Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).
Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637 (2015).
Colombo, S., Pedrozo-Peñafiel, E. & Vuletić, V. Entanglement-enhanced optical atomic clocks. Appl. Phys. Lett. 121, 210502 (2022).
Pedrozo-Peñafiel, E. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020).
Robinson, J. M. et al. Direct comparison of two spin-squeezed optical clock ensembles at the 10−17 level. Nat. Phys. 20, 208–213 (2024).
Eckner, W. J. et al. Realizing spin squeezing with Rydberg interactions in an optical clock. Nature 621, 734–739 (2023).
Norcia, M. A. et al. Seconds-scale coherence on an optical clock transition in a tweezer array. Science 366, 93–97 (2019).
Madjarov, I. S. et al. An atomic-array optical clock with single-atom readout. Phys. Rev. X 9, 041052 (2019).
Young, A. W. et al. Half-minute-scale atomic coherence and high relative stability in a tweezer clock. Nature 588, 408–413 (2020).
Shaw, A. L. et al. Multi-ensemble metrology by programming local rotations with atom movements. Nat. Phys. 20, 195–201 (2024).
Evered, S. J. et al. High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 622, 268–272 (2023).
Ma, S. et al. High-fidelity gates and mid-circuit erasure conversion in an atomic qubit. Nature 622, 279–284 (2023).
Huelga, S. F. et al. Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79, 3865 (1997).
Higgins, B. et al. Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements. New J. Phys. 11, 073023 (2009).
Berry, D. W. et al. How to perform the most accurate possible phase measurements. Phys. Rev. A 80, 052114 (2009).
Kessler, E. M. et al. Heisenberg-limited atom clocks based on entangled qubits. Phys. Rev. Lett. 112, 190403 (2014).
Komar, P. et al. A quantum network of clocks. Nat. Phys. 10, 582–587 (2014).
Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).
Schirhagl, R., Chang, K., Loretz, M. & Degen, C. L. Nitrogen-vacancy centers in diamond: nanoscale sensors for physics and biology. Annu. Rev. Phys. Chem. 65, 83–105 (2014).
Bongs, K. et al. Taking atom interferometric quantum sensors from the laboratory to real-world applications. Nat. Rev. Phys. 1, 731–739 (2019).
Tse, M. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).
Backes, K. M. et al. A quantum enhanced search for dark matter axions. Nature 590, 238–242 (2021).
Casacio, C. A. et al. Quantum-enhanced nonlinear microscopy. Nature 594, 201–206 (2021).
Bluvstein, D. et al. A quantum processor based on coherent transport of entangled atom arrays. Nature 604, 451–456 (2022).
Graham, T. M. et al. Multi-qubit entanglement and algorithms on a neutral-atom quantum computer. Nature 604, 457–462 (2022).
Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626, 58–65 (2024).
Jandura, S. & Pupillo, G. Time-optimal two- and three-qubit gates for Rydberg atoms. Quantum 6, 712 (2022).
Levine, H. et al. Parallel implementation of high-fidelity multiqubit gates with neutral atoms. Phys. Rev. Lett. 123, 170503 (2019).
Bloom, B. et al. An optical lattice clock with accuracy and stability at the 10−18 level. Nature 506, 71–75 (2014).
Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015).
McGrew, W. F. et al. Atomic clock performance enabling geodesy below the centimetre level. Nature 564, 87–90 (2018).
Brewer, S. M. et al. 27Al+ quantum-logic clock with a systematic uncertainty below 10−18. Phys. Rev. Lett. 123, 033201 (2019).
Oelker, E. et al. Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks. Nat. Photon. 13, 714–719 (2019).
Bothwell, T. et al. Resolving the gravitational redshift across a millimetre-scale atomic sample. Nature 602, 420–424 (2022).
Zheng, X. et al. Differential clock comparisons with a multiplexed optical lattice clock. Nature 602, 425–430 (2022).
Schine, N., Young, A. W., Eckner, W. J., Martin, M. J. & Kaufman, A. M. Long-lived Bell states in an array of optical clock qubits. Nat. Phys. 18, 1067–1073 (2022).
Scholl, P. et al. Erasure-cooling, control, and hyper-entanglement of motion in optical tweezers. Preprint at https://arxiv.org/abs/2311.15580 (2023).
Fröwis, F. & Dür, W. Measures of macroscopicity for quantum spin systems. New J. Phys. 14, 093039 (2012).
Tóth, G. & Apellaniz, I. Quantum metrology from a quantum information science perspective. J. Phys. A 47, 424006 (2014).
Pogorelov, I. et al. Compact ion-trap quantum computing demonstrator. PRX Quantum 2, 020343 (2021).
Moses, S. A. et al. A race-track trapped-ion quantum processor. Phys. Rev. X 13, 041052 (2023).
Bao, Z. et al. Schrödinger cats growing up to 60 qubits and dancing in a cat scar enforced discrete time crystal. Preprint at https://arxiv.org/abs/2401.08284 (2024).
Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004).
Nagata, T., Okamoto, R., O’Brien, J. L., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007).
Jones, J. A. et al. Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states. Science 324, 1166–1168 (2009).
