thermal smearing of the Fermi surface and thermal fluctuations are substantial. Going beyond mean-field theory, we find that the coupling of magnetic fluctuations to particle-hole excitations makes the transition more abrupt and further enhances the tendency of the gas to become fully polarized for smaller values of N and the gas parameter k F a s . In our study, we also clarify the role of time reversal symmetry in the microscopic Hamiltonian and obtain the temperature dependence of Tan’s contact. For the latter, the presence of the tri-critical point for N = 2 leads to a more pronounced temperature dependence around the transition than for SU(N > 2)-symmetric gases. Although the results are obtained for a microscopic model relevant to ultracold atomic gases, they may also apply to models of solid state systems with SU(N > 2) symmetry provided Coulomb interactions are sufficiently well screened.
This thesis reports on the experimental realization of the 3D SU(N) Fermi-Hubbard model and the direct probing of the equation of state with an ultracold quantum gas of fermionic ytterbium in an optical lattice. Ultracold atoms in optical lattices constitute a flexible and highly tunable system to investigate Hamiltonians of condensed matter physics such as the Hubbard model. In particular, ytterbium atoms are ideal candidates for the realization of the Fermi-Hubbard model with SU(N)-symmetry due to a high decoupling of the nuclear spin from the electronic configuration. As a consequence of this enlarged symmetry, thermodynamic properties of the atomic sample depend on N, the number of spin components in the quantum gas, and novel, exotic phases are predicted to emerge at low temperatures. By locally probing a quantum gas of 173Yb in a 3D optical lattice, we determine the equation of state of the SU(6) and SU(3) Fermi-Hubbard model. The measurement of the equation of state allows us to obtain direct, model-independent access to the thermodynamic quantities of the lattice gas. In this way, we can characterize the crossover from a Fermi liquid to an SU(N) Mott insulator when tuning the interaction strength, and can probe the compressibility of the quantum gas in different interaction regimes. Moreover, we find a low specific entropy of the SU(6) gas below that of uncorrelated spins, indicating the presence of partial spin correlations in the atomic sample. The ability to access the equation of state of such high spin systems, as well as the low obtained entropy, represent an important step towards the realization of SU(N) spin Hamiltonians and the characterization of novel SU(N) phases.
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 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.
We report the realization of a novel degenerate Fermi mixture with an $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(6)$ symmetry in a cold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium 171Yb^{171}\mathrm{Yb}171Yb with the nuclear spin I=1/2I=1/2I=1/2 and 173Yb^{173}\mathrm{Yb}173Yb with I=5/2I=5/2I=5/2 below the Fermi temperature TF{T}_{F}TF​ as 0.46TF0.46{T}_{F}0.46TF​ for 171Yb^{171}\mathrm{Yb}171Yb and 0.54TF0.54{T}_{F}0.54TF​ for 173Yb^{173}\mathrm{Yb}173Yb. The same scattering lengths for different spin components make this mixture featured with the novel $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(6)$ symmetry. The nuclear spin components are separately imaged by exploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice to implement the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(6)$ Hubbard model. This mixture will open the door to the study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid.
We investigate the zero-temperature phase diagram of two-orbital SU(N\mathrm{SU}(NSU(N) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the SU(N\mathrm{SU}(NSU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the N=2N=2N=2 case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of 2N2N2N fermions.