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We develop a theory to derive effective Floquet Hamiltonians in the weak drive and low-frequency regime. We construct the theory in analogy with band theory for electrons in a spatially-periodic and weak potential, such as occurs in some…

Mesoscale and Nanoscale Physics · Physics 2020-01-15 Michael Vogl , Martin Rodriguez-Vega , Gregory A. Fiete

Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In…

Mesoscale and Nanoscale Physics · Physics 2010-12-14 Takuya Kitagawa , Erez Berg , Mark Rudner , Eugene Demler

The spin in a rotating frame has attracted a lot of attentions recently, as it deeply relates to both fundamental physics such as pseudo-magnetic field and geometric phase, and applications such as gyroscopic sensors. However, previous…

Quantum Physics · Physics 2019-04-02 Xing-Yan Chen , Tongcang Li , Zhang-qi Yin

Detection of weak electromagnetic waves and hypothetical particles aided by quantum amplification is important for fundamental physics and applications. However, demonstrations of quantum amplification are still limited; in particular, the…

Quantum Physics · Physics 2022-06-22 Min Jiang , Yushu Qin , Xin Wang , Yuanhong Wang , Haowen Su , Xinhua Peng , Dmitry Budker

Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band…

Disordered Systems and Neural Networks · Physics 2018-05-22 Sthitadhi Roy , Ivan M. Khaymovich , Arnab Das , Roderich Moessner

Periodically driven systems, or Floquet systems, exhibit many novel dynamics and interesting out-of-equilibrium phases of matter. Those phases arising with the quantum systems' symmetries, such as global $U(1)$ symmetry, can even show…

Periodically driven quantum systems, known as Floquet systems, provide a versatile platform for engineering novel topological phases absent in static settings. However, dynamically characterizing these non-equilibrium topological invariants…

Quantum Physics · Physics 2026-05-08 Xin Shen , Bing Lu , Yan-Qing Zhu

It is proved that the energy absorption in a periodically driven classical spin system is exponentially slow in frequency, which results in a two-step relaxation called the Floquet prethermalization. This result is shown by establishing the…

Statistical Mechanics · Physics 2018-09-19 Takashi Mori

Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial "infinite-temperature" Floquet-ergodic phase. In contrast, here we show that their disordered Floquet many-body localized counterparts can…

Disordered Systems and Neural Networks · Physics 2016-08-23 Vedika Khemani , Achilleas Lazarides , Roderich Moessner , S. L. Sondhi

Floquet theory is a widely used framework to describe the dynamics of periodically-driven quantum systems. The usual set up to describe such kind of systems is to consider the effect of an external control with a definite period in time…

Quantum Physics · Physics 2025-10-10 V. M. Bastidas

Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be…

Floquet engineering, in which the properties of a quantum system are modified through the application of strong periodic drives, is an indispensable tool in atomic and condensed matter systems. However, it is inevitably limited by intrinsic…

Quantum Physics · Physics 2026-02-05 Martin Ritter , David M. Long , Qianao Yue , Anushya Chandran , Alicia J. Kollár

We study a dynamical phase transition in optical bistable systems subject to a time-periodic driving field. The phase transition occurs in the structure of limit cycle as a function of the frequency of the driving field. In the…

Statistical Mechanics · Physics 2020-01-13 Tatsuhiko Shirai , Synge Todo , Seiji Miyashita

Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating…

Quantum Physics · Physics 2022-07-13 Huan-Yu Wang , Xiao-Ming Zhao , Lin Zhuang , Wu-Ming Liu

"Floquet engineering" - designing band structures "on-demand" through the application of coherent time-periodic drives - has recently emerged as a powerful tool for creating new topological and anomalous phases of matter. In this…

Strongly Correlated Electrons · Physics 2021-09-16 Iliya Esin , Gaurav Kumar Gupta , Erez Berg , Mark S. Rudner , Netanel H. Lindner

We study the quantum version of a tilting and flashing Hamiltonian ratchets, consisting of a periodic potential and a time-periodic driving field. The system dynamics is governed by a Floquet evolution matrix bearing the symmetry of the…

Quantum Physics · Physics 2009-11-13 S. Denisov , L. Morales-Molina , S. Flach , P. Hanggi

We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is analyzed by comparing it to an equivalent implementation in undriven…

We propose a `Floquet engineering' formalism to systematically design a periodic driving protocol in order to stroboscopically realize the desired system starting from a given static Hamiltonian. The formalism is applicable to quantum…

Quantum Physics · Physics 2022-01-12 Jayendra N. Bandyopadhyay , Juzar Thingna

We study the effects of a periodically driven electric field applied to a variety of tight-binding models in one dimension. We first consider a non-interacting system with or without a staggered on-site potential, and we find that that…

Mesoscale and Nanoscale Physics · Physics 2021-02-17 Samudra Sur , Diptiman Sen

In Floquet engineering, periodic driving is used to realize novel phases of matter which are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe of obtaining a static effective Hamiltonian.…

Statistical Mechanics · Physics 2023-03-29 Takashi Mori