Abstract
The dynamical trajectory of a dissipative Rydberg many-body system could be flipped under a microwave field driving, displaying an enhanced sensitivity. This is because the intersection of the folded hysteresis trajectories exhibits a sharp peak near the phase transition, amplifying the response to small changes in the microwave field. Here, we demonstrate an experiment of enhanced metrology through flipping the hysteresis trajectory in a cold atomic system, displaying an approach to improve sensitivity by the gap-closing points. By measuring the intersection points of hysteresis trajectories versus Rabi frequency of the microwave field, we quantify the equivalent sensitivity to be 1.6(5) nV cm−1Hz−1/2. The measurement is also dependent on the interaction time, optical depth and principal quantum number since the long-range interaction between Rydberg atoms could dramatically change the shape of hysteresis trajectories. The reported results suggest that flipping trajectory features in cold Rydberg many-body systems could advance sensing and metrology applications.
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The data generated in this study have been deposited in the Zenodo database (https://zenodo.org/records/17451657).
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The custom codes used to produce the results presented in this paper are available from the corresponding authors upon request.
References
Jin, B., Su, G. & Zheng, Q.-R. First-and second-order phase transitions, Fulde-Ferrell inhomogeneous state, and quantum criticality in ferromagnet/superconductor double tunnel junctions. Phys. Rev. B 71, 144514 (2005).
Sarkar, S., Mukhopadhyay, C., Alase, A. & Bayat, A. Free-fermionic topological quantum sensors. Phys. Rev. Lett. 129, 090503 (2022).
Li, L., Lee, C. H., Mu, S. & Gong, J. Critical non-hermitian skin effect. Nat. Commun. 11, 5491 (2020).
Zhang, X., Zhang, T., Lu, M.-H. & Chen, Y.-F. A review on non-hermitian skin effect. Adv. Phys.: X 7, 2109431 (2022).
Lee, J. Y., Ahn, J., Zhou, H. & Vishwanath, A. Topological correspondence between hermitian and non-hermitian systems: Anomalous dynamics. Phys. Rev. Lett. 123, 206404 (2019).
De Léséleuc, S. et al. Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms. Science 365, 775 (2019).
Porta, S., Cavaliere, F., Sassetti, M. & Traverso Ziani, N. Topological classification of dynamical quantum phase transitions in the xy chain. Sci. Rep. 10, 12766 (2020).
Pérez-Espigares, C., Lesanovsky, I., Garrahan, J. P. & Gutiérrez, R. Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases. Phys. Rev. A 98, 021804 (2018).
Hao, D. et al. Topological atomic spin wave lattices by dissipative couplings. Phys. Rev. Lett. 130, 153602 (2023).
Wu, X. et al. Dissipative time crystal in a strongly interacting Rydberg gas. Nat. Phys. 1 https://www.nature.com/articles/s41567-024-02542-9 (2024).
Jiang, M. et al. Floquet spin amplification. Phys. Rev. Lett. 128, 233201 (2022).
Liu, B. et al. Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms. Nat. Commun. 15, 9730 (2024).
Liu, B. et al. Bifurcation of time crystals in driven and dissipative Rydberg atomic gas. Nat. Commun. 16, 1419 (2025).
O’Connor, E. et al. Quantum-enhanced parameter estimation in continuously monitored boundary time crystals, arXiv:2508.15448 https://doi.org/10.48550/arXiv.2508.15448 (2025).
Lourenço, J. A., Higgins, G., Zhang, C., Hennrich, M. & Macrì, T. Non-hermitian dynamics and pt-symmetry breaking in interacting mesoscopic Rydberg platforms. Phys. Rev. A 106, 023309 (2022).
Chen, C. et al. Continuous symmetry breaking in a two-dimensional Rydberg array. Nature 616, 691 (2023).
Shen, R. et al. Proposal for observing Yang-Lee criticality in Rydberg atomic arrays. Phys. Rev. Lett. 131, 080403 (2023).
