Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015).
Ushijima, I., Takamoto, M., Das, M., Ohkubo, T. & Katori, H. Cryogenic optical lattice clocks. Nat. Photon. 9, 185–189 (2015).
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).
Schioppo, M. et al. Ultrastable optical clock with two cold-atom ensembles. Nat. Photon. 11, 48–52 (2017).
Li, J. et al. A strontium lattice clock with both stability and uncertainty below 5 × 10−18. Metrologia 61, 015006 (2024).
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).
Zheng, X. et al. Differential clock comparisons with a multiplexed optical lattice clock. Nature 602, 425–430 (2022).
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).
Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).
Pogorelov, I. et al. Compact ion-trap quantum computing demonstrator. PRX Quantum 2, 020343 (2021).
Leibfried, D. et al. Creation of a six-atom ‘Schrödinger cat’ state. Nature 438, 639–642 (2005).
Cao, A. et al. Multi-qubit gates and Schrödinger cat states in an optical clock. Nature 634, 315–320 (2024).
Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993).
Yurke, B., McCall, S. L. & Klauder, J. R. SU(2) and SU(1,1) interferometers. Phys. Rev. A 33, 4033–4054 (1986).
Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. J. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67–88 (1994).
Davis, E., Bentsen, G. & Schleier-Smith, M. Approaching the Heisenberg limit without single-particle detection. Phys. Rev. Lett. 116, 053601 (2016).
Fröwis, F., Sekatski, P. & Dür, W. Detecting large quantum Fisher information with finite measurement precision. Phys. Rev. Lett. 116, 090801 (2016).
Sjöqvist, E. Nonadiabatic holonomic single-qubit gates in off-resonant Λ systems. Phys. Lett. A 380, 65–67 (2016).
Aharonov, Y. & Anandan, J. Phase change during a cyclic quantum evolution. Phys. Rev. Lett. 58, 1593–1596 (1987).
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).
Liu, Q. et al. Enhancing dynamic range of sub-standard-quantum-limit measurements via quantum deamplification. Phys. Rev. Lett. 135, 040801 (2025).
Marciniak, C. D. et al. Optimal metrology with programmable quantum sensors. Nature 603, 604–609 (2022).
Mehlstäubler, T. E., Grosche, G., Lisdat, C., Schmidt, P. O. & Denker, H. Atomic clocks for geodesy. Rep. Prog. Phys. 81, 064401 (2018).
Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).
Kolkowitz, S. et al. Gravitational wave detection with optical lattice atomic clocks. Phys. Rev. D 94, 124043 (2016).
Sanner, C. et al. Optical clock comparison for Lorentz symmetry testing. Nature 567, 204–208 (2019).
Wcisło, P. et al. New bounds on dark matter coupling from a global network of optical atomic clocks. Sci. Adv. 4, eaau4869 (2018).
Song, C. et al. Generation of multicomponent atomic Schrödinger cat states of up to 20 qubits. Science 365, 574–577 (2019).
Omran, A. et al. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570–574 (2019).
Finkelstein, R. et al. Universal quantum operations and ancilla-based read-out for tweezer clocks. Nature 634, 321–327 (2024).
Gross, C., Zibold, T., Nicklas, E., Estève, J. & Oberthaler, M. K. Nonlinear atom interferometer surpasses classical precision limit. Nature 464, 1165–1169 (2010).
Riedel, M. F. et al. Atom-chip-based generation of entanglement for quantum metrology. Nature 464, 1170–1173 (2010).
Hosten, O., Engelsen, N. J., Krishnakumar, R. & Kasevich, M. A. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).
Bao, H. et al. Spin squeezing of 1011 atoms by prediction and retrodiction measurements. Nature 581, 159–163 (2020).
Anders, F. et al. Momentum entanglement for atom interferometry. Phys. Rev. Lett. 127, 140402 (2021).
Greve, G. P., Luo, C., Wu, B. & Thompson, J. K. Entanglement-enhanced matter-wave interferometry in a high-finesse cavity. Nature 610, 472–477 (2022).
