Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations

Hassan Manshouri1, Moslem Zarei1, Mehdi Abdi2, Sougato Bose3, and Abolfazl Bayat4,5

1Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran
2Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
3Department of Physics and Astronomy, University College London, Gower Street, WC1E6BT, London, United Kingdom
4Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
5Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling behaviors in two different phases, namely localized and extended. Our results provide a quantitative ansatz for quantum Fisher information in terms of time, probe size, and the number of excitations. In the long-time regime, the quantum Fisher information is a quadratic function of time, touching the Heisenberg limit. The system size scaling drastically depends on the phase changing from quantum-enhanced scaling in the extended phase to size-independent behavior in the localized phase. Furthermore, increasing the number of excitations always enhances the precision of the probe, although, in the interacting systems the enhancement becomes less eminent than the non-interacting probes. This is due to the induced localization by increasing the interaction between the excitations. We show that a simple particle configuration measurement together with a maximum likelihood estimation can closely reach the ultimate precision limit in both single- and multi-particle probes.

► BibTeX data

► References

[1] Christian L Degen, Friedemann Reinhard, and Paola Cappellaro. ``Quantum sensing''. Rev. Mod. Phys. 89, 035002 (2017).
https:/​/​doi.org/​10.1103/​RevModPhys.89.035002

[2] Ronald A Fisher. ``On the mathematical foundations of theoretical statistics''. Philos. Trans. Royal Soc. 222, 309–368 (1922).
https:/​/​doi.org/​10.1098/​rsta.1922.0009

[3] Matteo GA Paris. ``Quantum estimation for quantum technology''. International Journal of Quantum Information 7, 125–137 (2009).
https:/​/​doi.org/​10.1142/​S0219749909004839

[4] Johannes Jakob Meyer. ``Fisher Information in Noisy Intermediate-Scale Quantum Applications''. Quantum 5, 539 (2021).
https:/​/​doi.org/​10.22331/​q-2021-09-09-539

[5] Jing Liu, Haidong Yuan, Xiao-Ming Lu, and Xiaoguang Wang. ``Quantum fisher information matrix and multiparameter estimation''. Journal of Physics A: Mathematical and Theoretical 53, 023001 (2019).
https:/​/​doi.org/​10.1088/​1751-8121/​ab5d4d

[6] James O Berger. ``Statistical decision theory and bayesian analysis''. Springer Science & Business Media. (2013).
https:/​/​doi.org/​10.1007/​978-1-4757-4286-2

[7] Erich L Lehmann and George Casella. ``Theory of point estimation''. Springer Science & Business Media. (2006).
https:/​/​doi.org/​10.1007/​b98854

[8] Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. ``Quantum-enhanced measurements: beating the standard quantum limit''. Science 306, 1330–1336 (2004).
https:/​/​doi.org/​10.1126/​science.1104149

[9] Victor Montenegro, Chiranjib Mukhopadhyay, Rozhin Yousefjani, Saubhik Sarkar, Utkarsh Mishra, Matteo G.A. Paris, and Abolfazl Bayat. ``Review: Quantum metrology and sensing with many-body systems''. Physics Reports 1134, 1–62 (2025).
https:/​/​doi.org/​10.1016/​j.physrep.2025.05.005

[10] Saubhik Sarkar, Abolfazl Bayat, Sougato Bose, and Roopayan Ghosh. ``Exponentially-enhanced quantum sensing with many-body phase transitions''. Nature Communications 16 (2025).
https:/​/​doi.org/​10.1038/​s41467-025-60291-6

[11] Meghana Raghunandan, Jörg Wrachtrup, and Hendrik Weimer. ``High-density quantum sensing with dissipative first order transitions''. Phys. Rev. Lett. 120, 150501 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.120.150501

[12] Toni L Heugel, Matteo Biondi, Oded Zilberberg, and Ramasubramanian Chitra. ``Quantum transducer using a parametric driven-dissipative phase transition''. Phys. Rev. Lett. 123, 173601 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.173601

[13] Li-Ping Yang and Zubin Jacob. ``Engineering first-order quantum phase transitions for weak signal detection''. J. Appl. Phys. 126, 174502 (2019).
https:/​/​doi.org/​10.1063/​1.5121558

[14] Paolo Zanardi and Nikola Paunković. ``Ground state overlap and quantum phase transitions''. Phys. Rev. E 74, 031123 (2006).
https:/​/​doi.org/​10.1103/​PhysRevE.74.031123

