Abstract
The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is fundamental for many studies in quantum metrology1, simulation2 and information3. However, the simultaneous realization of these properties remains a central challenge in quantum science across atomic and condensed-matter systems2,4,5,6,7. Here we leverage the favourable properties of tweezer-trapped alkaline-earth (strontium-88) atoms8,9,10, and introduce a hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout and preservation of atomic coherence. With this approach, we achieve trapping and optical-clock excited-state lifetimes exceeding 40 seconds in ensembles of approximately 150 atoms. This leads to half-minute-scale atomic coherence on an optical-clock transition, corresponding to quality factors well in excess of 1016. These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is comparable with that of leading atomic systems, which use optical lattices to interrogate many thousands of atoms in parallel11,12. The result is a relative fractional frequency stability of 5.2(3) × 10−17τ−1/2 (where τ is the averaging time in seconds) for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout that are available in this system, these results pave the way towards long-lived engineered entanglement on an optical-clock transition13 in tailored atom arrays.
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Data availability
The experimental data presented in this manuscript are available from the corresponding author upon reasonable request. Source data are provided with this paper.
Code availability
The code used for analysis and simulation in this work is available from the corresponding author upon reasonable request.
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Acknowledgements
We acknowledge discussions with R. B. Hutson, J. K. Thompson, M. Foss-Feig, S. Kolkowitz and J. Simon. We further acknowledge F. Vietmeyer and M. O. Brown for assistance in the design and development of our FPGA-based tweezer control system. This work was supported by ARO, AFOSR, DARPA, the National Science Foundation Physics Frontier Center at JILA (1734006) and NIST. M.A.N., E.O. and N.S. acknowledge support from the NRC research associateship programme.
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A.W.Y., W.J.E., M.A.N., N.S. and A.M.K. built and operated the tweezer apparatus, and the silicon-crystal-stabilized clock laser was operated by W.R.M., D.K., E.O. and J.Y. All authors contributed to the data analysis and the development of the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Sideband cooling and inhomogeneous broadening.
The trap frequency and cooling performance in the radial direction is uniform across the entire array, as further confirmed by spectra taken along a radial axis orthogonal to that of the data presented in Fig. 1d (left). However, in a reduced 6 × 6 region at the centre of the array (shown in the far-right inset), the axial cooling performance is vastly improved (right), with an average phonon occupation of \(\bar{n}={0.00}_{-0.00}^{+0.06}\) (\(\bar{n}={0.06}_{-0.06}^{+0.10}\)) before (after) the handoff. This is due to the comparable extent of the lattice beams to the tweezer array (the light-green contour in the far-right inset shows the region over which the lattice intensity stays within 90% of its maximal value). Each data point corresponds to 20 repetitions of the experiment.
Extended Data Fig. 2 Lattice alignment.
a, b, Spatial phase of the standing-wave lattice at each tweezer, inferred from measurements at 15 values of the lattice phase averaged over 100 trials (see Supplementary Information) with an intentional tilt (a, left) and properly aligned (a, right). These show that it is possible flatten the lattice relative to the entire tweezer array to within 1/10 of a lattice period (b). This allows for high-fidelity sideband cooling in all axes. ‘Cts’, counts; ‘arb.’, arbitrary units.
Extended Data Fig. 3 Timing of experimental sequence.
a, The green and black curves track the depths of the 515-nm and 813-nm tweezers, respectively. The coloured regions above and below the graph categorize each step of the experiment (described in more detail in Methods). We find that maintaining the 813-nm tweezers at a depth greater than 20Er during the ramp down improves the fidelity of the handoff procedure. Not shown is the time required to load atoms into the 515-nm tweezers from the magneto-optical traps used for initial trapping and cooling, which takes roughly 120 ms. LAC, light-assisted collisions. b, Zoomed-in view of our cooling procedure, showing the depth of the axial lattice. We perform two rounds of sideband cooling, indicated by the two regions shaded in grey. The first, done before ramping up the axial lattice, does not cool axial motion to the ground state. Instead, it is important for reducing the size of the atomic wave packet to ensure loading of a single lattice fringe.
Extended Data Fig. 4 Measuring atom–laser coherence.
Fitting measured Ramsey fringes with fringes of a fixed frequency provides a conservative estimate of atom–laser coherence. Callouts share x-axis units with the main plot, and show the fitted Ramsey data (the same data as used in Fig. 2b). ‘pop.’, population.
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This file contains Supplementary Text and Supplementary Figures S1–S5.
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Young, A.W., Eckner, W.J., Milner, W.R. et al. Half-minute-scale atomic coherence and high relative stability in a tweezer clock. Nature 588, 408–413 (2020). https://doi.org/10.1038/s41586-020-3009-y
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DOI: https://doi.org/10.1038/s41586-020-3009-y
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