Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Alberto Biella1,2,3 and Marco Schiró3

1Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
2INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
3JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France

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Abstract

It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

How an observer influences the fate of a quantum system is a fundamental longstanding question in quantum theory. Recent advances in the experimental manipulation of large ensembles of particles in the quantum regime made this question relevant also for extended systems coupled to a measurement apparatus. In this work we study the emergence of a Zeno phase triggered by the measurement rate in a prototypical spin-1/2 chain with continuous monitoring. We show that the onset of the Zeno regime is sharp and encoded in the rare events of the stochastic dynamics. The latter are governed by a non-Hermitian Hamiltonian which feature a subradiance transition.

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[1] Howard M. Wisemanand Gerard J. Milburn ``Quantum Measurement and Control'' Cambridge University Press (2009).
https:/​/​doi.org/​10.1017/​CBO9780511813948

[2] B. Misraand E. C. G. Sudarshan ``The Zeno’s paradox in quantum theory'' Journal of Mathematical Physics 18, 756–763 (1977).
https:/​/​doi.org/​10.1063/​1.523304

[3] Asher Peres ``Zeno paradox in quantum theory'' American Journal of Physics 48, 931–932 (1980).
https:/​/​doi.org/​10.1119/​1.12204

[4] Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, ``Quantum Zeno effect'' Phys. Rev. A 41, 2295–2300 (1990).
https:/​/​doi.org/​10.1103/​PhysRevA.41.2295

[5] P. Facchi, H. Nakazato, and S. Pascazio, ``From the Quantum Zeno to the Inverse Quantum Zeno Effect'' Phys. Rev. Lett. 86, 2699–2703 (2001).
https:/​/​doi.org/​10.1103/​PhysRevLett.86.2699

[6] P. Facchiand S. Pascazio ``Quantum Zeno Subspaces'' Phys. Rev. Lett. 89, 080401 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.89.080401

[7] Adrien Signoles, Adrien Facon, Dorian Grosso, Igor Dotsenko, Serge Haroche, Jean-Michel Raimond, Michel Brune, and Sébastien Gleyzes, ``Confined quantum Zeno dynamics of a watched atomic arrow'' Nature Physics 10, 715–719 (2014).
https:/​/​doi.org/​10.1038/​nphys3076

[8] Kyrylo Snizhko, Parveen Kumar, and Alessandro Romito, ``Quantum Zeno effect appears in stages'' Phys. Rev. Research 2, 033512 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033512

[9] L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, ``Long-distance quantum communication with atomic ensembles and linear optics'' Nature 414, 413–418 (2001).
https:/​/​doi.org/​10.1038/​35106500

[10] Anders S. Sørensenand Klaus Mølmer ``Measurement Induced Entanglement and Quantum Computation with Atoms in Optical Cavities'' Phys. Rev. Lett. 91, 097905 (2003).
https:/​/​doi.org/​10.1103/​PhysRevLett.91.097905

[11] C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, ``Measurement-induced entanglement for excitation stored in remote atomic ensembles'' Nature 438, 828–832 (2005).
https:/​/​doi.org/​10.1038/​nature04353

[12] N. Roch, M. E. Schwartz, F. Motzoi, C. Macklin, R. Vijay, A. W. Eddins, A. N. Korotkov, K. B. Whaley, M. Sarovar, and I. Siddiqi, ``Observation of Measurement-Induced Entanglement and Quantum Trajectories of Remote Superconducting Qubits'' Phys. Rev. Lett. 112, 170501 (2014).
https:/​/​doi.org/​10.1103/​PhysRevLett.112.170501

[13] Jia Kong, Ricardo Jiménez-Martínez, Charikleia Troullinou, Vito Giovanni Lucivero, Géza Tóth, and Morgan W. Mitchell, ``Measurement-induced, spatially-extended entanglement in a hot, strongly-interacting atomic system'' Nature Communications 11, 2415 (2020).
https:/​/​doi.org/​10.1038/​s41467-020-15899-1

[14] N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze, J. J. García-Ripoll, J. I. Cirac, G. Rempe, and S. Dürr, ``Strong Dissipation Inhibits Losses and Induces Correlations in Cold Molecular Gases'' Science 320, 1329–1331 (2008).
https:/​/​doi.org/​10.1126/​science.1155309
https:/​/​science.sciencemag.org/​content/​320/​5881/​1329

[15] Y. S. Patil, S. Chakram, and M. Vengalattore, ``Measurement-Induced Localization of an Ultracold Lattice Gas'' Phys. Rev. Lett. 115, 140402 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.115.140402