[15] Paolo Zanardi, HT Quan, Xiaoguang Wang, and CP Sun. ``Mixed-state fidelity and quantum criticality at finite temperature''. Phys. Rev. A 75, 032109 (2007).
https:/​/​doi.org/​10.1103/​PhysRevA.75.032109

[16] Shi-Jian Gu, Ho-Man Kwok, Wen-Qiang Ning, Hai-Qing Lin, et al. ``Fidelity susceptibility, scaling, and universality in quantum critical phenomena''. Phys. Rev. B 77, 245109 (2008).
https:/​/​doi.org/​10.1103/​PhysRevB.77.245109

[17] Paolo Zanardi, Matteo GA Paris, and Lorenzo Campos Venuti. ``Quantum criticality as a resource for quantum estimation''. Phys. Rev. A 78, 042105 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.78.042105

[18] Carmen Invernizzi, Michael Korbman, Lorenzo Campos Venuti, and Matteo GA Paris. ``Optimal quantum estimation in spin systems at criticality''. Phys. Rev. A 78, 042106 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.78.042106

[19] Shi-Jian Gu. ``Fidelity approach to quantum phase transitions''. Int. J. Mod. Phys. B 24, 4371–4458 (2010).
https:/​/​doi.org/​10.1142/​S0217979210056335

[20] Søren Gammelmark and Klaus Mølmer. ``Phase transitions and Heisenberg limited metrology in an Ising chain interacting with a single-mode cavity field''. New J. Phys. 13, 053035 (2011).
https:/​/​doi.org/​10.1088/​1367-2630/​13/​5/​053035

[21] Michael Skotiniotis, Pavel Sekatski, and Wolfgang Dür. ``Quantum metrology for the Ising Hamiltonian with transverse magnetic field''. New J. Phys. 17, 073032 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​7/​073032

[22] Marek M Rams, Piotr Sierant, Omyoti Dutta, Pawel Horodecki, and Jakub Zakrzewski. ``At the limits of criticality-based quantum metrology: Apparent super-heisenberg scaling revisited''. Phys. Rev. X 8, 021022 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.021022

[23] Bo-Bo Wei. ``Fidelity susceptibility in one-dimensional disordered lattice models''. Phys. Rev. A 99, 042117 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.99.042117

[24] Yaoming Chu, Shaoliang Zhang, Baiyi Yu, and Jianming Cai. ``Dynamic framework for criticality-enhanced quantum sensing''. Phys. Rev. Lett. 126, 010502 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.010502

[25] Ran Liu, Yu Chen, Min Jiang, Xiaodong Yang, Ze Wu, Yuchen Li, Haidong Yuan, Xinhua Peng, and Jiangfeng Du. ``Experimental critical quantum metrology with the Heisenberg scaling''. npj Quantum Inf. 7, 1–7 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00507-x

[26] Victor Montenegro, Utkarsh Mishra, and Abolfazl Bayat. ``Global sensing and its impact for quantum many-body probes with criticality''. Phys. Rev. Lett. 126, 200501 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.200501

[27] Safoura S Mirkhalaf, Daniel Benedicto Orenes, Morgan W Mitchell, and Emilia Witkowska. ``Criticality-enhanced quantum sensing in ferromagnetic bose-einstein condensates: Role of readout measurement and detection noise''. Phys. Rev. A 103, 023317 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.103.023317

[28] R. Di Candia, F. Minganti, K. V. Petrovnin, G. S. Paraoanu, and S. Felicetti. ``Critical parametric quantum sensing''. npj Quantum Information 9 (2023).
https:/​/​doi.org/​10.1038/​s41534-023-00690-z

[29] Raffaele Salvia, Mohammad Mehboudi, and Martí Perarnau-Llobet. ``Critical quantum metrology assisted by real-time feedback control''. Phys. Rev. Lett. 130, 240803 (2023).
https:/​/​doi.org/​10.1103/​PhysRevLett.130.240803

[30] Louis Garbe, Obinna Abah, Simone Felicetti, and Ricardo Puebla. ``Exponential time-scaling of estimation precision by reaching a quantum critical point''. Phys. Rev. Res. 4, 043061 (2022).
https:/​/​doi.org/​10.1103/​PhysRevResearch.4.043061

[31] Samuel Fernández-Lorenzo and Diego Porras. ``Quantum sensing close to a dissipative phase transition: Symmetry breaking and criticality as metrological resources''. Phys. Rev. A 96, 013817 (2017).
https:/​/​doi.org/​10.1103/​PhysRevA.96.013817