Gao, H. et al. Experimental observation of the Yang-Lee quantum criticality in open quantum systems. Phys. Rev. Lett. 132, 176601 (2024).
Wang, Y.-C., You, J.-S. & Jen, H.-H. A non-hermitian optical atomic mirror. Nat. Commun. 13, 4598 (2022).
Li, Z. et al. Synergetic positivity of loss and noise in nonlinear non-Hermitian resonators. Sci. Adv. 9, eadi0562 (2023).
Laflorencie, N. Quantum entanglement in condensed matter systems. Phys. Rep. 646, 1 (2016).
Ma, G., Xiao, M. & Chan, C. T. Topological phases in acoustic and mechanical systems. Nat. Rev. Phys. 1, 281 (2019).
Barik, S. et al. A topological quantum optics interface. Science 359, 666 (2018).
Parto, M., Liu, Y. G., Bahari, B., Khajavikhan, M. & Christodoulides, D. N. Non-hermitian and topological photonics: optics at an exceptional point. Nanophotonics 10, 403 (2020).
Roushan, P. et al. Observation of topological transitions in interacting quantum circuits. Nature 515, 241 (2014).
Imhof, S. et al. Topolectrical-circuit realization of topological corner modes. Nat. Phys. 14, 925 (2018).
Yoshida, T., Danshita, I., Peters, R. & Kawakami, N. Reduction of topological Z classification in cold-atom systems. Phys. Rev. Lett. 121, 025301 (2018).
Li, L., Lee, C. H. & Gong, J. Topological switch for non-hermitian skin effect in cold-atom systems with loss. Phys. Rev. Lett. 124, 250402 (2020).
Montenegro, V., Mishra, U. & Bayat, A. Global sensing and its impact for quantum many-body probes with criticality. Phys. Rev. Lett. 126, 200501 (2021).
Ilias, T., Yang, D., Huelga, S. F. & Plenio, M. B. Criticality-enhanced quantum sensing via continuous measurement. PRX Quantum 3, 010354 (2022).
Montenegro, V. et al. Quantum metrology and sensing with many-body systems, arXiv:2408.15323 https://arxiv.org/abs/2408.15323 (2024).
Lau, H.-K. & Clerk, A. A. Fundamental limits and non-reciprocal approaches in non-hermitian quantum sensing. Nat. Commun. 9, 4320 (2018).
Budich, J. C. & Bergholtz, E. J. Non-hermitian topological sensors. Phys. Rev. Lett. 125, 180403 (2020).
Koch, F. & Budich, J. C. Quantum non-hermitian topological sensors. Phys. Rev. Res. 4, 013113 (2022).
Sarkar, S., Ciccarello, F., Carollo, A. & Bayat, A. Critical non-hermitian topology induced quantum sensing. N. J. Phys. 26, 073010 (2024).
Sarkar, S., Bayat, A., Bose, S. & Ghosh, R. Exponentially-enhanced quantum sensing with many-body phase transitions. Nat. Commun. 16, 5159 (2025).
Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313 (2010).
Adams, C. S., Pritchard, J. D. & Shaffer, J. P. Rydberg atom quantum technologies. J. Phys. B: Mol. Opt. Phys. 53, 012002 (2019).
Browaeys, A. & Lahaye, T. Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132 (2020).
Lee, T. E., Häffner, H. & Cross, M. C. Collective quantum jumps of Rydberg atoms. Phys. Rev. Lett. 108, 023602 (2012).
Carr, C., Ritter, R., Wade, C., Adams, C. S. & Weatherill, K. J. Nonequilibrium phase transition in a dilute Rydberg ensemble. Phys. Rev. Lett. 111, 113901 (2013).
Schempp, H. et al. Full counting statistics of laser excited Rydberg aggregates in a one-dimensional geometry. Phys. Rev. Lett. 112, 013002 (2014).
