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arXiv:1005.3670 · Physical Review Letters

Realization of a SU(2)×SU(6) System of Fermions in a Cold Atomic Gas

Shintaro Taie, Yosuke Takasu, Seiji Sugawa, Rekishu Yamazaki, Takuya Tsujimoto, Ryo Murakami, Yoshiro Takahashi

Published Nov 1, 2010• 294 citations
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Abstract

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 $^{171}\mathrm{Yb}$ with the nuclear spin $I=1/2$ and $^{173}\mathrm{Yb}$ with $I=5/2$ below the Fermi temperature ${T}_{F}$ as $0.46{T}_{F}$ for $^{171}\mathrm{Yb}$ and $0.54{T}_{F}$ for $^{173}\mathrm{Yb}$. 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.

DOI
10.1103/physrevlett.105.190401

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We report the realization of a novel degenerate Fermi mixture with an SU(2)\ifmmode×\else\texttimes\fiSU(6)\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(6)SU(2)\ifmmode×\else\texttimes\fiSU(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 SU(2)\ifmmode×\else\texttimes\fiSU(6)\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(6)SU(2)\ifmmode×\else\texttimes\fiSU(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 SU(2)\ifmmode×\else\texttimes\fiSU(6)\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(6)SU(2)\ifmmode×\else\texttimes\fiSU(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 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.
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.
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.
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.
A degenerate three-component Fermi gas of atoms with identical attractive interactions is expected to exhibit superfluidity and magnetic order at low temperature and, for sufficiently strong pairwise interactions, become a Fermi liquid of weakly interacting trimers. The phase diagram of this system is analogous to that of quark matter at low temperature, motivating strong interest in its investigation. We describe how a three-component gas below the superfluid critical temperature can be prepared in an optical lattice. To realize an SU(3)-symmetric system, we show how pairwise interactions in the three-component atomic system can be made equal by applying radiofrequency and microwave radiation. Finally, motivated by the aim to make more accurate models of quark matter, which have color, flavor and spin degrees of freedom, we discuss how an atomic system with SU(2)⊗SU(3) symmetry can be achieved by confining a three-component Fermi gas in the p-orbital band of an optical lattice potential.
We characterize interisotope interorbital interactions between atoms in the 1S0^{1}S_{0}1S0​ ground state and the 3P0^{3}P_{0}3P0​ metastable state in interacting Fermi-Fermi mixtures of 171Yb^{171}\mathrm{Yb}171Yb and 173Yb^{173}\mathrm{Yb}173Yb. We perform high-precision clock spectroscopy to measure interaction-induced energy shifts in a deep three-dimensional optical lattice and determine the corresponding scattering lengths. We find the elastic interaction of the interisotope mixtures $^{173}\mathrm{Yb}_{\mathrm{e}}\text{\ensuremath{-}}^{171}\mathrm{Yb}_{\mathrm{g}}$ and $^{173}\mathrm{Yb}_{\mathrm{g}}\text{\ensuremath{-}}^{171}\mathrm{Yb}_{\mathrm{e}}$ to be weakly attractive and very similar, while the corresponding two-body decay coefficients differ by more than two orders of magnitude. By comparing different spin mixtures we experimentally demonstrate the $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{SU}(6)$ symmetry of the elastic interactions. Furthermore, we measure the interorbital spin-exchange interaction in 171Yb^{171}\mathrm{Yb}171Yb and confirm its previously observed antiferromagnetic nature.