[32] Kristian Baumann, Christine Guerlin, Ferdinand Brennecke, and Tilman Esslinger. ``Dicke quantum phase transition with a superfluid gas in an optical cavity''. Nature 464, 1301–1306 (2010).
https:/​/​doi.org/​10.1038/​nature09009

[33] Markus P Baden, Kyle J Arnold, Arne L Grimsmo, Scott Parkins, and Murray D Barrett. ``Realization of the Dicke model using cavity-assisted raman transitions''. Phys. Rev. Lett. 113, 020408 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.113.020408

[34] Jens Klinder, Hans Keßler, Matthias Wolke, Ludwig Mathey, and Andreas Hemmerich. ``Dynamical phase transition in the open dicke model''. Proc. Natl. Acad. Sci. U.S.A. 112, 3290–3295 (2015).
https:/​/​doi.org/​10.1073/​pnas.1417132112

[35] SRK Rodriguez, W Casteels, F Storme, N Carlon Zambon, I Sagnes, L Le Gratiet, E Galopin, A Lemaı̂tre, A Amo, C Ciuti, et al. ``Probing a dissipative phase transition via dynamical optical hysteresis''. Phys. Rev. Lett. 118, 247402 (2017).
https:/​/​doi.org/​10.1103/​physrevlett.118.247402

[36] Mattias Fitzpatrick, Neereja M Sundaresan, Andy CY Li, Jens Koch, and Andrew A Houck. ``Observation of a dissipative phase transition in a one-dimensional circuit QED lattice''. Phys. Rev. X 7, 011016 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.011016

[37] Johannes M Fink, András Dombi, András Vukics, Andreas Wallraff, and Peter Domokos. ``Observation of the photon-blockade breakdown phase transition''. Phys. Rev. X 7, 011012 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.011012

[38] Theodoros Ilias, Dayou Yang, Susana F Huelga, and Martin B Plenio. ``Criticality-enhanced quantum sensing via continuous measurement''. PRX Quantum 3, 010354 (2022).
https:/​/​doi.org/​10.1103/​PRXQuantum.3.010354

[39] Theodoros Ilias, Dayou Yang, Susana F. Huelga, and Martin B. Plenio. ``Criticality-enhanced electromagnetic field sensor with single trapped ions''. npj Quantum Inf. 10, 36 (2024).
https:/​/​doi.org/​10.1038/​s41534-024-00833-w

[40] S. Alipour, M. Mehboudi, and A. T. Rezakhani. ``Quantum metrology in open systems: Dissipative cramér-rao bound''. Phys. Rev. Lett. 112, 120405 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.120405

[41] Jan Carl Budich and Emil J. Bergholtz. ``Non-hermitian topological sensors''. Phys. Rev. Lett. 125, 180403 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.180403

[42] Saubhik Sarkar, Chiranjib Mukhopadhyay, Abhijeet Alase, and Abolfazl Bayat. ``Free-fermionic topological quantum sensors''. Phys. Rev. Lett. 129, 090503 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.129.090503

[43] Florian Koch and Jan Carl Budich. ``Quantum non-Hermitian topological sensors''. Phys. Rev. Res. 4, 013113 (2022).
https:/​/​doi.org/​10.1103/​PhysRevResearch.4.013113

[44] Min Yu, Xiangbei Li, Yaoming Chu, Bruno Mera, F Nur Unal, Pengcheng Yang, Yu Liu, Nathan Goldman, and Jianming Cai. ``Experimental demonstration of topological bounds in quantum metrology''. Natl. Sci. Rev. (2024).
https:/​/​doi.org/​10.1093/​nsr/​nwae065

[45] Utkarsh Mishra and Abolfazl Bayat. ``Driving enhanced quantum sensing in partially accessible many-body systems''. Phys. Rev. Lett. 127, 080504 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.127.080504

[46] Utkarsh Mishra and Abolfazl Bayat. ``Integrable quantum many-body sensors for ac field sensing''. Sci. Rep. 12, 1–13 (2022).
https:/​/​doi.org/​10.1038/​s41598-022-17381-y

[47] Victor Montenegro, Marco G Genoni, Abolfazl Bayat, and Matteo GA Paris. ``Quantum metrology with boundary time crystals''. Commun. Phys. 6, 304 (2023).
https:/​/​doi.org/​10.1038/​s42005-023-01423-6

