Universal Gate Operations on Nuclear Spin Qubits in an Optical Tweezer Array of ${}^{171}\mathrm{Yb}$ Atoms

Neutral atom arrays are a rapidly developing platform for quantum science. Recently, alkaline earth atoms (AEAs) have attracted interest because their unique level structure provides several opportunities for improved performance. In this work, we present the first demonstration of a universal set of quantum gate operations on a nuclear spin qubit in an AEA, using ${}^{171}\mathrm{Yb}$. We implement narrow-line cooling and imaging using a newly discovered magic trapping wavelength at $\lambda =486.78\mathrm{nm}$. We also demonstrate nuclear spin initialization, readout, and single-qubit gates and observe long coherence times [$T_1\approx 20\mathrm{s}$ and $T_2^{*}=1.24(5)\mathrm{s}$] and a single-qubit operation fidelity ${\mathcal{F}}_{1Q}=0.99959(6)$. We also demonstrate two-qubit entangling gates using the Rydberg blockade, as well as coherent control of these gate operations using light shifts on the ${\mathrm{Yb}}^{+}$ ion core transition at 369 nm. These results are a significant step toward highly coherent quantum gates in AEA tweezer arrays.

Popular Summary

Neutral atom arrays are a rapidly developing platform for quantum computing and simulation, with demonstrated scaling to large system sizes and highly coherent operations. To date, most experiments have used alkali atoms, but alkaline earthlike atoms (AEAs) with a more complex electronic structure offer several advantages. Recently, experiments with AEAs in tweezer arrays have shown extremely efficient cooling and detection, higher fidelity entangling operations, and applications to optical atomic clocks. However, universal gate operations on a ground-state spin have not been realized. Here, we implement a universal set of gate operations on an AEA spin qubit, using ytterbium-171 atoms.

Encoding the qubit in the nuclear spin of the atomic ground state, we observe coherence times for the nuclear spin of more than one second, several orders of magnitude longer than typical alkali atom qubits in optical tweezers. The qubit can be manipulated using hyperfine coupling in excited states, including Rydberg states, and we use this approach to realize both one- and two-qubit gate operations on the nuclear spin.

This work opens the door to large-scale, highly coherent quantum computing and programmable simulation using nuclear spin qubits in AEA tweezer arrays. It will also benefit the field of tweezer-based optical clocks, allowing extensions to fermionic isotopes and entanglement-enhanced metrology.

Figure 1

(a) ${}^{171}\mathrm{Yb}$ level diagram. A qubit is encoded in the nuclear spin sublevels of the ${{}^{1}S}_0$ ground state and initialized into $|1⟩$ via optical pumping (OP). Spin rotations are performed using an rf field. Two-qubit gates are performed using the $6s74s$ ${}^3{S}_1$ $|F,m_F⟩=|3/2,3/2⟩$ level, accessed via two-photon excitation through ${}^3{P}_1$. State readout is performed by blowing out atoms in $|1⟩$ by autoionization from the Rydberg state. (b) Orientation of the control fields and tweezers. (c) Histogram of photons detected in a single tweezer region during a 25 ms image, and a fluorescence image of a 30-site array averaged over 1000 single-shot images without rearrangement. (d) Differential light shift measurement on the ${}^{171}\mathrm{Yb}$ ${{}^{1}S}_0\text{−}{}^3{P}_1$ transition in tweezers with $\lambda =486.78\mathrm{nm}$. The $F^{\prime }=3/2$ manifold is split by the tensor light shift, giving a differential shift of $0.3U_0$ for $|m_{F^{\prime }}|=3/2$ and $0.0001(6)U_0$ for $|m_{F^{\prime }}|=1/2$. The error bar corresponds to one standard deviation uncertainty in the fitted resonant frequency.

Figure 2

(a) Atom survival probability after $N_r$ repetitions of the blowout sequence through the Rydberg state, after preparing an atom in $|1⟩$ (black) and $|0⟩$ (orange). (b) Rabi oscillations of the nuclear spin qubit, with ${\mathrm{\Omega }}_{\mathrm{rf}}=2\pi \times 161.7(5)\mathrm{Hz}$. The error bars indicate the statistical uncertainty ($\pm 1\sigma$) in the measured survival probability.

