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arXiv:1103.1933 · Physics

Exotic many-body physics with large-spin Fermi gases

Congjun Wu

Published Nov 1, 2010• 39 citations
arXivHTMLPDF

Abstract

We report the realization of a novel degenerate Fermi mixture with an SUð2Þ Â SUð6Þ symmetry in a cold atomic gas.We successfully cool the mixture of the two fermionic isotopes of ytterbium 171 Yb with the nuclear spin I ¼ 1=2 and 173 Yb with I ¼ 5=2 below the Fermi temperature T F as 0:46T F for 171 Yb and 0:54T F for 173 Yb.The same scattering lengths for different spin components make this mixture featured with the novel SUð2Þ Â SUð6Þ 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 SUð2Þ Â SUð6Þ 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.

DOI
10.1103/physics.3.92

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We report the realization of a novel degenerate Fermi mixture with an SUð2Þ Â SUð6Þ symmetry in a cold atomic gas.We successfully cool the mixture of the two fermionic isotopes of ytterbium 171 Yb with the nuclear spin I ¼ 1=2 and 173 Yb with I ¼ 5=2 below the Fermi temperature T F as 0:46T F for 171 Yb and 0:54T F for 173 Yb.The same scattering lengths for different spin components make this mixture featured with the novel SUð2Þ Â SUð6Þ 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 SUð2Þ Â SUð6Þ 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 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 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 quantum degenerate mixed gases of ytterbium (Yb) isotopes using all-optical methods. We have succeeded in cooling attractively interacting 176Yb^{176}\mathrm{Yb}176Yb atoms via sympathetic cooling down to below the Bose-Einstein transition temperature, coexisting with a stable condensate of 174Yb^{174}\mathrm{Yb}174Yb atoms with a repulsive interaction. We have observed a rapid atom loss in 176Yb^{176}\mathrm{Yb}176Yb atoms after cooling down below the transition temperature, which indicates the collapse of a 176Yb^{176}\mathrm{Yb}176Yb condensate. The sympathetic cooling technique has been applied to cool a $^{173}\mathrm{Yb}\text{\ensuremath{-}}^{174}\mathrm{Yb}$ Fermi-Bose mixture to the quantum degenerate regime.
We realize simultaneous quantum degeneracy in mixtures consisting of the alkali and alkaline-earth-like atoms Li and Yb. This is accomplished within an optical trap by sympathetic cooling of the fermionic isotope 6Li^{6}\mathrm{Li}6Li with evaporatively cooled bosonic 174Yb^{174}\mathrm{Yb}174Yb and, separately, fermionic 173Yb^{173}\mathrm{Yb}173Yb. Using cross-thermalization studies, we also measure the elastic sss-wave scattering lengths of both Li-Yb combinations, $|{a}_{^{6}\mathrm{Li}\ensuremath{-}^{174}\mathrm{Yb}}|=1.0\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{nm}$ and $|{a}_{^{6}\mathrm{Li}\ensuremath{-}^{173}\mathrm{Yb}}|=0.9\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{nm}$. The equality of these lengths is found to be consistent with mass-scaling analysis. The quantum degenerate mixtures of Li and Yb, as realized here, can be the basis for creation of ultracold molecules with electron spin degrees of freedom, studies of novel Efimov trimers, and impurity probes of superfluid systems.
These lecture notes contain an introduction to the physics of quantum mixtures of ultracold atoms trapped in multiple internal states. I will discuss the case of fermionic isotopes of alkaline-earth atoms, which feature an intrinsic SU(NNN) interaction symmetry and convenient methods for the optical manipulation of their nuclear spin. Some research directions will be presented, with focus on experiments performed in Florence with nuclear-spin mixtures of 173^{173}173Yb atoms in optical lattices.
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.