[48] Rozhin Yousefjani, Krzysztof Sacha, and Abolfazl Bayat. ``Discrete time crystal phase as a resource for quantum enhanced sensing'' (2024).
https:/​/​doi.org/​10.1103/​PhysRevB.111.125159

[49] Fernando Iemini, Rosario Fazio, and Anna Sanpera. ``Floquet time crystals as quantum sensors of ac fields''. Phys. Rev. A 109, L050203 (2024).
https:/​/​doi.org/​10.1103/​PhysRevA.109.L050203

[50] Jan Wiersig. ``Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: Application to microcavity sensors for single-particle detection''. Phys. Rev. Lett. 112, 203901 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.203901

[51] Zhong-Peng Liu, Jing Zhang, Şahin Kaya Özdemir, Bo Peng, Hui Jing, Xin-You Lü, Chun-Wen Li, Lan Yang, Franco Nori, and Yu-xi Liu. ``Metrology with $\mathcal{PT}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{PT}$-phase transition''. Phys. Rev. Lett. 117, 110802 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.117.110802

[52] W. Langbein. ``No exceptional precision of exceptional-point sensors''. Phys. Rev. A 98, 023805 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.023805

[53] Hoi-Kwan Lau and Aashish A. Clerk. ``Fundamental limits and non-reciprocal approaches in non-hermitian quantum sensing''. Nature Communications 9, 4320 (2018).
https:/​/​doi.org/​10.1038/​s41467-018-06477-7

[54] Mengzhen Zhang, William Sweeney, Chia Wei Hsu, Lan Yang, A. D. Stone, and Liang Jiang. ``Quantum noise theory of exceptional point amplifying sensors''. Phys. Rev. Lett. 123, 180501 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.180501

[55] Chong Chen, Liang Jin, and Ren-Bao Liu. ``Sensitivity of parameter estimation near the exceptional point of a non-hermitian system''. New Journal of Physics 21, 083002 (2019).
https:/​/​doi.org/​10.1088/​1367-2630/​ab32ab

[56] Xingjian He, Rozhin Yousefjani, and Abolfazl Bayat. ``Stark localization as a resource for weak-field sensing with super-Heisenberg precision''. Phys. Rev. Lett. 131, 010801 (2023).
https:/​/​doi.org/​10.1103/​PhysRevLett.131.010801

[57] Rozhin Yousefjani, Xingjian He, and Abolfazl Bayat. ``Long-range interacting Stark many-body probes with super-Heisenberg precision''. Chin. Phys. B 32, 100313 (2023).
https:/​/​doi.org/​10.1088/​1674-1056/​acf302

[58] Rozhin Yousefjani, Xingjian He, Angelo Carollo, and Abolfazl Bayat. ``Nonlinearity-enhanced quantum sensing in stark probes'' (2024).
https:/​/​doi.org/​10.1103/​PhysRevApplied.23.014019

[59] Dong-Sheng Ding, Zong-Kai Liu, Bao-Sen Shi, Guang-Can Guo, Klaus Mølmer, and Charles S Adams. ``Enhanced metrology at the critical point of a many-body rydberg atomic system''. Nat. Phys. 18, 1447–1452 (2022).
https:/​/​doi.org/​10.1038/​s41567-022-01777-8

[60] Alexander V Balatsky, Pedram Roushan, Joris Schaltegger, and Patrick J Wong. ``Quantum sensing from gravity as universal dephasing channel for qubits'' (2024).
https:/​/​doi.org/​10.1103/​PhysRevA.111.012411

[61] Aparajita Bhattacharyya, Debarupa Saha, and Ujjwal Sen. ``Even-body interactions favour asymmetry as a resource in metrological precision'' (2024). url: https:/​/​arxiv.org/​abs/​2401.06729.
arXiv:2401.06729

[62] Aparajita Bhattacharyya, Ahana Ghoshal, and Ujjwal Sen. ``Restoring metrological quantum advantage of measurement precision in a noisy scenario''. Phys. Rev. A 109, 052626 (2024).
https:/​/​doi.org/​10.1103/​PhysRevA.109.052626

[63] Victor Montenegro, Gareth Siôn Jones, Sougato Bose, and Abolfazl Bayat. ``Sequential measurements for quantum-enhanced magnetometry in spin chain probes''. Phys. Rev. Lett. 129, 120503 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.129.120503

