This thesis reviews our implementation of a quantum simulator for the Fermi-Hubbard modelwith strontium 87. Closed-shell 87 Sr with large nuclear spin I=9/2 benefits from a 7.4 kHz narrowintercombination line that played a central role in this thesis. It offers ideal conditions for the realizationof spin orbit coupling schemes to coherently manipulate the 10 nuclear spin states with minimalspontaneous emission. First, we demonstrated a method to measure local densities smaller than theresolution limit of our imaging system. We overcome the limits due to aberrations and fast variationsof the density profiles. Derived from the Beer-Lambert law, the non-linear correction lets us infer sizesas small as 1/4 pixel. Then, we prepare polarized Fermi seas of 87 Sr at T /TF ≃ 0.25, with a spinpurification by optical pumping. The spin populations are measured with a spin orbit coupling schemeassociated with the narrow line, realizing a spin dependent momentum transfer. We then demonstratea method to coherently and selectively flip the spin states. The degeneracy of the ground state is liftedwith a quadratic light shift. With a Raman adiabatic passage, the spins are flipped with 80 % efficiencythat will be improved up to 95 %. Designed as an optical super lattice, this scheme will permit to writedeterministic spin textures that will be the initial state for the quantum simulator. Finally, we studythe loading of Fermi gases into the ground band of a 1D lattice with large sites spacing 2 µm. Ourexperiment highlights the critical importance of maintening a sufficient collision rate to adiabaticallyfollow the 3D to 2D dimensionnality cross-over, and we simultaneously produce four 2D Fermi seas.
Manipulation des spins nucléaires du strontium 87 dans des gaz de Fermi dégénérés en symétrie SU(N) Cette thèse présente notre implémentation d'un simulateur quantique (SQ) pour le modèle de Fermi-Hubbard avec des atomes de strontium 87. Le 87Sr de grand spin nucléaire I=9/2 bénéficie d'une raie d'intercombinaison étroite de 7.4 kHz jouant un rôle central dans cette thèse. Elle offre un cadre idéal pour manipuler les 10 états de spin nucléaires par couplage spin-orbite (CSO) avec une émission spontanée minimale.D'abord, nous démontrons une méthode pour mesurer des densités locales non résolues par notre système d'imagerie. Nous surpassons les limites dues aux abbérations et variations rapides du profile de densité, par une correction non-linéaire établie à partir de la loi de Beer-Lambert. Nous déduisons des tailles jusqu'à 1/4 pixel. Ensuite, nous préparons des mers de Fermi de 87Sr polarisées à T/TF=0.25 en utilisant une purification de spin par pompage optique. Les populations de spin sont mesurées par des transferts d'impulsion sélectifs en spin grâce au CSO. Nous démontrons de plus une méthode pour retourner les spins de manière cohérente et sélective. La dégénéréscence de l'état fondamental est levée par un déplacement lumineux quadratique. Par passage Raman adiabatique, les spins sont retournés avec une efficacité de 80% qui sera améliorée à 95%. Conçu comme un réseau optique, cette méthode pemettra l'écriture deterministe d'une texture de spin qui sera l'état initial du SQ. Enfin, nous étudions le chargement d'un gaz de Fermi dans la bande fondamentale d'un réseau 1D de grande période 2µm. Nous montrons l'importance de maintenir un taux de collision suffisant pour suivre le cross-over de géométrie de 3D à 2D, et nous produisons simultanément 4 mers de Fermi 2D
Fermionic
87Sr has a nuclear spin of
I=9/2, higher than any other element with a similar electronic structure. This large nuclear spin has many applications in quantum simulation and computation, for which preparation and detection of the spin state are requirements. For an ultracold
87Sr cloud, we show two complementary methods to characterize the spin-state mixture: optical Stern-Gerlach state separation and state-selective absorption imaging. We use these methods to optimize the preparation of a variety of spin-state mixtures by optical pumping and to measure an upper bound of the
87Sr spin-relaxation rate.