Pedrozo-Peñafiel, E. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020).
Sewell, R. J. et al. Magnetic sensitivity beyond the projection noise limit by spin squeezing. Phys. Rev. Lett. 109, 253605 (2012).
Muessel, W., Strobel, H., Linnemann, D., Hume, D. B. & Oberthaler, M. K. Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates. Phys. Rev. Lett. 113, 103004 (2014).
Cassens, C., Meyer-Hoppe, B., Rasel, E. & Klempt, C. Entanglement-enhanced atomic gravimeter. Phys. Rev. X 15, 011029 (2025).
Kruse, I. et al. Improvement of an atomic clock using squeezed vacuum. Phys. Rev. Lett. 117, 143004 (2016).
Appel, J. et al. Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit. Proc. Natl Acad. Sci. USA 106, 10960–10965 (2009).
Nolan, S. P., Szigeti, S. S. & Haine, S. A. Optimal and robust quantum metrology using interaction-based readouts. Phys. Rev. Lett. 119, 193601 (2017).
Hosten, O., Krishnakumar, R., Engelsen, N. J. & Kasevich, M. A. Quantum phase magnification. Science 352, 1552–1555 (2016).
Linnemann, D. et al. Quantum-enhanced sensing based on time reversal of nonlinear dynamics. Phys. Rev. Lett. 117, 013001 (2016).
Gilmore, K. A. et al. Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals. Science 373, 673–678 (2021).
Colombo, S. et al. Time-reversal-based quantum metrology with many-body entangled states. Nature Physics 18, 925–930 (2022).
Schleier-Smith, M. H., Leroux, I. D. & Vuletić, V. Squeezing the collective spin of a dilute atomic ensemble by cavity feedback. Phys. Rev. A 81, 021804 (2010).
Braverman, B. et al. Near-unitary spin squeezing in 171Yb. Phys. Rev. Lett. 122, 223203 (2019).
Bishof, M., Zhang, X., Martin, M. J. & Ye, J. Optical spectrum analyzer with quantum-limited noise floor. Phys. Rev. Lett. 111, 093604 (2013).
Solomon, I. Rotary spin echoes. Phys. Rev. Lett. 2, 301–302 (1959).
Blatt, S. et al. Rabi spectroscopy and excitation inhomogeneity in a one-dimensional optical lattice clock. Phys. Rev. A 80, 052703 (2009).
Norcia, M. A. et al. Seconds-scale coherence on an optical clock transition in a tweezer array. Science 366, 93–97 (2019).
Takamoto, M., Takano, T. & Katori, H. Frequency comparison of optical lattice clocks beyond the Dick limit. Nat. Photon. 5, 288–292 (2011).
Nicholson, T. L. et al. Comparison of two independent Sr optical clocks with 1 × 10−17 stability at 103 s. Phys. Rev. Lett. 109, 230801 (2012).
Riehle, F. Optical clock networks. Nat. Photon. 11, 25–31 (2017).
Li, Y. et al. Multiparameter estimation with an array of entangled atomic sensors. Preprint at https://arxiv.org/abs/2504.08677 (2025).
Malia, B. K., Wu, Y., Martínez-Rincón, J. & Kasevich, M. A. Distributed quantum sensing with mode-entangled spin-squeezed atomic states. Nature 612, 661–665 (2022).
Dzuba, V. A. et al. Strongly enhanced effects of Lorentz symmetry violation in entangled Yb+ ions. Nat. Phys. 12, 465–468 (2016).
Zhou, Z., Carrasco, S. C., Sanner, C., Malinovsky, V. S. & Folman, R. Geometric phase amplification in a clock interferometer for enhanced metrology. Sci. Adv. 11, eadr6893 (2025).
Koczor, B., Zeier, R. & Glaser, S. J. Fast computation of spherical phase-space functions of quantum many-body states. Phys. Rev. A 102, 062421 (2020).