Time crystallinity in open quantum systems

Andreu Riera-Campeny1, Maria Moreno-Cardoner1, and Anna Sanpera1,2

1Física Teòrica: Informació i Fenòmens Quàntics. Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
2ICREA, Passeig Lluís Companys 23, 08001 Barcelona, Spain.

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

Abstract

Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not such a phase survives when systems are coupled to an environment. Although dissipation caused by the coupling to a bath may stabilize time crystals in some regimes, the introduction of incoherent noise may also destroy the time crystalline order. Therefore, the mechanisms that stabilize a time crystal in open and closed systems are not necessarily the same. Here, we propose a way to identify an open system time crystal based on a single object: the Floquet propagator. Armed with such a description we show time-crystalline behavior in an explicitly short-range interacting open system and demonstrate the crucial role of the nature of the decay processes.

► BibTeX data

► References

[1] Ronnie Kosloff. Quantum thermodynamics: A dynamical viewpoint. Entropy, 15 (6): 2100–2128, 2013. 10.3390/​e15062100.
https:/​/​doi.org/​10.3390/​e15062100

[2] Robert Alicki and David Gelbwaser-Klimovsky. Non-equilibrium quantum heat machines. New Journal of Physics, 17 (11): 115012, 2015. 10.1088/​1367-2630/​17/​11/​115012.
https:/​/​doi.org/​10.1088/​1367-2630/​17/​11/​115012

[3] Sebastian Restrepo, Javier Cerrillo, Philipp Strasberg, and Gernot Schaller. From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation. New Journal of Physics, 20 (5): 053063, 2018. 10.1088/​1367-2630/​aac583.
https:/​/​doi.org/​10.1088/​1367-2630/​aac583

[4] Wolfgang Niedenzu and Gershon Kurizki. Cooperative many-body enhancement of quantum thermal machine power. New Journal of Physics, 20 (11): 113038, 2018. 10.1088/​1367-2630/​aaed55.
https:/​/​doi.org/​10.1088/​1367-2630/​aaed55

[5] Andreu Riera-Campeny, Mohammad Mehboudi, Marisa Pons, and Anna Sanpera. Dynamically induced heat rectification in quantum systems. Phys. Rev. E, 99: 032126, Mar 2019. 10.1103/​PhysRevE.99.032126.
https:/​/​doi.org/​10.1103/​PhysRevE.99.032126

[6] Marin Bukov, Luca D'Alessio, and Anatoli Polkovnikov. Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. Advances in Physics, 64 (2): 139–226, 2015. 10.1080/​00018732.2015.1055918.
https:/​/​doi.org/​10.1080/​00018732.2015.1055918

[7] Jérôme Cayssol, Balázs Dóra, Ferenc Simon, and Roderich Moessner. Floquet topological insulators. physica status solidi (RRL)–Rapid Research Letters, 7 (1-2): 101–108, 2013. 10.1002/​pssr.201206451.
https:/​/​doi.org/​10.1002/​pssr.201206451

[8] Adolfo del Campo. Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett., 111: 100502, Sep 2013. 10.1103/​PhysRevLett.111.100502.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.100502

[9] C. W. von Keyserlingk, Vedika Khemani, and S. L. Sondhi. Absolute stability and spatiotemporal long-range order in Floquet systems. Phys. Rev. B, 94: 085112, Aug 2016. 10.1103/​PhysRevB.94.085112.
https:/​/​doi.org/​10.1103/​PhysRevB.94.085112

[10] Vedika Khemani, C. W. von Keyserlingk, and S. L. Sondhi. Defining time crystals via representation theory. Phys. Rev. B, 96: 115127, Sep 2017. 10.1103/​PhysRevB.96.115127.
https:/​/​doi.org/​10.1103/​PhysRevB.96.115127

[11] Dominic V. Else, Bela Bauer, and Chetan Nayak. Floquet time crystals. Phys. Rev. Lett., 117: 090402, Aug 2016. 10.1103/​PhysRevLett.117.090402.
https:/​/​doi.org/​10.1103/​PhysRevLett.117.090402

[12] Dominic V. Else, Bela Bauer, and Chetan Nayak. Prethermal phases of matter protected by time-translation symmetry. Phys. Rev. X, 7: 011026, Mar 2017. 10.1103/​PhysRevX.7.011026.
https:/​/​doi.org/​10.1103/​PhysRevX.7.011026

[13] J Zhang, PW Hess, A Kyprianidis, P Becker, A Lee, J Smith, G Pagano, I-D Potirniche, Andrew C Potter, A Vishwanath, et al. Observation of a discrete time crystal. Nature, 543 (7644): 217, 2017. 10.1038/​nature21413.
https:/​/​doi.org/​10.1038/​nature21413

