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.
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.
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.
Local Hilbert spaces with large dimension are of key interest for quantum information with applications in quantum computing and memories, quantum simulations and metrology. Thanks to its weak coupling to external perturbations, the large ground-state nuclear spin manifold of fermionic alkaline-earth atoms is an exciting resource to explore for quantum information. Simultaneous single atom and state-resolved detection however remains an outstanding challenge limiting the development of novel quantum computing and simulation schemes beyond qubits. Here, we report on a new imaging technique enabling the simultaneous detection of up to four quantum states encoded in the nuclear spin manifold of a single fermionic strontium atom within 100 microseconds, with state-resolved detection fidelities ranging from 0.936 to 0.997. This technique is further used to track the highly coherent nuclear spin dynamics after a quench highlighting the potential of this system for quantum information. These results offer fascinating perspectives for quantum science with multi-electron atoms ranging from qudit-based quantum computing to quantum simulations of the SU(N) Fermi-Hubbard model.
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.
Nuclear-spin relaxation rates are usually measured by pulsed radio frequency excitation of nuclear-spin transitions. When the number of spins is too small for direct detection with conventional nuclear-magnetic-resonance spectrometers, pulsed excitation may be combined with optical detection of the nuclear spins for increased sensitivity. Here we demonstrate that such measurements can also be done purely optically, without radio frequency fields. This is achieved by preparing nonthermal populations by optical hole-burning and time-resolved probing of the populations as a function of the decay time. Measurements of the nuclear-spin relaxation of
141Pr in the electronic ground state of
Pr3+:YAlO3 show that the relaxation rates for the three transitions differ by a factor of 3.