Figure 3

Coherence measurements of the ${}^{171}\mathrm{Yb}$ nuclear spin qubit. (a) Array-averaged Ramsey fringes with fitted $1/e$ decay time of ${\overline{T}}_2^{*}=1.00(4)\mathrm{s}$ [fitting sites individually yields an average $T_2^{*}=1.24(5)\mathrm{s}$]. The gray shaded envelope indicates the contribution from a magnetic field gradient across the array. (b) Spin-echo measurement. The phase of the final $\pi /2$ pulse is scanned for each wait time $T$, and the coherence is extracted from the visibility (insets) and normalized to the mean survival. The normalized coherence decays to $1/e$ after a time $T_2=5(1)\mathrm{s}$. (c) Spin $T_1$ measurement. The orange (black) points show the probability to detect an atom in $|0⟩$ following initialization in $|0⟩$ ($|1⟩$). The gray points show survival probability without the spin readout sequence (i.e., atom loss), which decays to $1/e$ after $T_a=9.0(3)\mathrm{s}$. Using survival-normalized populations, we infer an intrinsic $1/e$ spin flip time for each state: $T_1^{|0⟩}=13(2)\mathrm{s}$ and $T_1^{|1⟩}=27(2)\mathrm{s}$. (d) Randomized benchmarking of single-qubit rotations. Orange (black) points show the probability to obtain the correct result for sequences ending in $|0⟩$ ($|1⟩$). From the decay rates, we obtain an average gate fidelity of 99.959(6)%. In all panels, the error bars show $\pm 1\sigma$ statistical error.

Figure 4

Two-qubit gate. (a) Circuit diagram of the two-qubit gate characterization experiment. (b) Single-shot image of atom pairs created using rearrangement. The gate consists of two Rydberg pulses, with a phase shift on the second pulse. The level diagrams and Bloch sphere trajectories indicate the dynamics for the computational states $|01⟩$ (red) and $|11⟩$ (blue). (c) Evolution of the states $|1⟩$ (blue, used as a proxy for $|01⟩$) and $|11⟩$ (red) state during the gate. The solid lines are simulations using the master equation with a phenomenological dephasing contribution. (d) Measured state populations at the circuit location indicated by the red dashed line. (e) Parity oscillations, with contrast $\mathcal{C}=0.79(3)$. In all panels, the error bars show $\pm 1\sigma$ statistical error.

Figure 5

Coherent control of a Rydberg gate using an ion core light shift. (a) The two-qubit gate is suppressed by applying light near resonance with a ${\mathrm{Yb}}^{+}$ ion core transition (369 nm) during the gate. (b) Evolution of the states $|1⟩$ (red stars) and $|11⟩$ (blue stars) during a suppressed gate. The dynamics without the control light are shown for comparison [reproduced from Fig. 4]. (c) Measured state populations with (purple) and without (blue) the control light. (d) Coherence of the nuclear spin in ${{}^{1}S}_0$ under continuous illumination with the control light (purple). The measured $T_2=5.1(7)\mathrm{s}$ is consistent with Fig. 3 (reproduced here, in blue). In all panels, the error bars show $\pm 1\sigma$ statistical error.

Figure 6

Ratio of the differential light shifts for the ${{}^{1}S}_0\text{−}{}^3{P}_1$ transition in ${}^{174}\mathrm{Yb}$, for the $m_{J^{\prime }}=0$ ($\mathrm{\Delta }{U}_0=U_0-{\tilde{U}}_0$) and $|m_{J^{\prime }}|=1$ ($\mathrm{\Delta }{U}_1=U_1-{\tilde{U}}_0$) transitions. The black points show measurements from ${}^{174}\mathrm{Yb}$, while the red points show inferred values from measurements with ${}^{171}\mathrm{Yb}$. A magic wavelength for the ${}^{171}\mathrm{Yb}$ ${{}^{1}S}_0$-${}^3{P}_1$ $F^{\prime }=3/2,|m_{F^{\prime }}|=1/2$ transition occurs when $\mathrm{\Delta }{U}_0/\mathrm{\Delta }{U}_1=-1/2$ (dashed red line), which we confirm in ${}^{171}\mathrm{Yb}$ at 486.78 nm and near 759 nm. The gray line is an approximate model to guide the eye. Inset: level diagram indicating the light shift on each state in ${}^{174}\mathrm{Yb}$.

Figure 7

Measuring the blockade radius. (a) We observe Rabi oscillations dimers with atom separations between 36 (dark blue) and $2.4\mu \mathrm{m}$ (light blue). (b) The fitted oscillation frequency as a function of atomic spacing. The oscillation frequency increases from ${\mathrm{\Omega }}_r=2\pi \times 0.63\mathrm{MHz}$ (green dashed line) to approximately $\sqrt{2}{\mathrm{\Omega }}_r$ (red dashed line) in the blockade regime. The deviation from the exact $\sqrt{2}$ ratio is attributed to a drift in the UV power over the duration of the measurement. The line is a phenomenological fit to extract the blockade radius $R_b$, where $C_6/R_b^6={\mathrm{\Omega }}_r$. This occurs when the oscillation frequency is halfway between ${\mathrm{\Omega }}_r$ and $\sqrt{2}{\mathrm{\Omega }}_r$. In all panels, the error bars show $\pm 1\sigma$ statistical error.