Quantum-gas microscopes provide direct access to the phases of the Hubbard model, bringing microscopic insight into the complex competition between interactions, SU(2) magnetism, and doping. Alkaline-earth(-like) fermions extend this spin-1/2 paradigm by realizing higher symmetries and giving access to SU(
N) Hubbard models, with rich phase diagrams to be unveiled. Despite its fundamental interest, a microscopic exploration of SU(
N) quantum systems has remained elusive. Here we report the realization of a quantum-gas microscope for fermionic
87Sr. Our imaging scheme, based on cooling and fluorescence on the narrow intercombination line at 689 nm, enables spin-resolved single-atom detection. By implementing a spin-selective optical pumping protocol, we determine the occupation of each of the 10 spin states in a single experimental realization, a crucial capability for probing site-resolved magnetic correlations. We benchmark our method by observing single-particle Larmor precession across the full spin-9/2 ground-state manifold and use numerical simulations of SU(
N) Fermi-Hubbard chains, incorporating the measured detection fidelities, to demonstrate its capability to resolve many-body spin correlations. Our results establish
87Sr quantum-gas microscopy as a powerful approach to study exotic magnetism in the SU(
N) Fermi-Hubbard model, and provide a new detection tool for studies in quantum simulation, computation, and metrology.
We demonstrate coherent manipulation of the nuclear degrees of freedom of ultracold ground-state strontium-87 atoms, thus providing a toolkit for fully exploiting the corresponding large Hilbert space as a quantum resource and for quantum simulation experiments with s u ( N ) -symmetric matter. By controlling the resonance conditions of Raman transitions with a tensor light shift, we can perform rotations within a restricted Hilbert space of two isolated spin states among the 2 F + 1 = 10 possible states. These manipulations correspond to engineering unitary operations derived from generators of the s u ( N ) algebra beyond what can be done by simple spin precession. We present Ramsey interferometers involving an isolated pair of Zeeman states with no measurable decoherence after 3 s. We also demonstrate that one can harness the large spin degrees of freedom as a qudit resource by implementing two interferometer schemes over four states. The first scheme senses in parallel multiple external fields acting on the atoms, and the second scheme simultaneously measures multiple observables of a collective atomic state—including noncommuting ones. Engineering unitary transformations of the large spin driven by other generators than the usual spin- F representation of the s u ( 2 ) group offers new possibilities from the point of view of quantum metrology and quantum many-body physics, notably for the quantum simulation of large-spin s u ( N ) -symmetric quantum magnetism with fermionic alkaline-earth atoms.
We report on an improved scheme to generate Bose-Einstein condensates (BECs) and degenerate Fermi gases of strontium. This scheme allows us to create quantum gases with higher atom number, a shorter time of the experimental cycle, or deeper quantum degeneracy than before. We create a BEC of
84Sr exceeding
107 atoms, which is a 30-fold improvement over previously reported experiments. We increase the atom number of
86Sr BECs to $2.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ (a fivefold improvement) and refine the generation of attractively interacting
88Sr BECs. We present a scheme to generate
84Sr BECs with a cycle time of 2 s. We create deeply degenerate
87Sr Fermi gases with
T/TF as low as 0.10(1), where the number of populated nuclear spin states can be set to any value between one and ten. Furthermore, we report on a total of five different double-degenerate Bose-Bose and Bose-Fermi mixtures. These studies prepare an excellent starting point for applications of strontium quantum gases anticipated in the near future.
Degenerate quantum gases of alkaline-earth-like elements open new opportunities in research areas ranging from molecular physics to the study of strongly correlated systems. These experiments exploit the rich electronic structure of these elements, which is markedly different from the one of other species for which quantum degeneracy has been attained. Specifically, alkaline-earth-like atoms, such as strontium, feature metastable triplet states, narrow intercombination lines, and a non-magnetic, closed-shell ground state. This review covers the creation of quantum degenerate gases of strontium and the first experiments performed with this new system. It focuses on laser-cooling and evaporation schemes, which enable the creation of Bose-Einstein condensates and degenerate Fermi gases of all strontium isotopes, and shows how they are used for the investigation of optical Feshbach resonances, the study of degenerate gases loaded into an optical lattice, as well as the coherent creation of Sr_2 molecules.