{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T23:02:22Z","timestamp":1771023742717,"version":"3.50.1"},"reference-count":58,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T00:00:00Z","timestamp":1770940800000},"content-version":"vor","delay-in-days":17,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-026-36403-7","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T10:28:19Z","timestamp":1769509699000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multipassage Landau-Zener tunneling oscillations in the dual dressing of atomic qubits"],"prefix":"10.1038","volume":"16","author":[{"given":"Alessandro","family":"Fregosi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carmela","family":"Marinelli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlo","family":"Gabbanini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valerio","family":"Biancalana","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria","family":"Allegrini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ennio","family":"Arimondo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesco","family":"Petiziol","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sandro","family":"Wimberger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Fioretti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"Bevilacqua","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"36403_CR1","doi-asserted-by":"publisher","first-page":"B979","DOI":"10.1103\/PhysRev.138.B979","volume":"138","author":"JH Shirley","year":"1965","unstructured":"Shirley, J. H. Solution of the Schr\u00f6dinger equation with a Hamiltonian periodic in time. Phys. Rev. 138, B979\u2013B987. https:\/\/doi.org\/10.1103\/PhysRev.138.B979 (1965).","journal-title":"Phys. Rev."},{"key":"36403_CR2","doi-asserted-by":"publisher","first-page":"2203","DOI":"10.1103\/PhysRevA.7.2203","volume":"7","author":"H Sambe","year":"1973","unstructured":"Sambe, H. Steady states and quasienergies of a quantum-mechanical system in an oscillating field. Phys. Rev. A 7, 2203\u20132213. https:\/\/doi.org\/10.1103\/PhysRevA.7.2203 (1973).","journal-title":"Phys. Rev. A"},{"key":"36403_CR3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.4.031027","volume":"4","author":"N Goldman","year":"2014","unstructured":"Goldman, N. & Dalibard, J. Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields. Phys. Rev. X 4, 031027. https:\/\/doi.org\/10.1103\/PhysRevX.4.031027 (2014).","journal-title":"Phys. Rev. X"},{"key":"36403_CR4","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1080\/00018732.2015.1055918","volume":"64","author":"M Bukov","year":"2015","unstructured":"Bukov, M., D\u2019Alessio, L. & Polkovnikov, A. Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. Advances in Physics 64, 139\u2013226. https:\/\/doi.org\/10.1080\/00018732.2015.1055918 (2015).","journal-title":"Advances in Physics"},{"key":"36403_CR5","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.89.011004","volume":"89","author":"A Eckardt","year":"2017","unstructured":"Eckardt, A. Colloquium: Atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004. https:\/\/doi.org\/10.1103\/RevModPhys.89.011004 (2017).","journal-title":"Rev. Mod. Phys."},{"key":"36403_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.111.185301","volume":"111","author":"M Aidelsburger","year":"2013","unstructured":"Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301. https:\/\/doi.org\/10.1103\/PhysRevLett.111.185301 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.205301","volume":"116","author":"F Meinert","year":"2016","unstructured":"Meinert, F., Mark, M. J., Lauber, K., Daley, A. J. & N\u00e4gerl, H.-C. Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms. Phys. Rev. Lett. 116, 205301. https:\/\/doi.org\/10.1103\/PhysRevLett.116.205301 (2016).