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.
Ultracold neutral atoms in optical lattices are rich systems for the investigation of many-body physics as well as for the implementation of quantum information processing. While traditionally alkali atoms were used for this research, in recent years alkaline-earth-like atoms have attracted considerable interest. This is due to their more complex but tractable internal structure and easily accessible transitions. Furthermore, alkaline-earth-like atoms have extremely narrow
1S→3P intercombination transitions, which lend themselves for the implementation of next generation atomic clocks. In this dissertation, I show that exquisite control of alkaline-earth-like atoms can be reached with optical methods, and elucidate ways to use this controllability to further different aspects of research, mainly quantum information processing. Additionally, the control of alkaline-earth-like atoms is very interesting in many-body physics and the improvement of atomic clocks. Since heating usually degrades the performance of quantum gates, recooling of qubits is a necessity for the implementation of large scale quantum computers. Laser cooling has advantages over the usually used sympathetic cooling, given that it requires no additional atoms, which have to be controlled separately. However, for qubits stored in hyperfine states, as usually done in alkali atoms, laser cooling leads to optical pumping and therefore to loss of coherence. On the other hand, in the ground state, the nuclear spin of alkaline-earth-like atoms is decoupled from the electronic degrees of freedom. As I show in this dissertation, this allows for the storage of quantum information in the nuclear spin and laser cooling on the electronic degrees of freedom. The recooling protocol suggested here consists of two steps: resolved sideband cooling on the extremely narrow
1S0→3P0 clock transition and subsequent quenching on the much shorter lived
1P1 state. A magnetic field is used to overcome the hyperfine interaction in this excited state and thus ensures decoupling of the nuclear spin degrees of freedom during the quenching. The application of this magnetic field also allows for photon scattering on the
1P1 state, while preserving the nuclear spin, e. g. for electronic qubit detection. The manipulation of the scattering properties of neutral atoms is an important aspect of quantum control. In contrast to alkali atoms, whose broad linewidths cause large losses, this can be done with purely optical methods via the implementation of an optical Feshbach resonance for alkaline-earth-like atoms. Here, the scattering length resulting from the application of an optical Feshbach resonance on the
1S0→3P1 intercombination line, including hyperfine interaction and rotation is calculated for
171Yb. Due to their different parities, the p-wave scattering length can be controlled independently from the s-wave scattering length, thus allowing for unprecedented control over the scattering properties of neutral atoms. Furthermore, I also show how optical Feshbach resonances in alkaline-earth-like atoms can be used together with the underlying quantum symmetry to implement collisional gates between nuclear-spin qubits over comparatively long ranges.
We study the ability to implement unitary maps on states of the
I=9/2 nuclear spin in
87Sr, a
d=10 dimensional (qudecimal) Hilbert space, using quantum optimal control. Through a combination of nuclear spin resonance and a tensor ac Stark shift, by solely modulating the phase of a radio-frequency magnetic field, the system is quantum controllable. Alkaline-earth-metal atoms, such as
87Sr, have a very favorable figure of merit for such control due to narrow intercombination lines and the large hyperfine splitting in the excited states. We numerically study the quantum speed limit, optimal parameters, and the fidelity of arbitrary state preparation and full SU(10) maps, including the presence of decoherence due to optical pumping induced by the light-shifting laser. We also study the use of robust control to mitigate some dephasing due to inhomogeneities in the light shift. We find that with an rf Rabi frequency of ${\mathrm{\ensuremath{\Omega}}}_{\text{rf}}$ and 0.5% inhomogeneity in the the light shift we can prepare an arbitrary Haar-random state in a time $T=4.5\ensuremath{\pi}/{\mathrm{\ensuremath{\Omega}}}_{\text{rf}}$ with average fidelity $\ensuremath{\langle}{\mathcal{F}}_{\ensuremath{\psi}}\ensuremath{\rangle}=0.9992$, and an arbitrary Haar-random SU(10) map in a time $T=24\ensuremath{\pi}/{\mathrm{\ensuremath{\Omega}}}_{\text{rf}}$ with average fidelity $\ensuremath{\langle}{\mathcal{F}}_{U}\ensuremath{\rangle}=0.9923$.
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.
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.
We study quantum control of the full hyperfine manifold in the ground-electronic state of alkali-metal atoms based on applied radio frequency and microwave fields. Such interactions should allow essentially decoherence-free dynamics and the application of techniques for robust control developed for NMR spectroscopy. We establish the conditions under which the system is controllable in the sense that one can generate an arbitrary unitary map on the system. We apply this to the case of
133Cs with its
d=16 dimensional Hilbert space of magnetic sublevels in the
6S1∕2 state, and design control wave forms that generate an arbitrary target state from an initial fiducial state. We develop a generalized Wigner function representation for this space consisting of the direct sum of two irreducible representations of SU(2), allowing us to visualize these states. The performance of different control scenarios is evaluated based on the ability to generate a high-fidelity operation in an allotted time with the available resources. We find good operating points commensurate with modest laboratory requirements.