[14] Soonwon Choi, Joonhee Choi, Renate Landig, Georg Kucsko, Hengyun Zhou, Junichi Isoya, Fedor Jelezko, Shinobu Onoda, Hitoshi Sumiya, Vedika Khemani, et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature, 543 (7644): 221, 2017. 10.1038/​nature21426.
https:/​/​doi.org/​10.1038/​nature21426

[15] Wen Wei Ho, Soonwon Choi, Mikhail D. Lukin, and Dmitry A. Abanin. Critical time crystals in dipolar systems. Phys. Rev. Lett., 119: 010602, Jul 2017. 10.1103/​PhysRevLett.119.010602.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.010602

[16] N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath. Discrete time crystals: Rigidity, criticality, and realizations. Phys. Rev. Lett., 118: 030401, Jan 2017. 10.1103/​PhysRevLett.118.030401.
https:/​/​doi.org/​10.1103/​PhysRevLett.118.030401

[17] Zongping Gong, Ryusuke Hamazaki, and Masahito Ueda. Discrete time-crystalline order in cavity and circuit QED systems. Phys. Rev. Lett., 120: 040404, Jan 2018. 10.1103/​PhysRevLett.120.040404.
https:/​/​doi.org/​10.1103/​PhysRevLett.120.040404

[18] F. Iemini, A. Russomanno, J. Keeling, M. Schirò, M. Dalmonte, and R. Fazio. Boundary time crystals. Phys. Rev. Lett., 121: 035301, Jul 2018. 10.1103/​PhysRevLett.121.035301.
https:/​/​doi.org/​10.1103/​PhysRevLett.121.035301

[19] Frank Wilczek. Quantum time crystals. Phys. Rev. Lett., 109: 160401, Oct 2012. 10.1103/​PhysRevLett.109.160401.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.160401

[20] Patrick Bruno. Impossibility of spontaneously rotating time crystals: A no-go theorem. Phys. Rev. Lett., 111: 070402, Aug 2013. 10.1103/​PhysRevLett.111.070402.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.070402

[21] Angelo Russomanno, Fernando Iemini, Marcello Dalmonte, and Rosario Fazio. Floquet time crystal in the Lipkin-Meshkov-Glick model. Phys. Rev. B, 95: 214307, Jun 2017. 10.1103/​PhysRevB.95.214307.
https:/​/​doi.org/​10.1103/​PhysRevB.95.214307

[22] Biao Huang, Ying-Hai Wu, and W. Vincent Liu. Clean Floquet time crystals: Models and realizations in cold atoms. Phys. Rev. Lett., 120: 110603, Mar 2018. 10.1103/​PhysRevLett.120.110603.
https:/​/​doi.org/​10.1103/​PhysRevLett.120.110603

[23] Achilleas Lazarides and Roderich Moessner. Fate of a discrete time crystal in an open system. Phys. Rev. B, 95: 195135, May 2017. 10.1103/​PhysRevB.95.195135.
https:/​/​doi.org/​10.1103/​PhysRevB.95.195135

[24] F. M. Gambetta, F. Carollo, M. Marcuzzi, J. P. Garrahan, and I. Lesanovsky. Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems. Phys. Rev. Lett., 122: 015701, Jan 2019. 10.1103/​PhysRevLett.122.015701.
https:/​/​doi.org/​10.1103/​PhysRevLett.122.015701

[25] Bihui Zhu, Jamir Marino, Norman Yao, Mikhail D Lukin, and Eugene Demler. Dicke time crystals in driven-dissipative quantum many-body systems. New Journal of Physics, 2019. 10.1088/​1367-2630/​ab2afe.
https:/​/​doi.org/​10.1088/​1367-2630/​ab2afe

[26] Achilleas Lazarides, Sthitadhi Roy, Francesco Piazza, and Roderich Moessner. Time crystallinity in dissipative Floquet systems. Phys. Rev. Research, 2: 022002, Apr 2020. 10.1103/​PhysRevResearch.2.022002.
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.022002

[27] Heinz-Peter Breuer, Francesco Petruccione, et al. The theory of open quantum systems. Oxford University Press on Demand, 2002. 10.1093/​acprof:oso/​9780199213900.001.0001.
https:/​/​doi.org/​10.1093/​acprof:oso/​9780199213900.001.0001

[28] Robert Alicki and Karl Lendi. Quantum dynamical semigroups and applications, volume 717. Springer, 2007. 10.1007/​3-540-70861-8.
https:/​/​doi.org/​10.1007/​3-540-70861-8

[29] Goran Lindblad. On the generators of quantum dynamical semigroups. Communications in Mathematical Physics, 48 (2): 119–130, 1976. 10.1007/​BF01608499.
https:/​/​doi.org/​10.1007/​BF01608499

[30] Ravinder R Puri. Mathematical methods of quantum optics, volume 79. Springer Science & Business Media, 2001. 10.1007/​978-3-540-44953-9.
https:/​/​doi.org/​10.1007/​978-3-540-44953-9

