Laser cooling and qubit measurements on a forbidden transition in neutral Cs atoms

TL;DR

This work demonstrates background-free, hyperfine-resolved readout of a single neutral Cs qubit by simultaneous cooling and imaging on the forbidden $6s_{1/2}\rightarrow 5d_{5/2}$ $E2$ transition, achieving a state-detection fidelity of $F=0.9993(4)$ with atom retention $0.9954(5)$. By integrating 3D cooling, the method enables repeated low-loss measurements, and a quantitative analysis shows that exciting-state quenching via the $5d_{5/2}\rightarrow 6p_{3/2}$ pathway could boost the scattering rate by ~50× and reduce the readout time to ~$60\ \mu$s with fidelity near $0.9995$, approaching the regime needed for scalable error correction. The work combines detailed modeling (Lindblad dynamics with full hyperfine structure) and experimental demonstrations, including precise depumping-rate analysis, fidelity/atom-loss determination, and an exploration of a fast, qubit-friendly readout protocol. Overall, the approach bridges fast measurement requirements with high fidelity and low loss in neutral-atom qubit platforms, offering a path toward faster, scalable quantum error correction in free-space Cs arrays.

Abstract

We experimentally demonstrate background-free, hyperfine-level-selective measurements of individual Cs atoms by simultaneous cooling to $5.3~μ\rm K$ and imaging on the $6s_{1/2}\rightarrow 5d_{5/2}$ electric-quadrupole transition. We achieve hyperfine resolved detection with fidelity 0.9993(4) and atom retention of 0.9954(5), limited primarily by vacuum lifetime. Performing state measurements in a 3D cooling configuration enables repeated low loss measurements. A theoretical analysis of an extension of the demonstrated approach based on quenching of the excited state with an auxiliary field, identifies parameters for hyperfine-resolved measurements with a projected fidelity of $\sim 0.9995 $ in $\sim 60~μ\rm s$.

Figures (8)

• Figure 1: Representative measurements of neutral atom qubit states in free space reported in the literature. The results are quantified in terms of the measurement time and the generalized fidelity given by the state detection fidelity $F$ times the atom retention probability $1-P_{\rm loss}$ . The experiments a,b,g,h with the shortest integration times used single photon counting detectors and all others used cameras: a Fuhrmanek2011, b Gibbons2011, c Kwon2017, d Martinez-Dorantes2017, e TYWu2019, f Covey2019a, g Shea2020, h Chow2023, i Huie2023, j Lis2023, k Norcia2024, l RTao2024, m SMa2023. The open square shows the predicted performance with excited state quenching.
• Figure 2: Laser cooling on the Cs 685 nm quadrupole transition. a) Experimental setup with magnetic quadrupole axis along the front-back beams and magnetic bias field along the axis of the objective lens, b) transitions used for first and 2$^{\rm nd}$ stage cooling, c) time of flight measurement of temperature of 2$^{\rm nd}$ stage MOT, d) Ramsey coherence of a single atom cooled with 685 nm light. The fit functions in panels c) and d) are defined in the sections on MOT temperature and $T_2^*$ measurements in SMScott2025.
• Figure 3: Single atom state measurements with 685 nm 3D molasses. a) Histogram of photoelectron counts with 200 ms integration time, $\Delta=-2.54\Gamma$, $\sum_j I_j = 1.8~\rm W/cm^2$. The atom loading fraction is 41%. b) State characterization error $E_c$ as a function of the count threshold Radnaev2025 c) Atom retention in the $f=4$ level after repeated measurements. The inset shows a two-measurement density plot with a few loss events (lower right quadrant) and no reloading events (upper left quadrant).
• Figure 4: Measured atom loss and hyperfine depumping as a function of the duration of the quadrupole imaging pulse. At the beginning and end of the pulse, the occupancy of $\ket{6s_{1/2}, f=4}$ is measured, which is labeled as camera exposure. To measure the hyperfine depumping fraction a resonant $\ket{6s_{1/2}, f=4} \rightarrow \ket{6p_{3/2}, f=5}$ "blow-away" beam removes all remaining $f=4$ atoms, and a short repump pulse moves all depumped atoms back into the $f=4$ level followed by a third imaging pulse. See SMScott2025 for additional explanation.
• Figure 5: Simulation of quadrupole imaging with auxiliary quenching field showing the dependence of measurement infidelity due to Raman events and the measurement time needed to scatter 100 photons. The detunings were set to $\Delta_{E_1} = 2\pi\times 0.6$ MHz, $\Delta_{E_2} = -2\pi \times 0.42~{\rm MHz} = -3.56\, \Gamma_{5d}$. A minimum infidelity of $5.03\times 10^{-4}$ at a measurement time of $60~\mu\rm s$ is found for $\Omega_{E_1} = 2\pi\times 2.8$ MHz and $\Omega_{E_2} = 2\pi\times 1.2$ MHz. The dipole Rabi frequency of the quenching beam is defined on the transition $\ket{5d_{5/2},f"=6,m_{f"}=1} - \ket{6p_{3/2},f'=5,m_{f'}=0}.$ The quadrupole Rabi frequency is defined on the transition $\ket{6s_{1/2},f=4,m_{f}=0} - \ket{5d_{5/2},f"=6,m_{f"}=\pm1}.$