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR8","doi-asserted-by":"publisher","first-page":"1149","DOI":"10.1126\/science.abd9547","volume":"374","author":"S Geier","year":"2021","unstructured":"Geier, S. et al. Floquet Hamiltonian engineering of an isolated many-body spin system. Science 374, 1149\u20131152. https:\/\/doi.org\/10.1126\/science.abd9547 (2021).","journal-title":"Science"},{"key":"36403_CR9","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.1038\/s41567-021-01316-x","volume":"17","author":"C Weitenberg","year":"2021","unstructured":"Weitenberg, C. & Simonet, J. Tailoring quantum gases by Floquet engineering. Nature Physics 17, 1342\u20131348. https:\/\/doi.org\/10.1038\/s41567-021-01316-x (2021).","journal-title":"Nature Physics"},{"key":"36403_CR10","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.3.020303","volume":"3","author":"P Scholl","year":"2022","unstructured":"Scholl, P. et al. Microwave engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms. PRX Quantum 3, 020303. https:\/\/doi.org\/10.1103\/PRXQuantum.3.020303 (2022).","journal-title":"PRX Quantum"},{"key":"36403_CR11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.073603","volume":"128","author":"M-J Yin","year":"2022","unstructured":"Yin, M.-J. et al. Floquet engineering Hz-level Rabi spectra in shallow optical lattice clock. Phys. Rev. Lett. 128, 073603. https:\/\/doi.org\/10.1103\/PhysRevLett.128.073603 (2022).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.130.043201","volume":"130","author":"J-Y Zhang","year":"2023","unstructured":"Zhang, J.-Y. et al. Tuning anomalous Floquet topological bands with ultracold atoms. Phys. Rev. Lett. 130, 043201. https:\/\/doi.org\/10.1103\/PhysRevLett.130.043201 (2023).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.5.021027","volume":"5","author":"Y Salath\u00e9","year":"2015","unstructured":"Salath\u00e9, Y. et al. Digital quantum simulation of spin models with circuit quantum electrodynamics. Phys. Rev. X 5, 021027. https:\/\/doi.org\/10.1103\/PhysRevX.5.021027 (2015).","journal-title":"Phys. Rev. X"},{"key":"36403_CR14","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1038\/nphys3609","volume":"12","author":"F Mahmood","year":"2016","unstructured":"Mahmood, F. et al. Selective scattering between Floquet-Bloch and Volkov states in a topological insulator. Nature Physics 12, 306. https:\/\/doi.org\/10.1038\/nphys3609 (2016).","journal-title":"Nature Physics"},{"key":"36403_CR15","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1038\/s41567-020-01120-z","volume":"17","author":"P Peng","year":"2021","unstructured":"Peng, P., Yin, C., Huang, X., Ramanathan, C. & Cappellaro, P. Floquet prethermalization in dipolar spin chains. Nature Physics 17, 444\u2013447. https:\/\/doi.org\/10.1038\/s41567-020-01120-z (2021).","journal-title":"Nature Physics"},{"key":"36403_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.107.195441","volume":"107","author":"MP Liul","year":"2023","unstructured":"Liul, M. P. et al. Coherent dynamics of a photon-dressed qubit. Phys. Rev. B 107, 195441. https:\/\/doi.org\/10.1103\/PhysRevB.107.195441 (2023).","journal-title":"Phys. Rev. B"},{"key":"36403_CR17","doi-asserted-by":"publisher","first-page":"60","DOI":"10.3390\/physics6010005","volume":"6","author":"M Allegrini","year":"2024","unstructured":"Allegrini, M. & Arimondo, E. Atoms dressed by virtual and real photons. Physics 6, 60\u201374. https:\/\/doi.org\/10.3390\/physics6010005 (2024).","journal-title":"Physics"},{"key":"36403_CR18","doi-asserted-by":"publisher","unstructured":"Passante, R. & Rizzuto, L. Vacuum self-dressing of an atom and its physical effects. Physics 7. https:\/\/doi.org\/10.3390\/physics7020020 (2025).","DOI":"10.3390\/physics7020020"},{"key":"36403_CR19","doi-asserted-by":"publisher","unstructured":"Haroche, S., Cohen-Tannoudji, C., Audoin, C. & Schermann, J. P. Modified Zeeman hyperfine spectra observed in H$$^{1}$$ and Rb$$^{87}$$ ground states interacting with