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 $^{87}$Sr. 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. These results establish $^{87}$Sr 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.
Spin-resolved microscopy of 87Sr SU(N) Fermi-Hubbard systems
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. These 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.
The development of quantum-gas microscopes has brought novel ways of probing quantum degenerate many-body systems at the single-atom level. Until now, most of these setups have focused on alkali atoms. Expanding quantum-gas microscopy to alkaline-earth elements will provide new tools, such as SU( N )-symmetric fermionic isotopes or ultranarrow optical transitions, to the field of quantum simulation. Here we demonstrate the site-resolved imaging of a 84 Sr bosonic quantum gas in a Hubbard-regime optical lattice. The quantum gas is confined by a two-dimensional in-plane lattice and a light-sheet potential, which operate at the strontium clock-magic wavelength of 813.4 nm. We realize fluorescence imaging using the broad 461-nm transition, which provides high spatial resolution. Simultaneously, we perform attractive Sisyphus cooling with the narrow 689-nm intercombination line. We reconstruct the atomic occupation from the fluorescence images, obtaining imaging fidelities above 94 % . Finally, we realize a 84 Sr superfluid in the Bose-Hubbard regime. We observe its interference pattern upon expansion, a probe of phase coherence, with single-atom resolution. Our strontium quantum-gas microscope provides a new platform to study dissipative Hubbard models, quantum optics in atomic arrays, and SU( N ) fermions at the microscopic level. Published by the American Physical Society 2024
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.
Two-dimensional quantum gas microscopy provides an unparalleled tool to study quantum many-body systems using ultracold atoms. For the SU(2) Fermi Hubbard model (FHM), access to spin-resolved projective measurements has been vital for quantifying correlation functions and mapping out the phase diagram. Recent progress in quantum gas microscopy for experiments with ultracold alkaline-earth atoms, which are well described by the SU(N) FHM and are predicted to host exotic ground-state phases, calls for the development of theory-free numerical techniques to extract physical information from their projective measurements. To that end, we evaluate the multiscale structural complexity of snapshots of an SU(3) FHM in the square lattice at 1/3-filling. We employ mean-field theory to generate spin-resolved density distributions and compute their structural complexity using rectangular coarse-graining windows. We demonstrate that these complexities are linked to relevant physical observables such as the entanglement entropy, and are extremely sensitive for locating phase boundaries. The results presented here validate the structural complexity as an efficient and reliable tool for analyzing the outputs of SU(N) quantum gas microscopes, offering a theory-free property, immediately accessible to experiments.
Quantum gas microscopes have expanded the capabilities of quantum simulation of Hubbard models by enabling the study of spatial spin and density correlations in square lattices.However, quantum gas microscopes have not been realized for fermionic atoms in frustrated geometries.Here, we demonstrate the single-atom resolved imaging of ultracold fermionic 6 Li atoms in a triangular optical lattice with a lattice constant of 1003 nm.The optical lattice is formed by a recycled narrow-linewidth, high-power laser combined with a light sheet to allow for Raman sideband cooling on the D 1 line.We optically resolve single atoms on individual lattice sites using a high-resolution objective to collect scattered photons while cooling them close to the two-dimensional ground vibrational level in each lattice site.By reconstructing the lattice occupation, we measure an imaging fidelity of approximately 98%.Our triangular lattice microscope platform for fermions clears the path for studying spin-spin correlations, entanglement, and dynamics of geometrically frustrated Hubbard systems which are expected to exhibit exotic emergent phenomena including spin liquids and kinetic frustration.
The repulsive Hubbard Hamiltonian is one of the foundational models describing strongly correlated electrons and is believed to capture essential aspects of high-temperature superconductivity. Ultracold fermions in optical lattices allow for the simulation of the Hubbard Hamiltonian with control over kinetic energy, interactions, and doping. A great challenge is to reach the required low entropy and to observe antiferromagnetic spin correlations beyond nearest neighbors, for which quantum gas microscopes are ideal. Here, we report on the direct, single-site resolved detection of antiferromagnetic correlations extending up to three sites in spin-1/2 Hubbard chains, which requires entropies per particle well below s* = ln(2). The simultaneous detection of spin and density opens the route toward the study of the interplay between magnetic ordering and doping in various dimensions.
