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($N$) 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 $^{173}$Yb atoms in optical lattices.
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(N) 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 173Yb atoms in optical lattices.
Recently, alkaline-earth (-like) atoms and alkaline earth metals (AEL) gained experimental and theoretical interest principally related to the possibility offered in metrological field by the excitation of visible and UV clock transitions. AEL atoms, in their neutral \nform and in the ground state, have a null total electronic momentum, resulting nearly insensitive to external magnetic fields. While the absence of magnetic coupling does not allow the simply interactions tuning by exploiting Feshbach resonances as it occurs \nin alkaline atoms, these atoms are characterized by highly symmetric ground states allowing the simulation of SU(N) systems. This characteristic, that can be attributed in AEL atoms to the decoupling between electronic and nuclear atomic momenta, can be \nexploited to perform quantum simulation of a wealth of novel systems and constitutes a fundamental property of isotopes that have a nonzero nuclear spin, as it occurs for all the fermionic species and in particular for 173Yb and 87Sr. This feature also ensures the \nabsence of spin-changing collisions in ground state sublevels, implying that nuclear-spin mixtures are observationally stable. This attribute is fundamental for the study of transitions between different nuclear-spin states, for example by exploiting the two-photon \nRaman coupling. The degeneracy related to the SU(N) symmetry can be controllably removed by applying a two-photon Raman coupling, allowing for the simulation of systems with broken symmetries. \nBesides the possibility to induce couplings within the nuclear-spin degree of freedom, AEL atoms also offer the possibility to access a second, electronic degree of freedom; the possibility to address visible doubly-forbidden transitions between long-lived electronic \nclock states comprises a fantastic tool that allowed the building of optical lattice clocks improving metrological measurements and offering a richer platform for simulating complex systems. \nThe main difference between the two internal degrees of freedom offered by AEL atoms is that the possibility to address ultranarrow optical clock transitions exists also for AEL bosonic isotopes in which the nuclear-spin degree of freedom is not present because the \ntotal atomic momentum is absent. \nThe possibilities related to the excitation of long-lived metastable triplet levels, that, referring only to the lowest lying atomic levels are 3P(0;2) (in Russell-Saunders approximation they result doubly forbidden with respect to the electric dipole operator), are \nmultiple. If bosonic atoms are considered, the metrological applications based on the clock transition at the state of the art have performances comparable to optical lattice clocks realized with fermionic isotopes. Bosonic isotopes, requiring external fields in order \nto excite transitions from the ground state to long-lived states, have been proposed as good candidates in order to build a reliable and fast system in which controllable qu-bits could be realized. Most of these applications, and in particular the possibility to create \nquantum computers with neutral atoms, crucially rely on the control of the scattering properties of atoms in different electronic states. \nRegarding fermionic isotopes, the clock transitions recently allowed for the demonstration of spin-orbit coupling and quantum simulation via the synthetic dimension approach. As recently discovered, the clock transitions from the ground to the 3P(0;2) states give rise to rich interactions possibilities between atoms in the fundamental and in the metastable states. The spin-exchange interaction that has been observed between ground and metastable states, supports also a new kind of Feshbach resonance, called Orbital Feshbach Resonance (OrbFR). As occurs in magnetic Feshbach resonances for alkali atoms, also the OrbFR, that occurs in AEL atoms, supports the existence of extremely shallow homonuclear molecules. After considering the (s-wave) scattering parameters of all the AEL atoms that have been characterized experimentally, 173Yb is the only isotope in which the production and manipulation of Orbital Feshbach molecules (produced e.g. with photoassociation) is experimentally viable. Molecules generated by employing this atom, may lead to the investigation of fermionic superfluidity in still-unexplored regimes. In this thesis we report the characterization of interactions in bosonic 174Yb isotope by probing the clock transition between the singlet 1S0 ground state and the triplet 3P0 \nmetastable excited state. Interactions and inelastic losses between ground-state and excited metastable-state atoms have been experimentally determined with high accuracy, resulting consistent with an indipendent evaluation realized in the same period by Yb \nBEC group at LKB. \nThe obtained values for the interactions among ground and metastable atoms for the specified isotope constitute a first step in order to design an experimental system in which quantum information can be realized by means of exploiting the clock transition of bosonic Yb atoms. \nThis work, by exploiting the internal degrees of freedom of 173Yb atoms, reports a study on Orbital Feshbach molecules, showing experimentally the possibility to employ the nuclear degree of freedom in 173Yb atoms to manipulate and precisely detect homo-nuclear photoassociated molecules. \nThis first result regarding this new kind of shallow-bound molecules allowed the characterization of interactions between ground-state and metastable-state of 173Yb atoms. \nThis first intensive study of orbital Feshbach molecules is a fundamental step for future studies on the possibilities offered by these homo-nuclear molecules. \nFinally, we exploited the ground state SU(N) symmetry and its controlled breaking via Raman coupling (in 173Yb N = 1...6) to simulate the physical processes that are supposed to be driven by the hybridation of d-orbitals of iron atoms in iron based-superconductors, \nin which orbital-selective Mott insulating phases have been experimentally observed and are suspected to be the fundamental ingredient to achieve high-temperature superconductivity in these compounds.
Abstract Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU( N ) symmetry have provided important insights into many-body phenomena. However, these models have generally remained a theoretical idealization, since it is very difficult to exactly realize the SU( N ) symmetry in conventional quantum materials for large N . Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU( N )-symmetric many-body models, where N is tunable and can be as large as 10. This symmetry emerges due to the closed shell structure of AEAs, thereby leading to a perfect decoupling of the electronic degrees of freedom from the nuclear spin. In this work, we provide a systematic review of recent theoretical and experimental work on the many-body physics of these systems. We first discuss the thermodynamic properties and collective modes of trapped Fermi gases, highlighting the enhanced interaction effects that appear as N increases. We then discuss the properties of the SU( N ) Fermi–Hubbard model, focusing on some of the major experimental achievements in this area. We conclude with a compendium highlighting some of the significant theoretical progress on SU( N ) lattice models and a discussion of some exciting directions for future research.
Rapid advancements in the experimental capabilities with ultracold alkaline-earth-like atoms (AEAs) bring to a surprisingly near term the prospect of performing quantum simulations of spin models and lattice field theories exhibiting SU( N ) symmetry. Motivated in particular by recent experiments preparing high density samples of strongly interacting 87 Sr atoms in a three-dimensional optical lattice, we develop a low-energy effective theory of fermionic AEAs which exhibits emergent multi-body SU( N )-symmetric interactions, where N is the number of atomic nuclear spin levels. Our theory is limited to the experimental regime of (i) a deep lattice, with (ii) at most one atom occupying each nuclear spin state on any lattice site. The latter restriction is a consequence of initial ground-state preparation. We fully characterize the low-lying excitations in our effective theory, and compare predictions of many-body interaction energies with direct measurements of many-body excitation spectra in an optical lattice clock. Our work makes the first step in enabling a controlled, bottom-up experimental investigation of multi-body SU( N ) physics.
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 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 with evaporatively cooled bosonic 174Yb and, separately, fermionic 173Yb. Using cross-thermalization studies, we also measure the elastic s-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.
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.