Fractional resonances and prethermal states in Floquet systems

R. Peña,1 V. M. Bastidas,2, 3 F. Torres,4, 5, 6 W. J. Munro,2, 3 and G. Romero1, 5, ∗ 1Departamento de Fı́sica, Universidad de Santiago de Chile, Avenida Vı́ctor Jara 3493, 9170124, Santiago, Chile 2NTT Basic Research Laboratories and Research Center for Theoretical Quantum Physics, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan 3National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku Tokio 101-8430, Japan 4Departamento de Fı́sica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile 7800024 5Center for the Development of Nanoscience and Nanotechnology, Estación Central, 9170124, Santiago, Chile 6Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA (Dated: November 29, 2021)

[1]  C. Weitenberg,et al.  Tailoring quantum gases by Floquet engineering , 2021, Nature Physics.

[2]  J. Knolle,et al.  Higher-order and fractional discrete time crystals in clean long-range interacting systems , 2019, Nature Communications.

[3]  B. Nath Annual Review of Astronomy and Astrophysics, 2019 , 2020 .

[4]  G. Romero,et al.  Dynamical dimerization phase in Jaynes–Cummings lattices , 2019, New Journal of Physics.

[5]  K. Sacha Time Crystals , 2020, Springer Series on Atomic, Optical, and Plasma Physics.

[6]  Vladimir A. Maksimenko,et al.  Coherent resonance in the distributed cortical network during sensory information processing , 2019, Scientific Reports.

[7]  Román Orús,et al.  Tensor networks for complex quantum systems , 2018, Nature Reviews Physics.

[8]  G. Refael,et al.  From Bloch oscillations to many-body localization in clean interacting systems , 2018, Proceedings of the National Academy of Sciences.

[9]  Nelson Leung,et al.  A dissipatively stabilized Mott insulator of photons , 2018, Nature.

[10]  T. Oka,et al.  Floquet Engineering of Quantum Materials , 2018, Annual Review of Condensed Matter Physics.

[11]  M. Heyl Dynamical quantum phase transitions: a review , 2017, Reports on progress in physics. Physical Society.

[12]  H Neven,et al.  A blueprint for demonstrating quantum supremacy with superconducting qubits , 2017, Science.

[13]  K. Sacha,et al.  Time crystals: a review , 2017, Reports on progress in physics. Physical Society.

[14]  Enrique Solano,et al.  Digital-analog quantum simulations with superconducting circuits , 2017, 1711.09810.

[15]  B. Foxen,et al.  Spectral signatures of many-body localization with interacting photons , 2017 .

[16]  C. Monroe,et al.  Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator , 2017, Nature.

[17]  M. Lukin,et al.  Probing many-body dynamics on a 51-atom quantum simulator , 2017, Nature.

[18]  A. Mitra Quantum Quench Dynamics , 2017, 1703.09740.

[19]  R. Moessner,et al.  Equilibration and order in quantum Floquet matter , 2017, Nature Physics.

[20]  P. W. Hess,et al.  Observation of a discrete time crystal , 2016, Nature.

[21]  Jae-yoon Choi,et al.  Exploring the many-body localization transition in two dimensions , 2016, Science.

[22]  François Huveneers,et al.  A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems , 2015, 1509.05386.

[23]  Tomotaka Kuwahara,et al.  Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems , 2015, 1508.05797.

[24]  J. Eisert,et al.  Quantum many-body systems out of equilibrium , 2014, Nature Physics.

[25]  L. D'alessio,et al.  Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering , 2014, 1407.4803.

[26]  Immanuel Bloch,et al.  Light-cone-like spreading of correlations in a quantum many-body system , 2011, Nature.

[27]  B. Lanyon,et al.  Universal Digital Quantum Simulation with Trapped Ions , 2011, Science.

[28]  R. Blatt,et al.  Quantum simulations with trapped ions , 2011, Nature Physics.

[29]  U. Schollwoeck The density-matrix renormalization group in the age of matrix product states , 2010, 1008.3477.

[30]  S. Blanes,et al.  A pedagogical approach to the Magnus expansion , 2010 .

[31]  Jacek Dziarmaga,et al.  Dynamics of a quantum phase transition and relaxation to a steady state , 2009, 0912.4034.

[32]  James S. Langer,et al.  Annual review of condensed matter physics , 2010 .

[33]  Michael J. Hartmann,et al.  Strongly interacting polaritons in coupled arrays of cavities , 2006, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[34]  Andrew D. Greentree,et al.  Quantum phase transitions of light , 2006, cond-mat/0609050.

[35]  B. Hall Lie Groups, Lie Algebras, and Representations , 2003 .

[36]  B. Kendall Nonlinear Dynamics and Chaos , 2001 .

[37]  B. Kramer,et al.  Localization: theory and experiment , 1993 .

[38]  David Mumford,et al.  Communications on Pure and Applied Mathematics , 1989 .

[39]  Per Bak,et al.  Commensurate phases, incommensurate phases and the devil's staircase , 1982 .

[40]  R. Carter Lie Groups , 1970, Nature.

[41]  W. Magnus On the exponential solution of differential equations for a linear operator , 1954 .