a nonresonant rf field. Phys. Rev. Lett. 24, 861. https:\/\/doi.org\/10.1103\/PhysRevLett.24.861 (1970).","DOI":"10.1103\/PhysRevLett.24.861"},{"key":"36403_CR20","doi-asserted-by":"publisher","unstructured":"Haroche, S. & Cohen-Tannoudji, C. Resonant transfer of coherence in nonzero magnetic field between atomic levels of different $$g$$ factors. Phys. Rev. Lett. 24, 974\u2013978. https:\/\/doi.org\/10.1103\/PhysRevLett.24.974 (1970).","DOI":"10.1103\/PhysRevLett.24.974"},{"key":"36403_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.093203","volume":"125","author":"G Bevilacqua","year":"2020","unstructured":"Bevilacqua, G., Biancalana, V., Vigilante, A., Zanon-Willette, T. & Arimondo, E. Harmonic fine tuning and triaxial spatial anisotropy of dressed atomic spins. Phys. Rev. Lett. 125, 093203. https:\/\/doi.org\/10.1103\/PhysRevLett.125.093203 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.105.022619","volume":"105","author":"G Bevilacqua","year":"2022","unstructured":"Bevilacqua, G., Biancalana, V., Zanon-Willette, T. & Arimondo, E. Harmonic dual dressing of spin-1\/2 systems. Phys. Rev. A 105, 022619. https:\/\/doi.org\/10.1103\/PhysRevA.105.022619 (2022).","journal-title":"Phys. Rev. A"},{"key":"36403_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.043436","volume":"98","author":"F Petiziol","year":"2018","unstructured":"Petiziol, F., Dive, B., Mintert, F. & Wimberger, S. Fast adiabatic evolution by oscillating initial Hamiltonians. Phys. Rev. A 98, 043436. https:\/\/doi.org\/10.1103\/PhysRevA.98.043436 (2018).","journal-title":"Phys. Rev. A"},{"key":"36403_CR24","doi-asserted-by":"publisher","first-page":"15001","DOI":"10.1209\/0295-5075\/ad19e3","volume":"145","author":"F Petiziol","year":"2024","unstructured":"Petiziol, F., Mintert, F. & Wimberger, S. Quantum control by effective counterdiabatic driving. Europhysics Letters 145, 15001. https:\/\/doi.org\/10.1209\/0295-5075\/ad19e3 (2024).","journal-title":"Europhysics Letters"},{"key":"36403_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2010.03.002","volume":"492","author":"S Shevchenko","year":"2010","unstructured":"Shevchenko, S., Ashhab, S. & Nori, F. Landau-Zener-St\u00fcckelberg interferometry. Physics Reports 492, 1\u201330. https:\/\/doi.org\/10.1016\/j.physrep.2010.03.002 (2010).","journal-title":"Physics Reports"},{"key":"36403_CR26","doi-asserted-by":"publisher","first-page":"1653","DOI":"10.1126\/science.1119678","volume":"310","author":"WD Oliver","year":"2005","unstructured":"Oliver, W. D. et al. Mach-Zehnder interferometry in a strongly driven superconducting qubit. Science 310, 1653\u20131657. https:\/\/doi.org\/10.1126\/science.1119678 (2005).","journal-title":"Science"},{"key":"36403_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.187002","volume":"96","author":"M Sillanp\u00e4\u00e4","year":"2006","unstructured":"Sillanp\u00e4\u00e4, M., Lehtinen, T., Paila, A., Makhlin, Y. & Hakonen, P. Continuous-time monitoring of Landau-Zener interference in a Cooper-pair box. Phys. Rev. Lett. 96, 187002. https:\/\/doi.org\/10.1103\/PhysRevLett.96.187002 (2006).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.86.121303","volume":"86","author":"J Stehlik","year":"2012","unstructured":"Stehlik, J. et al. Landau-Zener-St\u00fcckelberg interferometry of a single electron charge qubit. Phys. Rev. B 86, 121303. https:\/\/doi.org\/10.1103\/PhysRevB.86.121303 (2012).","journal-title":"Phys. Rev. B"},{"key":"36403_CR29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.112.010503","volume":"112","author":"J Zhou","year":"2014","unstructured":"Zhou, J. et al. Observation of time-domain Rabi oscillations in the Landau-Zener regime with a single electronic spin. Phys. Rev. Lett. 112, 010503. https:\/\/doi.org\/10.1103\/PhysRevLett.112.010503 (2014).