[31] Bernhard Baumgartner, Heide Narnhofer, and Walter Thirring. Analysis of quantum semigroups with GKS–Lindblad generators: I. simple generators. Journal of Physics A: Mathematical and Theoretical, 41 (6): 065201, 2008. 10.1088/​1751-8113/​41/​6/​065201.
https:/​/​doi.org/​10.1088/​1751-8113/​41/​6/​065201

[32] Victor V. Albert and Liang Jiang. Symmetries and conserved quantities in Lindblad master equations. Phys. Rev. A, 89: 022118, Feb 2014. 10.1103/​PhysRevA.89.022118.
https:/​/​doi.org/​10.1103/​PhysRevA.89.022118

[33] Victor V. Albert, Barry Bradlyn, Martin Fraas, and Liang Jiang. Geometry and response of Lindbladians. Phys. Rev. X, 6: 041031, Nov 2016. 10.1103/​PhysRevX.6.041031.
https:/​/​doi.org/​10.1103/​PhysRevX.6.041031

[34] N. Goldman and J. Dalibard. Periodically driven quantum systems: Effective hamiltonians and engineered gauge fields. Phys. Rev. X, 4: 031027, Aug 2014. 10.1103/​PhysRevX.4.031027.
https:/​/​doi.org/​10.1103/​PhysRevX.4.031027

[35] André Eckardt and Egidijus Anisimovas. High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective. New journal of physics, 17 (9): 093039, 2015. 10.1088/​1367-2630/​17/​9/​093039.
https:/​/​doi.org/​10.1088/​1367-2630/​17/​9/​093039

[36] D. A. Lidar, I. L. Chuang, and K. B. Whaley. Decoherence-free subspaces for quantum computation. Phys. Rev. Lett., 81: 2594–2597, Sep 1998. 10.1103/​PhysRevLett.81.2594.
https:/​/​doi.org/​10.1103/​PhysRevLett.81.2594

[37] Almut Beige, Daniel Braun, Ben Tregenna, and Peter L. Knight. Quantum computing using dissipation to remain in a decoherence-free subspace. Phys. Rev. Lett., 85: 1762–1765, Aug 2000. 10.1103/​PhysRevLett.85.1762.
https:/​/​doi.org/​10.1103/​PhysRevLett.85.1762

[38] Julio T Barreiro, Markus Müller, Philipp Schindler, Daniel Nigg, Thomas Monz, Michael Chwalla, Markus Hennrich, Christian F Roos, Peter Zoller, and Rainer Blatt. An open-system quantum simulator with trapped ions. Nature, 470 (7335): 486, 2011. 10.1038/​nature09801.
https:/​/​doi.org/​10.1038/​nature09801

[39] Fabio Franchini. An introduction to integrable techniques for one-dimensional quantum systems, volume 940. Springer, 2017. 10.1007/​978-3-319-48487-7.
https:/​/​doi.org/​10.1007/​978-3-319-48487-7

[40] Malte Vogl, Gernot Schaller, and Tobias Brandes. Criticality in transport through the quantum Ising chain. Phys. Rev. Lett., 109: 240402, Dec 2012. 10.1103/​PhysRevLett.109.240402.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.240402

[41] Elliott Lieb, Theodore Schultz, and Daniel Mattis. Two soluble models of an antiferromagnetic chain. Annals of Physics, 16 (3): 407–466, 1961. 10.1016/​0003-4916(61)90115-4.
https:/​/​doi.org/​10.1016/​0003-4916(61)90115-4

[42] S Katsura, T Horiguchi, and M Suzuki. Dynamical properties of the isotropic xy model. Physica, 46 (1): 67–86, 1970. 10.1016/​0031-8914(70)90118-7.
https:/​/​doi.org/​10.1016/​0031-8914(70)90118-7

[43] J Tindall, C Sánchez Muñoz, B Buča, and D Jaksch. Quantum synchronisation enabled by dynamical symmetries and dissipation. New Journal of Physics, 22 (1): 013026, jan 2020. 10.1088/​1367-2630/​ab60f5.
https:/​/​doi.org/​10.1088/​1367-2630/​ab60f5

[44] Mary Beth Ruskai. Beyond strong subadditivity? improved bounds on the contraction of generalized relative entropy. Reviews in Mathematical Physics, 6 (05a): 1147–1161, 1994. 10.1142/​S0129055X94000407.
https:/​/​doi.org/​10.1142/​S0129055X94000407

[45] Andy CY Li, F Petruccione, and Jens Koch. Perturbative approach to Markovian open quantum systems. Scientific reports, 4: 4887, 2014. 10.1038/​srep04887.
https:/​/​doi.org/​10.1038/​srep04887

Cited by

[1] Koki Chinzei and Tatsuhiko N. Ikeda, "Time Crystals Protected by Floquet Dynamical Symmetry in Hubbard Models", arXiv:2003.13315.

The above citations are from SAO/NASA ADS (last updated successfully 2020-07-14 07:12:16). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2020-07-14 07:12:15).