[64] Yaoling Yang, Victor Montenegro, and Abolfazl Bayat. ``Extractable information capacity in sequential measurements metrology''. Phys. Rev. Research 5, 043273 (2023).
https:/​/​doi.org/​10.1103/​PhysRevResearch.5.043273

[65] Matthew Rispoli, Alexander Lukin, Robert Schittko, Sooshin Kim, M Eric Tai, Julian Léonard, and Markus Greiner. ``Quantum critical behaviour at the many-body localization transition''. Nature 573, 385–389 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1527-2

[66] Johannes Franke, Sean R Muleady, Raphael Kaubruegger, Florian Kranzl, Rainer Blatt, Ana Maria Rey, Manoj K Joshi, and Christian F Roos. ``Quantum-enhanced sensing on optical transitions through finite-range interactions''. Nature 621, 740–745 (2023).
https:/​/​doi.org/​10.1038/​s41586-023-06472-z

[67] Xiao Mi, Michael Sonner, M Yuezhen Niu, Kenneth W Lee, Brooks Foxen, Rajeev Acharya, Igor Aleiner, Trond I Andersen, Frank Arute, Kunal Arya, et al. ``Noise-resilient edge modes on a chain of superconducting qubits''. Science 378, 785–790 (2022).
https:/​/​doi.org/​10.1126/​science.abq5769

[68] Ming Gong, Shiyu Wang, Chen Zha, Ming-Cheng Chen, He-Liang Huang, Yulin Wu, Qingling Zhu, Youwei Zhao, Shaowei Li, Shaojun Guo, et al. ``Quantum walks on a programmable two-dimensional 62-qubit superconducting processor''. Science 372, 948–952 (2021).
https:/​/​doi.org/​10.1126/​science.abg7812

[69] Thomas Kohlert, Sebastian Scherg, Pablo Sala, Frank Pollmann, Bharath Hebbe Madhusudhana, Immanuel Bloch, and Monika Aidelsburger. ``Exploring the regime of fragmentation in strongly tilted fermi-hubbard chains''. Phys. Rev. Lett. 130, 010201 (2023).
https:/​/​doi.org/​10.1103/​PhysRevLett.130.010201

[70] Felix Bloch. ``Über die quantenmechanik der elektronen in kristallgittern''. Zeitschrift für physik 52, 555–600 (1929).
https:/​/​doi.org/​10.1007/​BF01339455

[71] Gregory H Wannier. ``Wave functions and effective hamiltonian for bloch electrons in an electric field''. Physical Review 117, 432 (1960).
https:/​/​doi.org/​10.1103/​PhysRev.117.432

[72] Hidetoshi Fukuyama, Robert A Bari, and Hans C Fogedby. ``Tightly bound electrons in a uniform electric field''. Phys. Rev. B 8, 5579 (1973).
https:/​/​doi.org/​10.1103/​PhysRevB.8.5579

[73] M Holthaus, GH Ristow, and DW Hone. ``Random lattices in combined ac and dc electric fields: Anderson vs. Wannier-Stark localization''. EPL 32, 241 (1995).
https:/​/​doi.org/​10.1209/​0295-5075/​32/​3/​009

[74] AR Kolovsky and HJ Korsch. ``Bloch oscillations of cold atoms in two-dimensional optical lattices''. Phys. Rev. A 67, 063601 (2003).
https:/​/​doi.org/​10.1103/​PhysRevA.67.063601

[75] Andrey R Kolovsky. ``Interplay between Anderson and Stark localization in 2d lattices''. Phys. Rev. Lett. 101, 190602 (2008).
https:/​/​doi.org/​10.1103/​PhysRevLett.101.190602

[76] Andrey R Kolovsky and Evgeny N Bulgakov. ``Wannier-Stark states and Bloch oscillations in the honeycomb lattice''. Phys. Rev. A 87, 033602 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.87.033602

[77] Evert van Nieuwenburg, Yuval Baum, and Gil Refael. ``From Bloch oscillations to many-body localization in clean interacting systems''. Proc. Natl. Acad. Sci. U.S.A. 116, 9269–9274 (2019).
https:/​/​doi.org/​10.1073/​pnas.1819316116

[78] Maximilian Schulz, CA Hooley, Roderich Moessner, and F Pollmann. ``Stark many-body localization''. Phys. Rev. Lett. 122, 040606 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.040606

[79] Ling-Na Wu and André Eckardt. ``Bath-induced decay of Stark many-body localization''. Phys. Rev. Lett. 123, 030602 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.030602

