Rapid state-resolved single-atom imaging of alkaline-earth fermions

Abstract

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.

Figures (5)

• Figure 1: Experiment overview.a Individual $^{87}Sr$ atoms are trapped in an optical tweezer shined through a microscope objective in a ultra-high vacuum glass cell. Zoom in: A nuclear spin-dependent force is created by flashing a linearly polarized optical Stern-Gerlach beam (red, OSG) sent through the microscope objective with a slightly displaced center from the optical tweezer (violet) in the atomic plane. A subsequent free planar evolution in a light sheet dipole trap (gray plane) at the focus of the objective allows to infer the atomic spin from the atom position. b Fluorescence is induced by a pair of saturating alternating beams, which are propagating along $x$ and resonant with the blue transition of $Sr$. A few dozen photons collected via the objective are imaged on an EMCCD camera allowing to detect the presence of an atom with high fidelity (bottom experimental image). c Strontium level structure. Imaging is performed on the blue transition and the optical Stern-Gerlach beam operates near the red intercombination transition. In order to initialize ground-state atoms in the nuclear spin state $m_F=+9/2$, optical pumping is performed using a $\sigma^+$ polarized laser beam on the red intercombination line, in presence of a guiding magnetic field aligned with its propagation axis supp.
• Figure 2: Rapid imaging of $^{87}Sr$ in free space.a Left to right: Bias-corrected raw, binarized and low-pass filtered experimental images. b Histogram of the low-pass filtered images maxima, obtained for $15\,\mu s$ imaging time, displaying a characteristic double-peak structure allowing to distinguish the presence of an atom (high counts) from an empty shot (low-counts peak). A fit of the histogram (blue solid line) allows to define a threshold (vertical gray line) and to estimate the fidelity of this assignment. c Single-atom detection infidelity as a function of imaging time. d Spatial spread of the atomic fluorescence signal as a function of imaging time. The reported sizes are defined as the standard deviations of the fitted anisotropic gaussian along its major (yellow) and minor (blue) axis. Error bars represent one standard deviation of the mean.
• Figure 3: Spin-resolved imaging. a An optical Stern-Gerlach beam is detuned with $\Delta_{OSG}=+790\, MHz$ from the $F=9/2\to F^\prime=11/2$ red transition creating an $|m_F|$-dependent potential gradient at the atom location (left zoom-in, vertical dashed gray line). After illuminating the atom for $5\, \mu s$ with the OSG beam, the accumulated $|m_F|$-dependent momentum change is mapped during an in-plane expansion into spatially distinct locations detected by fluorescence imaging (right zoom-in: binarized images of individual realizations). The cross indicates the tweezer position. b Averaged fluorescence picture with one atom (left) displaying a four-regions structure, whereas after optical pumping to $m_F=+9/2$ only one region remains (right). c Left: Sum of all single atom locations in 3738 experimental realizations containing an atom. The spin region assignment is determined from a four-components gaussian mixture modeling of the atom locations supp. d Top: Distance of the spin regions centers from the tweezer position. Middle: Major and minor sizes of the four gaussian distributions used in the model. Bottom: $|m_F|$ assignment infidelities.
• Figure 4: Coherent spin dynamics.a Top: Atoms initialized in the $m_F=+9/2$ state evolve under a near-transverse magnetic field for a time $t$ before detection, which corresponds to a unitary evolution under a hamiltonian $\hat{H} \sim \hat{F}_x$ where $\hat{F}$ is a spin-$9/2$ operator. Bottom: Coherent spin dynamics theory expectations (left) induced by the field during the quench supp and as would be measured by our detection method only sensitive to $|m_F|$ (right). b Experimental time evolution of the $|m_F|$ populations. c Time evolutions of the $|m_F|=9/2$ (blue dots), $|m_F|=7/2$ (yellow squares), $|m_F|=5/2$ (red diamonds), and $|m_F|=3/2,1/2$ (green triangles) populations and theory expectations (solid lines). d Long time population dynamics for $|m_F|=9/2$ (blue dots) and $|m_F|=3/2,1/2$ (green triangles) and theory expectations (solid lines). Error bars represent one standard deviation of the mean.
• Figure S1: a Single-atom detection probability as a function of hold time with tweezer off. Solid line: classical Monte-Carlo expectation for a temperature of $750\,nK$. b Numerical simulations results of the optical Stern-Gerlach detection method for a cropped thermal distribution (36 lowest energy states) in the tweezer at $T=750\,nK$ (left), and for the harmonic oscillator ground state (right), taking into account the spatial resolution of our detection due to atomic motion during imaging. As seen on the experiment only four regions are well defined and both the center distances of the $|m_F|$-regions as well as their elliptical shape are in good agreement with the experiment. From a comparison with ground-state expectations the spin-detection fidelities for the experimental settings in this manuscript were limited by the initial atomic temperature, and the absence of visible splitting between $|m_F|=3/2$ and $|m_F|=1/2$ was attributed to the atomic motion during imaging.