[16] Heinrich Fröml, Alessio Chiocchetta, Corinna Kollath, and Sebastian Diehl, ``Fluctuation-Induced Quantum Zeno Effect'' Phys. Rev. Lett. 122, 040402 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.040402

[17] Heinrich Fröml, Christopher Muckel, Corinna Kollath, Alessio Chiocchetta, and Sebastian Diehl, ``Ultracold quantum wires with localized losses: Many-body quantum Zeno effect'' Phys. Rev. B 101, 144301 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.144301

[18] P L Krapivsky, Kirone Mallick, and Dries Sels, ``Free fermions with a localized source'' J. Stat. Mech. Theory Exp. 2019, 113108 (2019).
https:/​/​doi.org/​10.1088/​1742-5468/​ab4e8e

[19] P L Krapivsky, Kirone Mallick, and Dries Sels, ``Free bosons with a localized source'' J. Stat. Mech. Theory Exp. 2020, 063101 (2020).
https:/​/​doi.org/​10.1088/​1742-5468/​ab8118

[20] Yaodong Li, Xiao Chen, and Matthew P. A. Fisher, ``Quantum Zeno effect and the many-body entanglement transition'' Phys. Rev. B 98, 205136 (2018).
https:/​/​doi.org/​10.1103/​PhysRevB.98.205136

[21] Brian Skinner, Jonathan Ruhman, and Adam Nahum, ``Measurement-Induced Phase Transitions in the Dynamics of Entanglement'' Phys. Rev. X 9, 031009 (2019).
https:/​/​doi.org/​10.1103/​PhysRevX.9.031009

[22] M. Szyniszewski, A. Romito, and H. Schomerus, ``Entanglement transition from variable-strength weak measurements'' Phys. Rev. B 100, 064204 (2019).
https:/​/​doi.org/​10.1103/​PhysRevB.100.064204

[23] Soonwon Choi, Yimu Bao, Xiao-Liang Qi, and Ehud Altman, ``Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition'' Phys. Rev. Lett. 125, 030505 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.030505

[24] Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig, ``Measurement-induced criticality in random quantum circuits'' Phys. Rev. B 101, 104302 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.101.104302

[25] Xhek Turkeshi, Rosario Fazio, and Marcello Dalmonte, ``Measurement-induced criticality in $(2+1)$-dimensional hybrid quantum circuits'' Phys. Rev. B 102, 014315 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.014315

[26] D. Bernard, T. Jin, and O. Shpielberg, ``Transport in quantum chains under strong monitoring'' EPL (Europhysics Letters) 121, 60006 (2018).
https:/​/​doi.org/​10.1209/​0295-5075/​121/​60006

[27] Xiangyu Cao, Antoine Tilloy, and Andrea De Luca, ``Entanglement in a fermion chain under continuous monitoring'' SciPost Phys. 7, 24 (2019).
https:/​/​doi.org/​10.21468/​SciPostPhys.7.2.024

[28] D. A. Ivanov, T. Yu. Ivanova, S. F. Caballero-Benitez, and I. B. Mekhov, ``Feedback-Induced Quantum Phase Transitions Using Weak Measurements'' Phys. Rev. Lett. 124, 010603 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.010603

[29] Dayou Yang, Andrey Grankin, Lukas M. Sieberer, Denis V. Vasilyev, and Peter Zoller, ``Quantum non-demolition measurement of a many-body Hamiltonian'' Nature Communications 11, 775 (2020).
https:/​/​doi.org/​10.1038/​s41467-020-14489-5

[30] Yohei Fujiand Yuto Ashida ``Measurement-induced quantum criticality under continuous monitoring'' Phys. Rev. B 102, 054302 (2020).
https:/​/​doi.org/​10.1103/​PhysRevB.102.054302

[31] Yuto Ashida, Zongping Gong, and Masahito Ueda, ``Non-Hermitian physics'' (2020).
https:/​/​doi.org/​10.1080/​00018732.2021.1876991

[32] Tony E. Leeand Ching-Kit Chan ``Heralded Magnetism in Non-Hermitian Atomic Systems'' Phys. Rev. X 4, 041001 (2014).
https:/​/​doi.org/​10.1103/​PhysRevX.4.041001

[33] R. H. Dicke ``Coherence in Spontaneous Radiation Processes'' Phys. Rev. 93, 99–110 (1954).
https:/​/​doi.org/​10.1103/​PhysRev.93.99