[80] Devendra Singh Bhakuni, Ritu Nehra, and Auditya Sharma. ``Drive-induced many-body localization and coherent destruction of Stark many-body localization''. Phys. Rev. B 102, 024201 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.024201

[81] Devendra Singh Bhakuni and Auditya Sharma. ``Stability of electric field driven many-body localization in an interacting long-range hopping model''. Phys. Rev. B 102, 085133 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.085133

[82] Ruixiao Yao and Jakub Zakrzewski. ``Many-body localization of bosons in an optical lattice: Dynamics in disorder-free potentials''. Phys. Rev. B 102, 104203 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.104203

[83] Titas Chanda, Ruixiao Yao, and Jakub Zakrzewski. ``Coexistence of localized and extended phases: Many-body localization in a harmonic trap''. Phys. Rev. Res. 2, 032039 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.032039

[84] Scott Richard Taylor, Maximilian Schulz, Frank Pollmann, and Roderich Moessner. ``Experimental probes of Stark many-body localization''. Phys. Rev. B 102, 054206 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.054206

[85] Yong-Yi Wang, Zheng-Hang Sun, and Heng Fan. ``Stark many-body localization transitions in superconducting circuits''. Phys. Rev. B 104, 205122 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.104.205122

[86] Li Zhang, Yongguan Ke, Wenjie Liu, and Chaohong Lee. ``Mobility edge of Stark many-body localization''. Phys. Rev. A 103, 023323 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.103.023323

[87] Ruixiao Yao, Titas Chanda, and Jakub Zakrzewski. ``Many-body localization in tilted and harmonic potentials''. Phys. Rev. B 104, 014201 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.104.014201

[88] Elmer VH Doggen, Igor V Gornyi, and Dmitry G Polyakov. ``Many-body localization in a tilted potential in two dimensions''. Phys. Rev. B 105, 134204 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.105.134204

[89] Guy Zisling, Dante M Kennes, and Yevgeny Bar Lev. ``Transport in Stark many-body localized systems''. Phys. Rev. B 105, L140201 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.105.L140201

[90] Alexander L Burin. ``Exact solution of the minimalist Stark many-body localization problem in terms of spin-pair hopping''. Phys. Rev. B 105, 184206 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.105.184206

[91] C Bertoni, J Eisert, A Kshetrimayum, A Nietner, and SJ Thomson. ``Local integrals of motion and the stability of many-body localization in Wannier-Stark potentials''. Physical Review B 109, 024206 (2024).
https:/​/​doi.org/​10.1103/​PhysRevB.109.024206

[92] IV Lukin, Yu V Slyusarenko, and AG Sotnikov. ``Many-body localization in a quantum gas with long-range interactions and linear external potential''. Phys. Rev. B 105, 184307 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.105.184307

[93] E Vernek. ``Robustness of Stark many-body localization in the ${J}_{1}\text{{-}}{J}_{2}$ Heisenberg model''. Phys. Rev. B 105, 075124 (2022).
https:/​/​doi.org/​10.1103/​PhysRevB.105.075124

[94] Elmer V. H. Doggen, Igor V. Gornyi, and Dmitry G. Polyakov. ``Stark many-body localization: Evidence for Hilbert-space shattering''. Phys. Rev. B 103, L100202 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.103.L100202

[95] Ayan Sahoo, Utkarsh Mishra, and Debraj Rakshit. ``Localization-driven quantum sensing''. Phys. Rev. A 109, L030601 (2024).
https:/​/​doi.org/​10.1103/​PhysRevA.109.L030601

[96] William Morong, Fangli Liu, Patrick Becker, KS Collins, Lei Feng, Antonis Kyprianidis, Guido Pagano, Tianyu You, AV Gorshkov, and Christopher Monroe. ``Observation of Stark many-body localization without disorder''. Nature 599, 393–398 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03988-0

[97] Philipp M Preiss, Ruichao Ma, M Eric Tai, Alexander Lukin, Matthew Rispoli, Philip Zupancic, Yoav Lahini, Rajibul Islam, and Markus Greiner. ``Strongly correlated quantum walks in optical lattices''. Science 347, 1229–1233 (2015).
https:/​/​doi.org/​10.1126/​science.1260364

[98] Thomas Kohlert, Sebastian Scherg, Pablo Sala, Frank Pollmann, Bharath Hebbe Madhusudhana, Immanuel Bloch, and Monika Aidelsburger. ``Experimental realization of fragmented models in tilted Fermi-Hubbard chains'' (2021). url: https:/​/​arxiv.org/​abs/​2106.15586.
arXiv:2106.15586

