Gate-based Readout and Cooling of Neutral Atoms

Abstract

Neutral atom arrays have seen tremendous progress in quantum simulation, quantum metrology, and fault-tolerant quantum computing. However, hardware constraints such as atom loss and heating remain significant challenges. In this work, we introduce a comprehensive ancilla-based toolbox for optical tweezer experiments that utilizes high-fidelity Rydberg entangling gates and ancilla atoms to mitigate these physical limitations. First, we demonstrate repeated ancilla-based atom readout, achieving improved detection fidelity over multiple rounds with minimal perturbation to data atoms. Second, leveraging the quantized motional states in tweezer-trapped strontium atoms, we transduce quantum information from the electronic to the motional manifold. This enables us to perform mid-circuit ancilla-based atom loss detection in a coherence-preserving fashion. Finally, we demonstrate algorithmic cooling, a circuit-based sequence that deterministically cools data atoms by transferring their motional entropy to the electronic states of ancilla atoms. We observe a marked reduction in the atomic temperature of data atoms. These tools offer a pathway to continuous operation in tweezer clocks and complement recent developments in continuous reloading experiments.

Figures (4)

• Figure 1: Overview of ancilla-based toolbox for tweezer array experiments. (a) Sketch of our experimental setup. The one-dimensional tweezer array, generated by an acousto-optical deflector (not shown), supports in-situ dynamical array reconfiguration and local arbitrary $Z$ gate implementation via single-site atom movements. Global clock and Rydberg laser beams propagate co-linearly along the array, implementing single-qubit gates and entangling gates, respectively. Global imaging is achieved with a pair of counter-propagating angled beams overlapping with the whole array. (b) Relevant electronic states of atomic strontium. We encode quantum information in $^3\text{P}_0$ (the clock state) and $^1\text{S}_0$ (the ground state), which we denote $\ket{\uparrow}$ and $\ket{\downarrow}$, respectively. Motional Fock states in the tweezer are denoted by $\ket{n_m}$, with the first two $\ket{1_m}$ and $\ket{0_m}$ employed during mid-circuit readout. Collectively, these states constitute a motional omg-architecture, adapted for tweezer-trapped $^{88}\text{Sr}$ atoms. (c) The three main ancilla-based applications demonstrated with ancilla atoms (blue) and data atoms (purple) in this work: repeated atom readout, coherence-preserving atom loss detection, ancilla-assisted removal of motional excitation (i.e., algorithmic cooling).
• Figure 2: Repeated ancilla-based atom readout. (a) Circuit representation of the scheme. Data atoms, if present, are initialized in the electronic excited state $\ket{\uparrow}$. Under ideal conditions, the data atom remains unperturbed and a new ancilla atom is brought in via dynamical array reconfiguration after each round of ancilla-based atom detection. (b) Decomposition of CNOT gate (shown in (a)) and calibration of the single-atom phase $\phi$ after the Rydberg pulse. We maximize the ancilla atom population in $\ket{\downarrow}$ ($\ket{\uparrow}$) if data atom is present (absent). The electronic state of the data atom is insensitive to this phase $\phi$ thanks to the site-selective $Z$ gate implemented via local atom movement. Solid lines are sinusoidal fits. (c) Histograms of ancilla signal obtained from repeated mid-circuit readout for two distinct configurations: data atom absent (red), and data atom present (blue). The ancilla signals up to $N_{\text{cyc}}$ cycles are aggregated by an unweighted, cumulative sum. The initial overlap of the two distributions for $N_{\text{cyc}} = 1$ is limited by the fast imaging fidelity on the ancilla atom and CNOT gate fidelity. As $N_{\text{cyc}}$ increases, the distributions separate further, demonstrating improved detection with repeated ancilla-based readout. (d) From the histograms, we compute the detection fidelity $F$ with data atom presence prior $P_1$ and classification fidelity $F_1$ ($F_0$) in the presence (absence) of the data atom. For each $P_1$ and $N_{\text{cyc}}$, a classification threshold