Facon, A. et al. A sensitive electrometer based on a Rydberg atom in a Schrödinger-cat state. Nature 535, 262–265 (2016).
Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).
Urban, E. et al. Observation of Rydberg blockade between two atoms. Nat. Phys. 5, 110–114 (2009).
Dudin, Y., Li, L., Bariani, F. & Kuzmich, A. Observation of coherent many-body Rabi oscillations. Nat. Phys. 8, 790–794 (2012).
Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000).
Omran, A. et al. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570–574 (2019).
Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).
Leroux, I. D. et al. On-line estimation of local oscillator noise and optimisation of servo parameters in atomic clocks. Metrologia 54, 307 (2017).
Matei, D. G. et al. 1.5 μm lasers with sub-10 mHz linewidth. Phys. Rev. Lett. 118, 263202 (2017).
Kaubruegger, R., Vasilyev, D. V., Schulte, M., Hammerer, K. & Zoller, P. Quantum variational optimization of Ramsey interferometry and atomic clocks. Phys. Rev. X 11, 041045 (2021).
Marciniak, C. D. et al. Optimal metrology with programmable quantum sensors. Nature 603, 604–609 (2022).
Nichol, B. et al. An elementary quantum network of entangled optical atomic clocks. Nature 609, 689–694 (2022).
Norcia, M. A. et al. Iterative assembly of 171Yb atom arrays in cavity-enhanced optical lattices. PRX Quantum 5, 030316 (2024).
Gyger, F. et al. Continuous operation of large-scale atom arrays in optical lattices. Phys. Rev. Res. 6, 033104 (2024).
Lis, J. W. et al. Midcircuit operations using the omg architecture in neutral atom arrays. Phys. Rev. X 13, 041035 (2023).
Finkelstein, R. et al. Universal quantum operations and ancilla-based readout for tweezer clocks. Nature https://doi.org/10.1038/s41586-024-08005-8 (2024).
Kaubruegger, R. et al. Variational spin-squeezing algorithms on programmable quantum sensors. Phys. Rev. Lett. 123, 260505 (2019).
Colombe, Y., Slichter, D. H., Wilson, A. C., Leibfried, D. & Wineland, D. J. Single-mode optical fiber for high-power, low-loss UV transmission. Opt. Express 22, 19783–19793 (2014).
Young, A. W., Eckner, W. J., Schine, N., Childs, A. M. & Kaufman, A. M. Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice. Science 377, 885–889 (2022).
Dörscher, S. et al. Lattice-induced photon scattering in an optical lattice clock. Phys. Rev. A 97, 063419 (2018).
Scholl, P. et al. Erasure conversion in a high-fidelity Rydberg quantum simulator. Nature 622, 273–278 (2023).
Madjarov, I. S. et al. High-fidelity entanglement and detection of alkaline-earth Rydberg atoms. Nat. Phys. 16, 857–861 (2020).
Taichenachev, A. V. et al. Magnetic field-induced spectroscopy of forbidden optical transitions with application to lattice-based optical atomic clocks. Phys. Rev. Lett. 96, 083001 (2006).
Hein, M., Eisert, J. & Briegel, H. J. Multiparty entanglement in graph states. Phys. Rev. A 69, 062311 (2004).
Zeiher, J. et al. Microscopic characterization of scalable coherent Rydberg superatoms. Phys. Rev. X 5, 031015 (2015).
Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).
Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T. & Glaser, S. J. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296–305 (2005).
Löw, R. et al. An experimental and theoretical guide to strongly interacting Rydberg gases. J. Phys. B. 45, 113001 (2012).
Derevianko, A., Kómár, P., Topcu, T., Kroeze, R. M. & Lukin, M. D. Effects of molecular resonances on Rydberg blockade. Phys. Rev. A 92, 063419 (2015).
Young, A. W. et al. An atomic boson sampler. Nature 629, 311–316 (2024).
Jandura, S., Thompson, J. D. & Pupillo, G. Optimizing Rydberg gates for logical-qubit performance. PRX Quantum 4, 020336 (2023).
Demkowicz-Dobrzański, R., Jarzyna, M. & Kołodyński, J. in Progress in Optics (ed. Wolf, E.) 345–435 (Elsevier, 2015).
Rosenband, T. & Leibrandt, D. R. Exponential scaling of clock stability with atom number. Preprint at https://arxiv.org/abs/1303.6357 (2013).
Borregaard, J. & Sørensen, A. S. Efficient atomic clocks operated with several atomic ensembles. Phys. Rev. Lett. 111, 090802 (2013).
Macieszczak, K., Fraas, M. & Demkowicz-Dobrzański, R. Bayesian quantum frequency estimation in presence of collective dephasing. New J. Phys. 16, 113002 (2014).
Jarzyna, M. & Demkowicz-Dobrzański, R. True precision limits in quantum metrology. New J. Phys. 17, 013010 (2015).
Górecki, W., Demkowicz-Dobrzański, R., Wiseman, H. M. & Berry, D. W. π-corrected Heisenberg limit. Phys. Rev. Lett. 124, 030501 (2020).
Zheng, X., Dolde, J. & Kolkowitz, S. Reducing the instability of an optical lattice clock using multiple atomic ensembles. Phys. Rev. X 14, 011006 (2024).