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Long-lived Bell states in an array of optical clock qubits

Nature Physics volume 18, pages 1067–1073 (2022)Cite this article

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Abstract

The generation of long-lived entanglement in optical atomic clocks is one of the main goals of quantum metrology. Arrays of neutral atoms, where Rydberg-based interactions may generate entanglement between individually controlled and resolved atoms, constitute a promising quantum platform to achieve this. Here we leverage the programmable state preparation afforded by optical tweezers and the efficient strong confinement of a three-dimensional optical lattice to prepare an ensemble of strontium-atom pairs in their motional ground state. We engineer global single-qubit gates on the optical clock transition and two-qubit entangling gates via adiabatic Rydberg dressing, enabling the generation of Bell states with a state-preparation-and-measurement-corrected fidelity of 92.8(2.0)% (87.1(1.6)% without state-preparation-and-measurement correction). For use in quantum metrology, it is furthermore critical that the resulting entanglement be long lived; we find that the coherence of the Bell state has a lifetime of 4.2(6) s via parity correlations and simultaneous comparisons between entangled and unentangled ensembles. Such long-lived Bell states can be useful for enhancing metrological stability and bandwidth. In the future, atomic rearrangement will enable the implementation of many-qubit gates and cluster state generation, as well as explorations of the transverse field Ising model.

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Fig. 1: Quantum-enhanced optical frequency metrology.
Fig. 2: Clock-qubit-controlled phase gate via adiabatic Rydberg pulses.
Fig. 3: Bell-state fidelity.
Fig. 4: Bell-state coherence time.

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Data availability

The experimental data presented in this manuscript are available upon request and through Zenodo (https://doi.org/10.5281/zenodo.6626065).

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Acknowledgements

We acknowledge J. Ye and his lab, particularly D. Kedar, for the operation and provision of the silicon-crystalline-cavity-stabilized clock laser and helpful conversations. We thank I. Deutsch, A. M. Rey, C. Sanner and A. Cao for fruitful discussions and feedback on the manuscript. A.M.K. acknowledges support from ARO grant no. W911NF-19-1-0223, AFOSR grant no. FA9550-19-1-0275, DOE Quantum System Accelerator (QSA) grant no. 7565477+, NSF QSEnSE QLCI-2016244, NSF JILA-PFC PHY 1734006 and NIST. N.S. acknowledges support from the NRC research associateship program. W.J.E. acknowledges support from the NDSEG. M.J.M. was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory under project nos. 20190494ER and 20200015ER.

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Author notes

  1. These authors contributed equally: Nathan Schine, Aaron W. Young.

Authors and Affiliations

  1. JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO, USA

    Nathan Schine, Aaron W. Young, William J. Eckner & Adam M. Kaufman

  2. Los Alamos National Laboratory, Los Alamos, NM, USA

    Michael J. Martin

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Contributions

The experiment was designed and built by N.S., A.W.Y., W.J.E. and A.M.K. N.S., A.W.Y. and W.J.E. operated the experiment and analysed the data. All the authors contributed to the manuscript.

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Correspondence to Adam M. Kaufman.

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Extended data

Extended Data Fig. 1 FIG. M1. Trapping potentials of our apparatus.

Our experiments make use of three separate optical trapping potentials. After producing a cold atomic sample via standard MOT techniques, we load atoms into an array of 515 nm optical tweezers projected through a high-numerical-aperture objective. This forms a 2d array of atoms which are then transfered into a single plane of a 3d optical lattice which is formed by two separate optical systems. First, a 2d bowtie lattice is formed using a single beam redirected by a series of mirrors and lenses. A second, axial lattice is projected from the side by directing two path-length-matched beams into a single aspheric lens.

Extended Data Fig. 2 FIG. M2. Single atom control.

a) Tight atomic confinement and a 550 G magnetic field enable a clock Rabi frequency above 1 kHz with π-pulse fidelity well above 99%; however, fidelity is limited to 99.41(57)% in part by atomic heating (which also causes dephasing at later times, see SI). Inset shows the corresponding clock transition π-pulse spectrum. b) A UV laser near 317 nm drives a clock-Rydberg transition with Rabi with frequency Ωr = 2π × 13 MHz. We detect the Rydberg state via loss of the clock state atoms. The horizontal dashed line represents an 89% Rydberg detection fidelity estimated from branching ratios of intermediate triplet S states (see text).

Extended Data Fig. 3 FIG. M3. Experimental Sequence.

We present a more detailed view of the experimental sequence that includes the clock laser pulses (red), the Rydberg laser pulses (purple), the 2d lattice (orange), the axial lattice (pink), and the z-component of the magnetic field (blue). Typical lattice ramping times are 3-10 ms, and we allow the magnetic field to ramp and settle for 100 ms. Although we can achieve clock Rabi frequencies as high as 1 kHz, we operate a factor of 10 slower to reduce the effect of magnetic field noise. As such, the total gate time from the first π/2-pulse through the second π/2-pulse is 22.2 ms, with 12 ms arising from the four 2d lattice ramps within the gate sequence.

Extended Data Fig. 4 FIG. M4. Removing inhomogeneous lightshifts across the atom array.

The lattice potential that confines the atoms during hold times is not perfectly magic or homogeneous, which can limit array-averaged correlation signals. By increasing lattice laser detuning from the magic condition, we more clearly reveal the effects of a non-magic-lattice inhomogeneity in spatially resolved parity-parity correlation measurements at short times (a,d), after 1 second (b,e), and after 2 seconds (c,f). The location of each pixel corresponds to a displacement vector between fully filled doublets, while the color corresponds to the product of the parities of each doublet with that displacement vector. a-c) Even in a shallow lattice condition, significant residual inhomogeneous lightshifts result in negative parity-parity correlations appearing along the main diagonal, reducing the array-averaged parity-parity correlator. d-f) Introducing a π-pulse half way through the hold time spin-echoes away the inhomogeneity, increasing the array-averaged parity-parity correlator.

Extended Data Table 1 TABLE M1. Experimental Parameters.

Select parameters are tabulated for each dataset presented in the main text.

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Schine, N., Young, A.W., Eckner, W.J. et al. Long-lived Bell states in an array of optical clock qubits. Nat. Phys. 18, 1067–1073 (2022). https://doi.org/10.1038/s41567-022-01678-w

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