Marcuzzi, M., Levi, E., Diehl, S., Garrahan, J. P. & Lesanovsky, I. Universal nonequilibrium properties of dissipative Rydberg gases. Phys. Rev. Lett. 113, 210401 (2014).
Lesanovsky, I. & Garrahan, J. P. Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation. Phys. Rev. A 90, 011603 (2014).
Urvoy, A. et al. Strongly correlated growth of Rydberg aggregates in a vapor cell. Phys. Rev. Lett. 114, 203002 (2015).
Helmrich, S. et al. Signatures of self-organized criticality in an ultracold atomic gas. Nature 577, 481 (2020).
Ding, D.-S., Busche, H., Shi, B.-S., Guo, G.-C. & Adams, C. S. Phase diagram of non-equilibrium phase transition in a strongly-interacting Rydberg atom vapour. Phys. Rev. X 10, 021023 (2020).
Wintermantel, T. M. et al. Unitary and nonunitary quantum cellular automata with Rydberg arrays. Phys. Rev. Lett. 124, 070503 (2020).
Klocke, K., Wintermantel, T., Lochead, G., Whitlock, S. & Buchhold, M. Hydrodynamic stabilization of self-organized criticality in a driven Rydberg gas. Phys. Rev. Lett. 126, 123401 (2021).
Gambetta, F. M., Carollo, F., Marcuzzi, M., Garrahan, J. P. & Lesanovsky, I. Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems. Phys. Rev. Lett. 122, 015701 (2019).
Wadenpfuhl, K. & Adams, C. S. Emergence of synchronization in a driven-dissipative hot Rydberg vapor. Phys. Rev. Lett. 131, 143002 (2023).
Ding, D. et al. Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system. Sci. Adv. 10, eadl5893 (2024).
Liu, B. et al. Microwave seeding time crystal in Floquet-driven Rydberg atoms, arXiv:2404.12180 https://arxiv.org/abs/2404.12180 (2024).
Ma, Y. et al. Microwave-driven multistability in a strongly interacting Rydberg atoms, arXiv:2408.10514 https://arxiv.org/abs/2408.10514 (2024).
Samajdar, R., Ho, W. W., Pichler, H., Lukin, M. D. & Sachdev, S. Quantum phases of Rydberg atoms on a kagome lattice. Proc. Natl Acad. Sci. 118, e2015785118 (2021).
Kanungo, S. et al. Realizing topological edge states with Rydberg-atom synthetic dimensions. Nat. Commun. 13, 972 (2022).
Li, K., Wang, J.-H., Yang, Y.-B. & Xu, Y. Symmetry-protected topological phases in a Rydberg glass. Phys. Rev. Lett. 127, 263004 (2021).
Li, X. & Sarma, S. D. Exotic topological density waves in cold atomic Rydberg-dressed fermions. Nat. Commun. 6, 7137 (2015).
Verresen, R., Lukin, M. D. & Vishwanath, A. Prediction of toric code topological order from Rydberg blockade. Phys. Rev. X 11, 031005 (2021).
Sedlacek, J. A. et al. Microwave electrometry with Rydberg atoms in a vapour cell using bright atomic resonances. Nat. Phys. 8, 819 (2012).
Jing, M. et al. Atomic superheterodyne receiver based on microwave-dressed Rydberg spectroscopy. Nat. Phys. 16, 911 (2020).
Ding, D.-S. et al. Enhanced metrology at the critical point of a many-body Rydberg atomic system. Nat. Phys. 18, 1447 (2022).
Liu, B. et al. Highly sensitive measurement of a megahertz rf electric field with a Rydberg-atom sensor. Phys. Rev. Appl. 18, 014045 (2022).
Zhang, L.-H. et al. Rydberg microwave-frequency-comb spectrometer. Phys. Rev. Appl. 18, 014033 (2022).
Zhang, L.-H. et al. Ultra-wide dual-band Rydberg atomic receiver based on space division multiplexing radio-frequency chip modules. Chip 3, 100089 (2024).