[99] Amir H Karamlou, Jochen Braumüller, Yariv Yanay, Agustin Di Paolo, Patrick M Harrington, Bharath Kannan, David Kim, Morten Kjaergaard, Alexander Melville, Sarah Muschinske, et al. ``Quantum transport and localization in 1d and 2d tight-binding lattices''. npj Quantum Inf. 8, 1–8 (2022).
https:/​/​doi.org/​10.1038/​s41534-022-00528-0

[100] Karl Leo, Peter Haring Bolivar, Frank Brüggemann, Ralf Schwedler, and Klaus Köhler. ``Observation of bloch oscillations in a semiconductor superlattice''. Solid State Communications 84, 943–946 (1992).
https:/​/​doi.org/​10.1364/​UEO.1993.D5

[101] U. Peschel, T. Pertsch, and F. Lederer. ``Optical bloch oscillations in waveguide arrays''. Opt. Lett. 23, 1701–1703 (1998).
https:/​/​doi.org/​10.1103/​PhysRevLett.83.4752

[102] Ze-Kun Jiang, Ruo-Jing Ren, Yi-Jun Chang, Wen-Hao Zhou, Yong-Heng Lu, Xiao-Wei Wang, Li Wang, Chang-Shun Wang, Alexander S. Solntsev, and Xian-Min Jin. ``Direct observation of dynamically localized quantum optical states''. Phys. Rev. Lett. 129, 173602 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.129.173602

[103] Hao Tang, Xiao-Feng Lin, Zhen Feng, Jing-Yuan Chen, Jun Gao, Ke Sun, Chao-Yue Wang, Peng-Cheng Lai, Xiao-Yun Xu, Yao Wang, Lu-Feng Qiao, Ai-Lin Yang, and Xian-Min Jin. ``Experimental two-dimensional quantum walk on a photonic chip''. Sci. Adv. 4, eaat3174 (2018).
https:/​/​doi.org/​10.1126/​sciadv.aat3174

[104] Maxime Ben Dahan, Ekkehard Peik, Jakob Reichel, Yvan Castin, and Christophe Salomon. ``Bloch oscillations of atoms in an optical potential''. Phys. Rev. Lett. 76, 4508–4511 (1996).
https:/​/​doi.org/​10.1103/​PhysRevLett.76.4508

[105] Xue-Yi Guo, Zi-Yong Ge, Hekang Li, Zhan Wang, Yu-Ran Zhang, Pengtao Song, Zhongcheng Xiang, Xiaohui Song, Yirong Jin, Li Lu, et al. ``Observation of bloch oscillations and wannier-stark localization on a superconducting quantum processor''. npj Quantum Information 7, 51 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00385-3

[106] Qiujiang Guo, Chen Cheng, Hekang Li, Shibo Xu, Pengfei Zhang, Zhen Wang, Chao Song, Wuxin Liu, Wenhui Ren, Hang Dong, et al. ``Stark many-body localization on a superconducting quantum processor''. Physical review letters 127, 240502 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.127.240502

[107] Martin Holthaus and Daniel W. Hone. ``Localization effects in ac-driven tight-binding lattices''. Philosophical Magazine B 74, 105–137 (1996).
https:/​/​doi.org/​10.1080/​01418639608240331

[108] Sergio Boixo, Steven T. Flammia, Carlton M. Caves, and JM Geremia. ``Generalized limits for single-parameter quantum estimation''. Phys. Rev. Lett. 98, 090401 (2007).
https:/​/​doi.org/​10.1103/​PhysRevLett.98.090401

[109] Rozhin Yousefjani and Abolfazl Bayat. ``Mobility edge in long-range interacting many-body localized systems''. Physical Review B 107, 045108 (2023).
https:/​/​doi.org/​10.1103/​PhysRevB.107.045108

[110] B. M. Escher, R. L. de Matos Filho, and L. Davidovich. ``General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology''. Nature Physics 7, 406–411 (2011).
https:/​/​doi.org/​10.1038/​nphys1958

[111] Rafal Demkowicz-Dobrzanski, Jan Kolodynski, and Madalin Guta. ``The elusive heisenberg limit in quantum-enhanced metrology''. Nature Communications 3 (2012).
https:/​/​doi.org/​10.1038/​ncomms2067

Cited by

[1] Bin Yi, Abolfazl Bayat, and Saubhik Sarkar, "Quantum-enhanced sensing of spin-orbit coupling without fine tuning", Physical Review A 113 3, 032607 (2026).