needs to be determined to obtain $F_1$ and $F_0$. This threshold is optimized against the overall detection fidelity $F$. As $N_{\text{cyc}}$ increases, we see a gradual improvement in $F$, a quantitative trend supporting the visual separation of the two distributions in (c). (e) From sideband spectroscopy, we infer an average motional occupation number of $0.002^{+5}_{-2}$ for the data atoms after erasure-cooling, before ancilla-based detection (lower). This number is measured to be $0.010^{+7}_{-7}$ after one round of ancilla-based detection (upper). This shows that data atoms are minimally perturbed in this ancilla-based detection scheme. Error bars represent 1$\sigma$ confidence interval and are typically smaller than the markers.
• Figure 3: Coherence-preserving ancilla-based atom loss detection. (a) Circuit representation of the detection scheme. The detection scheme starts with motional shelving of the data atom, which transduces the quantum information $\ket{\psi}$ into the motional state manifold and prepares it into $\ket{\uparrow}$. A subsequent CNOT gate flips the ancilla to $\ket{\downarrow}$ contingent on the data atom's presence; otherwise, the ancilla remains in $\ket{\uparrow}$. This is followed by mid-circuit fast imaging of the ancilla. Finally, motional unshelving on the data atom restores the initial internal superposition $\ket{\psi}$, followed by a direct readout (purple). (b) Diagram representation. We site-selectively address a data atom with the shelving pulse by engineering different trap frequencies for the data and ancilla atoms. Fill colors denote electronic states: blue, $\ket{\uparrow}$; red, $\ket{\downarrow}$. Semicircles represent state superpositions, either in the electronic or motional manifold. In the depicted scenario, the data atom is present and initialized in $(\ket{\uparrow}+ \ket{\downarrow})/\sqrt{2}$. Consequently, the ancilla atom is flipped to $\ket{\downarrow}$ by the entangling gate and detected via fast imaging. (c) Ancilla signal histograms. The two distributions, conditioning on the presence of the data atom, have clear peak separations. Assuming $P_1 = 0.5$, the detection fidelity is $F=0.88$ (see text for discussion on technical limitations). (d) Post-detection coherence, limited by single-qubit coherence time. Blue circles: Data atom population directly read out with an analyzer pulse of phase $\phi$, following one round of ancilla-based protocol. Red circles: Reference experiment using an identical sequence, but with the Rydberg and fast imaging light blocked. The relative offset reduction between the Ramsey fringes is attributed to shelving errors (see text). Solid lines are sinusoidal fits. Error bars represent $1\sigma$ confidence interval and are typically smaller than the markers.
• Figure 4: Algorithmic cooling of atoms using entangling gates with ancilla atoms. (a) Algorithmic cooling quantum circuit, consisting of six gates. At the end of the circuit, data atoms are prepared in electronic state $\ket{\uparrow}$ and motional state $\ket{n_{m,f}}$. If the cooling round has been successful, $n_{m,f} = \mathrm{max}(n_{m,i} - 1,0)$. Ancilla atoms are left in the $\ket{+}$ or $\ket{-}$ state, depending on whether the data atom was in the motional ground state to begin with. (b) Bloch sphere representations of the rotations performed on the data and ancilla atoms at each step. The top row shows the trajectories when the data atoms are initially not in the motional ground state, and the bottom row shows the trajectories when they are. (c) Fraction of total atom population, after one round of algorithmic cooling, which is measured in both the motional ground state and the correct electronic state, as a function of initial motional ground state population. This represents the combined success of cooling and state preparation in the circuit. Dashed line: break-even threshold for total usable population. Solid red line: theoretical maximum, corresponding to the perfect removal of one motional quantum from an initial Boltzmann distribution. (d) Motional ground state population, post-selected on the correct electronic state ($\ket{\uparrow}$) at the end of the cooling round. Error bars represent $1\sigma$ confidence intervals.