Imagine a new generation of computers that dramatically surpasses the most powerful supercomputers, being able to tackle the most challenging of computational problems. These problems arise, for example, in quantum physics where the computational power required to model a many-particle system increases exponentially with the number of its constituents, and as a consequence the calculations become prohibitively time-consuming. Nobel laureate Richard Feynman proposed this new type of computer in the early 1980s: ‘Let the computer itself be built of quantum mechanical elements which obey quantum mechanical laws.’ Such a quantum simulator would allow researchers to tackle challenging problems in condensed-matter physics. In particular many-body fermionic quantum systems are very difficult to compute due to the antisymmetric nature of the wave function, and the resulting sign problem for quantum Monte Carlo methods. This is why a quantum simulator will be an excellent test bed to investigate phenomena and properties of strongly correlated fermionic quantum systems. A powerful experimental platform to realize a quantum simulator is laser-cooled atoms [1] held in an artificial crystal of light, generated by superimposing laser beams. The atoms are kept in this optical lattice similar to marbles in the hollows of an egg carton, and they can mimic the behaviour of electrons in a real crystal. These systems interface atomic physics with condensed matter physics in a new way, as the tools of atomic physics allow for exquisite control of many experimental parameters, which are often inaccessible in solid state experiments. In-situ imaging techniques [2] using ‘quantum-gas microscopes’ constitute a new approach to the study of many-body quantum systems in an optical lattice with unprecedented resolution at the single-particle and single-site level [3,4]. This new method is complementary to earlier optical lattice experiments measuring distributions in momentum space after a time-of-flight expansion. A quantum-gas microscope uses an optical imaging system (Fig. 1a) for collecting the fluorescence light of ultracold atoms in an optical lattice with high spatial resolution comparable to the lattice spacing of ≈ 500 nm. (a) Atoms in optical lattice atoms are imaged with a high-resolution microscope objective [4]. (b) Single-site addressing is achieved by focussing a laser beam through the microscope onto selected atoms, bringing them into resonance with microwave radiation which produces spin flips [12]. (c) and (d) Single-atom-resolved fluorescence images of bosonic Mottinsulators [4,9]. (e) Deterministically prepared atom distribution using single-site addressing [12]. (f) Direct observation of single-atom quantum walks [15]. Fluorescence imaging of atoms in a quantum-gas microscope has made it possible to directly observe bosonic Mott insulators with single-atom resolution [4–6], giving access to in-situ measurements of temperature and entropy distributions. Subsequently, ground-breaking experiments in many-body quantum dynamics have been performed, such as the first direct observation of correlation spreading after quenches of the system to lower lattice depths [7]. Other experiments include the quantum simulation of an antiferromagnetic spin-1/2 chain [8], the realization of algorithmic cooling [9], the direct measurement of correlations across the superfluid-to-Mott-insulator transition [10], or the observation of the ‘Higgs’ amplitude mode [11]. The high-resolution imaging system is also capable of optically addressing individual atoms with sub-diffraction-limited resolution. For this purpose, a laser beam is focussed though the microscope objective onto selected lattice sites, bringing the atoms into resonance with microwave radiation which produces spin flips [12,13]. The preparation of arbitrary atom distributions in the lattice not only opens perspectives for neutral-atom quantum information processing, but also allows the deterministic creation of specific out-of-equilibrium situations, and their ensuing system dynamics can be studied with single-atom resolution. Examples include the creation of spin impurities and the study of their dynamics in a many-body system [14], the observation of quantum walks [15] and magnon-bound states [16], and the measurement of entanglement entropy [17]. The technique used for single-site-resolved detection of individual atoms in the optical lattice is fluorescence imaging. It requires laser cooling of the atoms to sub-Doppler temperatures while detecting the fluorescence photons emitted during this process. A challenge is to achieve a low particle loss rate and to prevent the atoms from hopping between lattice sites. In the case of the first quantum-gas microscopes, this has been implemented with bosonic rubidium-87 atoms, and also recently for ytterbium-174. However, it has proven more challenging for fermionic alkaline species such as potassium-40 and lithium-6, as their low mass and small excited state hyperfine splitting-prevented standard sub-Doppler cooling from working. As a result, it took several years to extend the quantum-gas microscope technique to fermionic species, and in 2015 several groups have demonstrated single-atom-resolved imaging of fermions [18]. In these setups, the direct observation of band insulators [19], fermionic Mott insulators [20,21] and even antiferromagnetic correlations [22] has been reported most recently. These developments provide fascinating opportunities to study many-body fermionic quantum systems with single-particle access. The fermionic nature of the electron is vital to understanding a range of phenomena within solid-state physics, such as electron pairing in superconductivity, and quantum magnetism. In this context, the quantum simulator will allow, e.g. for direct measurement of ordered quantum phases and out-of-equilibrium dynamics, with access to quantities such as spin--spin correlation functions and the growth of many-body entanglement. The high-resolution imaging systems could also be used to project tailored time-varying light fields onto the atoms, allowing the removal of high-entropy regions by locally modifying the confining potential to attain very low-entropy states. Attaining these low-entropy many-particle states is one of the key challenges in our field. In summary, quantum-gas microscopes offer unprecedented access to many-body quantum systems, and they will allow us to gain an even deeper insight into the intriguing world of quantum physics that governs the properties of strongly correlated materials. Using a well-controlled quantum system to simulate other quantum systems could help resolve some of the most challenging problems scientists face in condensed matter physics and materials science, but it will also provide new insights in quantum chemistry, high-energy physics and biology. SK acknowledges funding from the EU (ERC FERMILATT, SIQS, QuProCs) and SUPA.