[2] George Mihailescu, Uesli Alushi, Roberto Di Candia, Simone Felicetti, and Karol Gietka, "Critical Quantum Sensing: A Tutorial on Parameter Estimation Near Quantum Phase Transitions", PRX Quantum 7 2, 020201 (2026).

[3] Ayan Sahoo and Debraj Rakshit, "Enhanced sensing of a weak Stark field under the influence of Aubry-André-Harper criticality", Physical Review A 113 2, 022601 (2026).

[4] Hao Li, Yaoling Yang, Yun-Hao Shi, Zheng-An Wang, Ziting Wang, Jintao Li, Yipeng Zhang, Kui Zhao, Yueshan Xu, Cheng-Lin Deng, Yu Liu, Wei-Guo Ma, Tian-Ming Li, Jiachi Zhang, Cai-Ping Fang, Jia-Cheng Song, Hao-Tian Liu, Si-Yun Zhou, Zheng-He Liu, Bing-Jie Chen, Gui-Han Liang, Xiaohui Song, Zhongcheng Xiang, Kai Xu, Kaixuan Huang, Abolfazl Bayat, and Heng Fan, "Non-equilibrium criticality-enhanced quantum sensing with superconducting qubits", Science Bulletin 71 12, 2996 (2026).

[5] Mohammad B. Arjmandi, "Super-Heisenberg non-equilibrium quantum sensing with waveguide-coupled emitters", AVS Quantum Science 8 2, 024406 (2026).

[6] Sayan Mondal, Ayan Sahoo, Ujjwal Sen, and Debraj Rakshit, "Multicritical quantum sensors driven by symmetry breaking", Physical Review B 112 23, 235165 (2025).

[7] Victor Montenegro, Chiranjib Mukhopadhyay, Rozhin Yousefjani, Saubhik Sarkar, Utkarsh Mishra, Matteo G. A. Paris, and Abolfazl Bayat, "Review: Quantum metrology and sensing with many-body systems", Physics Reports 1134, 1 (2025).

[8] Samuel L. Jacob, Laetitia P. Bettmann, Artur M. Lacerda, Krissia Zawadzki, Stephen R. Clark, John Goold, and Juan José Mendoza-Arenas, "Dephasing-assisted transport in a tight-binding chain with a linear potential", Frontiers in Physics 12, 1474018 (2024).

[9] Hao Li, Yaoling Yang, Yun-Hao Shi, Zheng-An Wang, Ziting Wang, Jintao Li, Yipeng Zhang, Kui Zhao, Yue-Shan Xu, Cheng-Lin Deng, Yu Liu, Wei-Guo Ma, Tian-Ming Li, Jia-Chi Zhang, Cai-Ping Fang, Jia-Cheng Song, Hao-Tian Liu, Si-Yun Zhou, Zheng-He Liu, Bing-Jie Chen, Gui-Han Liang, Xiaohui Song, Zhongcheng Xiang, Kai Xu, Kaixuan Huang, Abolfazl Bayat, and Heng Fan, "Non-Equilibrium Criticality-Enhanced Quantum Sensing with Superconducting Qubits", arXiv:2508.14409, (2025).

[10] Saubhik Sarkar and Abolfazl Bayat, "Noisy Stark probes as quantum-enhanced sensors", Physical Review A 111 6, 062602 (2025).

[11] Ricard Puig, Pavel Sekatski, Paolo Andrea Erdman, Paolo Abiuso, John Calsamiglia, and Martí Perarnau-Llobet, "From Dynamical to Steady-State Many-Body Metrology: Precision Limits and Their Attainability with Two-Body Interactions", PRX Quantum 6 3, 030309 (2025).

[12] Rozhin Yousefjani, Xingjian He, Angelo Carollo, and Abolfazl Bayat, "Nonlinearity-enhanced quantum sensing in Stark probes", Physical Review Applied 23 1, 014019 (2025).

[13] Keshav Das Agarwal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, and Aditi Sen De, "Critical quantum metrology using non-Hermitian spin model with RT-symmetry", arXiv:2503.24331, (2025).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 01:42:19) and SAO/NASA ADS (last updated successfully 2026-08-09 01:42:20). The list may be incomplete as not all publishers provide suitable and complete citation data.