[34] M. Grossand S. Haroche ``Superradiance: An essay on the theory of collective spontaneous emission'' Physics Reports 93, 301 –396 (1982).
https:/​/​doi.org/​10.1016/​0370-1573(82)90102-8
http:/​/​www.sciencedirect.com/​science/​article/​pii/​0370157382901028

[35] G. L. Celardoand L. Kaplan ``Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism'' Phys. Rev. B 79, 155108 (2009).
https:/​/​doi.org/​10.1103/​PhysRevB.79.155108

[36] Naftali Auerbachand Vladimir Zelevinsky ``Super-radiant dynamics, doorways and resonances in nuclei and other open mesoscopic systems'' Reports on Progress in Physics 74, 106301 (2011).
https:/​/​doi.org/​10.1088/​0034-4885/​74/​10/​106301

[37] A. Biella, F. Borgonovi, R. Kaiser, and G. L. Celardo, ``Subradiant hybrid states in the open 3D Anderson-Dicke model'' EPL (Europhysics Letters) 103, 57009 (2013).
https:/​/​doi.org/​10.1209/​0295-5075/​103/​57009

[38] William Guerin, Michelle O. Araújo, and Robin Kaiser, ``Subradiance in a Large Cloud of Cold Atoms'' Phys. Rev. Lett. 116, 083601 (2016).
https:/​/​doi.org/​10.1103/​PhysRevLett.116.083601

[39] I Rotterand J P Bird ``A review of progress in the physics of open quantum systems: theory and experiment'' Reports on Progress in Physics 78, 114001 (2015).
https:/​/​doi.org/​10.1088/​0034-4885/​78/​11/​114001

[40] Adam Nahum, Sthitadhi Roy, Brian Skinner, and Jonathan Ruhman, ``Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory'' PRX Quantum 2, 010352 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010352

[41] Xhek Turkeshi, Alberto Biella, Rosario Fazio, Marcello Dalmonte, and Marco Schiró, ``Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks'' Phys. Rev. B 103, 224210 (2021).
https:/​/​doi.org/​10.1103/​PhysRevB.103.224210

[42] O. Alberton, M. Buchhold, and S. Diehl, ``Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law'' Phys. Rev. Lett. 126, 170602 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.126.170602

[43] Michael E. Fisher ``Yang-Lee Edge Singularity and ${\phi^3}$ Field Theory'' Phys. Rev. Lett. 40, 1610 - 1613 (1978).
https:/​/​doi.org/​10.1103/​PhysRevLett.40.1610

[44] John L. Cardy ``Conformal Invariance and the Yang-Lee Edge Singularity in Two Dimensions'' Phys. Rev. Lett. 54, 1354–1356 (1985).
https:/​/​doi.org/​10.1103/​PhysRevLett.54.1354

[45] James M. Hickey, Sam Genway, Igor Lesanovsky, and Juan P. Garrahan, ``Time-integrated observables as order parameters for full counting statistics transitions in closed quantum systems'' Phys. Rev. B 87, 184303 (2013).
https:/​/​doi.org/​10.1103/​PhysRevB.87.184303

[46] Carl M Bender ``PT-symmetric quantum theory'' Journal of Physics: Conference Series 631, 012002 (2015).
https:/​/​doi.org/​10.1088/​1742-6596/​631/​1/​012002

[47] H. P. Breuerand F. Petruccione ``The theory of open quantum systems'' Oxford University Press (2002).
https:/​/​doi.org/​10.1093/​acprof:oso/​9780199213900.001.0001

[48] A B Harris ``Upper bounds for the transition temperatures of generalized Ising models'' Journal of Physics C: Solid State Physics 7, 3082–3102 (1974).
https:/​/​doi.org/​10.1088/​0022-3719/​7/​17/​018

[49] R B Stinchcombe ``Diluted quantum transverse Ising model'' Journal of Physics C: Solid State Physics 14, L263–L267 (1981).
https:/​/​doi.org/​10.1088/​0022-3719/​14/​10/​003

[50] Foster Thompsonand Rajiv R. P. Singh ``Griffiths-McCoy singularities in the dilute transverse-field Ising model: A numerical linked cluster expansion study'' Phys. Rev. E 99, 032129 (2019).
https:/​/​doi.org/​10.1103/​PhysRevE.99.032129

[51] T. Senthiland Subir Sachdev ``Higher Dimensional Realizations of Activated Dynamic Scaling at Random Quantum Transitions'' Phys. Rev. Lett. 77, 5292–5295 (1996).
https:/​/​doi.org/​10.1103/​PhysRevLett.77.5292

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