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.90.104516","volume":"90","author":"AM Satanin","year":"2014","unstructured":"Satanin, A. M., Denisenko, M. V., Gelman, A. I. & Nori, F. Amplitude and phase effects in Josephson qubits driven by a biharmonic electromagnetic field. Phys. Rev. B 90, 104516. https:\/\/doi.org\/10.1103\/PhysRevB.90.104516 (2014).","journal-title":"Phys. Rev. B"},{"key":"36403_CR31","doi-asserted-by":"publisher","first-page":"1614","DOI":"10.1021\/acs.nanolett.5b04356","volume":"16","author":"MF Gonzalez-Zalba","year":"2016","unstructured":"Gonzalez-Zalba, M. F. et al. Gate-sensing coherent charge oscillations in a silicon field-effect transistor. Nano Letters 16, 1614\u20131619. https:\/\/doi.org\/10.1021\/acs.nanolett.5b04356 (2016).","journal-title":"Nano Letters"},{"key":"36403_CR32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.97.045405","volume":"97","author":"A Chatterjee","year":"2018","unstructured":"Chatterjee, A. et al. A silicon-based single-electron interferometer coupled to a fermionic sea. Phys. Rev. B 97, 045405. https:\/\/doi.org\/10.1103\/PhysRevB.97.045405 (2018).","journal-title":"Phys. Rev. B"},{"key":"36403_CR33","doi-asserted-by":"publisher","unstructured":"Ono, K., Shevchenko, S. N., Mori, T., Moriyama, S. & Nori, F. Quantum interferometry with a $$g$$-factor-tunable spin qubit. Phys. Rev. Lett. 122, 207703. https:\/\/doi.org\/10.1103\/PhysRevLett.122.207703 (2019).","DOI":"10.1103\/PhysRevLett.122.207703"},{"key":"36403_CR34","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.94.195108","volume":"94","author":"YI Rodionov","year":"2016","unstructured":"Rodionov, Y. I., Kugel, K. I. & Nori, F. Floquet spectrum and driven conductance in dirac materials: Effects of Landau-Zener-St\u00fcckelberg-Majorana interferometry. Phys. Rev. B 94, 195108. https:\/\/doi.org\/10.1103\/PhysRevB.94.195108 (2016).","journal-title":"Phys. Rev. B"},{"key":"36403_CR35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.104.053318","volume":"104","author":"W-X Liu","year":"2021","unstructured":"Liu, W.-X., Wang, T., Zhang, X.-F. & Li, W.-D. Time-domain Landau-Zener-St\u00fcckelberg-Majorana interference in an optical lattice clock. Phys. Rev. A 104, 053318. https:\/\/doi.org\/10.1103\/PhysRevA.104.053318 (2021).","journal-title":"Phys. Rev. A"},{"key":"36403_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2022.10.002","volume":"995","author":"OV Ivakhnenko","year":"2023","unstructured":"Ivakhnenko, O. V., Shevchenko, S. N. & Nori, F. Nonadiabatic Landau-Zener-St\u00fcckelberg-Majorana transitions, dynamics, and interference. Physics Reports 995, 1\u201389. https:\/\/doi.org\/10.1016\/j.physrep.2022.10.002 (2023).","journal-title":"Physics Reports"},{"key":"36403_CR37","doi-asserted-by":"publisher","first-page":"5033","DOI":"10.1038\/s41598-023-31084-y","volume":"13","author":"PO Kofman","year":"2023","unstructured":"Kofman, P. O., Ivakhnenko, O. V., Shevchenko, S. N. & Nori, F. Majorana\u2019s approach to nonadiabatic transitions validates the adiabatic-impulse approximation. Scientific Reports 13, 5033. https:\/\/doi.org\/10.1038\/s41598-023-31084-y (2023).","journal-title":"Scientific Reports"},{"key":"36403_CR38","doi-asserted-by":"publisher","first-page":"1520","DOI":"10.1126\/science.1181193","volume":"326","author":"GD Fuchs","year":"2009","unstructured":"Fuchs, G. D., Dobrovitski, V. V., Toyli, D. M., Heremans, F. J. & Awschalom, D. D. Gigahertz dynamics of a strongly driven single quantum spin. Science 326, 1520\u20131522. https:\/\/doi.org\/10.1126\/science.1181193 (2009).","journal-title":"Science"},{"key":"36403_CR39","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.105.257003","volume":"105","author":"J Tuorila","year":"2010","unstructured":"Tuorila, J. et al. Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system. Phys. Rev. Lett. 105, 257003. https:\/\/doi.org\/10.1103\/PhysRevLett.105.257003 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR40","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/16\/9\/093022","volume":"16","author":"J Scheuer","year":"2014","unstructured":"Scheuer, J. et al. Precise qubit control beyond the rotating wave approximation. New Journal of Physics 16, 093022. https:\/\/doi.org\/10.1088\/1367-2630\/16\/9\/093022 (2014).","journal-title":"New Journal of Physics"},{"key":"36403_CR41","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.89.245311","volume":"89","author":"C Avinadav","year":"2014","unstructured":"Avinadav, C., Fischer, R., London, P. & Gershoni, D. Time-optimal universal control of two-level systems under strong driving. Phys. Rev. B 89, 245311. https:\/\/doi.org\/10.1103\/PhysRevB.89.245311 (2014).","journal-title":"Phys. Rev. B"},{"key":"36403_CR42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.133601","volume":"115","author":"C Deng","year":"2015","unstructured":"Deng, C., Orgiazzi, J.-L., Shen, F., Ashhab, S. & Lupascu, A. Observation of Floquet states in a strongly driven artificial atom. Phys. Rev. Lett. 115, 133601. https:\/\/doi.org\/10.1103\/PhysRevLett.115.133601 (2015).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR43","doi-asserted-by":"publisher","first-page":"1715","DOI":"10.1038\/s41467-017-01061-x","volume":"8","author":"NK Langford","year":"2017","unstructured":"Langford, N. K. et al. Experimentally simulating the dynamics of quantum light and matter at deep strong coupling. Nature Communications 8, 1715. https:\/\/doi.org\/10.1038\/s41467-017-01061-x (2017).","journal-title":"Nature Communications"},{"key":"36403_CR44","doi-asserted-by":"publisher","first-page":"15304","DOI":"10.1038\/s41598-023-41693-2","volume":"13","author":"A Fregosi","year":"2023","unstructured":"Fregosi, A. et al. Floquet space exploration for the dual-dressing of a qubit. Scientific Reports 13, 15304. https:\/\/doi.org\/10.1038\/s41598-023-41693-2 (2023).","journal-title":"Scientific Reports"},{"key":"36403_CR45","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6463\/adeb97","volume":"58","author":"G Bevilacqua","year":"2025","unstructured":"Bevilacqua, G., Biancalana, V., Dancheva, Y. & Fregosi, A. Tri-axial time-dependent magnetic field calibrated in-situ by harmonic analysis of adiabatically evolving atomic spins. Journal of Physics D: Applied Physics 58, 285001. https:\/\/doi.org\/10.1088\/1361-6463\/adeb97 (2025).","journal-title":"Journal of Physics D: Applied Physics"},{"key":"36403_CR46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.92.245422","volume":"92","author":"F Forster","year":"2015","unstructured":"Forster, F. et al. Landau-Zener interference at bichromatic driving. Phys. Rev. B 92, 245422. https:\/\/doi.org\/10.1103\/PhysRevB.92.245422 (2015).","journal-title":"Phys. Rev. B"},{"key":"36403_CR47","doi-asserted-by":"publisher","DOI":"10.1063\/5.0020415","volume":"117","author":"A Fregosi","year":"2020","unstructured":"Fregosi, A. et al. Magnetic induction imaging with a cold-atom radio frequency magnetometer. Applied Physics Letters 117, 144102. https:\/\/doi.org\/10.1063\/5.0020415 (2020).","journal-title":"Applied Physics Letters"},{"key":"36403_CR48","doi-asserted-by":"publisher","DOI":"10.1063\/1.5123653","volume":"115","author":"G Bevilacqua","year":"2019","unstructured":"Bevilacqua, G., Biancalana, V., Dancheva, Y. & Vigilante, A. Sub-millimetric ultra-low-field MRI detected in situ by a dressed atomic magnetometer. Appl. Phys. Lett. 115, 174102. https:\/\/doi.org\/10.1063\/1.5123653 (2019).","journal-title":"Appl. Phys. Lett."},{"key":"36403_CR49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.75.063414","volume":"75","author":"S Ashhab","year":"2007","unstructured":"Ashhab, S., Johansson, J. R., Zagoskin, A. M. & Nori, F. Two-level systems driven by large-amplitude fields. Phys. Rev. A 75, 063414. https:\/\/doi.org\/10.1103\/PhysRevA.75.063414 (2007).","journal-title":"Phys. Rev. A"},{"key":"36403_CR50","unstructured":"Fregosi, A. et al. Supplemental information. Scientific Reports ??, ?? (2025)."