Liu, B. et al. Electric field measurement and application based on Rydberg atoms. Electromagn. Sci. 1, 1 (2023).
Zhang, H. et al. Rydberg atom electric field sensing for metrology, communication and hybrid quantum systems. Sci. Bull. https://www.sciencedirect.com/science/article/pii/S2095927324001889 (2024).
Delplace, P., Yoshida, T. & Hatsugai, Y. Symmetry-protected multifold exceptional points and their topological characterization. Phys. Rev. Lett. 127, 186602 (2021).
Zhang, J. et al. Exceptional point and hysteresis trajectories in cold Rydberg atomic gases. Nat. Commun. 16, 3511 (2025).
Zhang, Z. et al. Microwave-coupled optical bistability in driven and interacting Rydberg gases. npj Quantum Inf. 11, 44 (2025).
Yuce, C. Stable topological edge states in a non-hermitian four-band model. Phys. Rev. A 98, 012111 (2018).
Hokmabadi, M. P., Schumer, A., Christodoulides, D. N. & Khajavikhan, M. Non-hermitian ring laser gyroscopes with enhanced sagnac sensitivity. Nature 576, 70 (2019).
Chen, W., Kaya Özdemir, Ş., Zhao, G., Wiersig, J. & Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192 (2017).
Zhang, S. et al. A dark-line two-dimensional magneto-optical trap of 85Rb atoms with high optical depth. Rev. Sci. Instrum. 83 https://pubs.aip.org/aip/rsi/article/83/7/073102/354527 (2012).
Fancher, C. T., Scherer, D. R., John, M. C. S. & Marlow, B. L. S. Rydberg atom electric field sensors for communications and sensing. IEEE Trans. Quantum Eng. 2, 1 (2021).
Bussey, L. W., Burton, F. A., Bongs, K., Goldwin, J. & Whitley, T. Quantum shot noise limit in a Rydberg rf receiver compared to thermal noise limit in a conventional receiver. IEEE Sens. Lett. 6, 1 (2022).
Simons, M. T., Gordon, J. A. & Holloway, C. L. Simultaneous use of cs and rb Rydberg atoms for dipole moment assessment and rf electric field measurements via electromagnetically induced transparency. J. Appl. Phys. 120 https://pubs.aip.org/aip/jap/article/120/12/123103/345712 (2016).
Šibalić, N., Pritchard, J. D., Adams, C. S. & Weatherill, K. J. Arc: An open-source library for calculating properties of alkali Rydberg atoms. Comput. Phys. Commun. 220, 319 (2017).
Acknowledgements
We acknowledge funding from the National Key R and D Program of China (Grant no. 2022YFA1404002), the National Natural Science Foundation of China (Grant nos. T2495253, 62435018), and the Major Science and Technology Projects in Anhui Province (Grant no. 202203a13010001).
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D.-S.D., L.-H.Z., and B.L. conceived the idea. J.Z., Y.J.W., and Z.Y.Z. conducted the physical experiments. D.-S.D. and Y.J.W. developed the theoretical model. The data was analyzed with the assistance of S.-Y.S., Q.L., H.-C.C., Y.M., T.-Y.H., Q.-F.W., J.-D.N., Y.-M.Y., D.-Y.Z., Q.-Q.F., Y.C., X.L., G.-C.G., B.L., L.-H.Z. and B.-S.S. The manuscript was written by D.-S.D., Y.J.W., J.Z., and Z.Y.Z. The research was supervised by D.-S.D. All authors contributed to discussions regarding the results and the analysis contained in the manuscript.
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Wang, YJ., Zhang, J., Zhang, ZY. et al. Quantum enhanced metrology based on flipping trajectory of cold Rydberg gases. Nat Commun (2026). https://doi.org/10.1038/s41467-025-67921-z
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DOI: https://doi.org/10.1038/s41467-025-67921-z