},{"key":"36403_CR51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.105.215301","volume":"105","author":"S Kling","year":"2010","unstructured":"Kling, S., Salger, T., Grossert, C. & Weitz, M. Atomic Bloch-Zener oscillations and St\u00fcckelberg interferometry in optical lattices. Phys. Rev. Lett. 105, 215301. https:\/\/doi.org\/10.1103\/PhysRevLett.105.215301 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"36403_CR52","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.82.065601","volume":"82","author":"A Zenesini","year":"2010","unstructured":"Zenesini, A., Ciampini, D., Morsch, O. & Arimondo, E. Observation of St\u00fcckelberg oscillations in accelerated optical lattices. Phys. Rev. A 82, 065601. https:\/\/doi.org\/10.1103\/PhysRevA.82.065601 (2010).","journal-title":"Phys. Rev. A"},{"key":"36403_CR53","doi-asserted-by":"publisher","first-page":"L022012","DOI":"10.1103\/PhysRevResearch.6.L022012","volume":"6","author":"T Rahman","year":"2024","unstructured":"Rahman, T. et al. Bloch oscillation phases investigated by multipath St\u00fcckelberg atom interferometry. Phys. Rev. Res. 6, L022012. https:\/\/doi.org\/10.1103\/PhysRevResearch.6.L022012 (2024).","journal-title":"Phys. Rev. Res."},{"key":"36403_CR54","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.7.041008","volume":"7","author":"I Martin","year":"2017","unstructured":"Martin, I., Refael, G. & Halperin, B. Topological frequency conversion in strongly driven quantum systems. Phys. Rev. X 7, 041008. https:\/\/doi.org\/10.1103\/PhysRevX.7.041008 (2017).","journal-title":"Phys. Rev. X"},{"key":"36403_CR55","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1038\/nature07262","volume":"455","author":"DM Berns","year":"2008","unstructured":"Berns, D. M. et al. Amplitude spectroscopy of a solid-state artificial atom. Nature 455, 51\u201357. https:\/\/doi.org\/10.1038\/nature07262 (2008).","journal-title":"Nature"},{"key":"36403_CR56","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/abd753","volume":"30","author":"Z-X Yang","year":"2021","unstructured":"Yang, Z.-X. et al. Phase-sensitive Landau-Zener-St\u00fcckelberg interference in superconducting quantum circuit*. Chinese Physics B 30, 024212. https:\/\/doi.org\/10.1088\/1674-1056\/abd753 (2021).","journal-title":"Chinese Physics B"},{"key":"36403_CR57","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.94.094519","volume":"94","author":"P Neilinger","year":"2016","unstructured":"Neilinger, P. et al. Landau-Zener-St\u00fcckelberg-Majorana lasing in circuit quantum electrodynamics. Phys. Rev. B 94, 094519. https:\/\/doi.org\/10.1103\/PhysRevB.94.094519 (2016).","journal-title":"Phys. Rev. B"},{"key":"36403_CR58","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.033340","volume":"6","author":"AI Ryzhov","year":"2024","unstructured":"Ryzhov, A. I., Ivakhnenko, O. V., Shevchenko, S. N., Gonzalez-Zalba, M. F. & Nori, F. Alternative fast quantum logic gates using nonadiabatic Landau-Zener-St\u00fcckelberg-Majorana transitions. Phys. Rev. Res. 6, 033340. https:\/\/doi.org\/10.1103\/PhysRevResearch.6.033340 (2024).","journal-title":"Phys. Rev. Res."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-36403-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-36403-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-36403-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T22:02:48Z","timestamp":1771020168000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-026-36403-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,27]]},"references-count":58,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["36403"],"URL":"https:\/\/doi.org\/10.1038\/s41598-026-36403-7","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,27]]},"assertion":[{"value":"4 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"6285"}}