Topological Micromotion of Floquet Quantum Systems

• URL: http://arxiv.org/abs/2106.14628v2
• Date: Sat, 26 Feb 2022 01:52:05 GMT
• Title: Topological Micromotion of Floquet Quantum Systems
• Authors: Peng Xu, Wei Zheng, and Hui Zhai
• Abstract summary: We show that an accurate description of a Floquet system requires a set of Hamiltonian exhausting all values of the micro-motion parameter. We show that a $d$-dimensional Floquet system can be described by a $d+1$-dimensional static Hamiltonian.
• Score: 5.76844077446399
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Floquet Hamiltonian has often been used to describe a time-periodic system. Nevertheless, because the Floquet Hamiltonian depends on a micro-motion parameter, the Floquet Hamiltonian with a fixed micro-motion parameter cannot faithfully represent a driven system, which manifests as the anomalous edge states. Here we show that an accurate description of a Floquet system requires a set of Hamiltonian exhausting all values of the micro-motion parameter, and this micro-motion parameter can be viewed as an extra synthetic dimension of the system. Therefore, we show that a $d$-dimensional Floquet system can be described by a $d+1$-dimensional static Hamiltonian, and the advantage of this representation is that the periodic boundary condition is automatically imposed along the extra-dimension, which enables a straightforward definition of topological invariants. The topological invariant in the $d+1$-dimensional system can ensure a $d-1$-dimensional edge state of the $d$-dimensional Floquet system. Here we show two examples where the topological invariant is a three-dimensional Hopf invariant. We highlight that our scheme of classifying Floquet topology on the micro-motion space is different from the previous classification of Floquet topology on the time space.

Related papers

• The Středa Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesàro Summation [0.0]
  This work introduces a general theoretical framework, which expresses the topological invariants of two-dimensional Floquet systems. We evaluate the flow of the unbounded Floquet density of states in response to a magnetic perturbation.
  arXiv  Detail & Related papers  (2024-08-24T12:58:23Z)
• Simultaneous symmetry breaking in spontaneous Floquet states: Floquet-Nambu-Goldstone modes, Floquet thermodynamics, and the time operator [49.1574468325115]
  We study simultaneous symmetry-breaking in a spontaneous Floquet state, focusing on the specific case of an atomic condensate. We first describe the quantization of the Nambu-Goldstone (NG) modes for a stationary state simultaneously breaking several symmetries of the Hamiltonian. We extend the formalism to Floquet states simultaneously breaking several symmetries, where Goldstone theorem translates into the emergence of Floquet-Nambu-Goldstone modes with zero quasi-energy.
  arXiv  Detail & Related papers  (2024-02-16T16:06:08Z)
• Dynamical characterization of $Z_{2}$ Floquet topological phases via quantum quenches [4.927579219242575]
  We develop the first full and unified dynamical characterization theory for the $Z_2$ Floquet topological phases. By measuring the minimal information of Floquet bands via the stroboscopic time-averaged spin polarizations, we show that the topological spin texture patterns emerging on certain discrete momenta of Brillouin zone. Our work provides a highly feasible way to detect the $Z_2$ Floquet topology and completes the dynamical characterization for the full classes of Floquet topological phases.
  arXiv  Detail & Related papers  (2023-10-31T19:43:08Z)
• Threshold size for the emergence of a classical-like behaviour [68.8204255655161]
  We design a procedure to estimate the minimum size beyond which a system is amenable to a classical-like description. The specific case of a magnetic system is considered, with details of a gedanken experiment presented and thoroughly commented.
  arXiv  Detail & Related papers  (2022-03-25T11:31:14Z)
• Square-root Floquet topological phases and time crystals [0.0]
  Periodically driven (Floquet) phases are attractive due to their ability to host unique physical phenomena with no static counterparts. We propose a general approach in nontrivially devising a square-root version of existing Floquet phases. The resulting systems are found to yield richer physics that is otherwise absent in the original counterparts.
  arXiv  Detail & Related papers  (2021-11-29T05:05:21Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Engineering, control and longitudinal readout of Floquet qubits [105.9098786966493]
  Time-periodic Hamiltonians can be exploited to increase the dephasing time of qubits and to design protected one and two-qubit gates. Here, we use the framework of many-mode Floquet theory to describe approaches to robustly control Floquet qubits in the presence of multiple drive tones. Following the same approach, we introduce a longitudinal readout protocol to measure the Floquet qubit without the need of first adiabatically mapping back the Floquet states to the static qubit states.
  arXiv  Detail & Related papers  (2021-08-25T14:35:02Z)
• High-frequency expansions for time-periodic Lindblad generators [68.8204255655161]
  Floquet engineering of isolated systems is often based on the concept of the effective time-independent Floquet Hamiltonian. We show that the emerging non-Markovianity of the Floquet generator can entirely be attributed to the micromotion of the open driven system.
  arXiv  Detail & Related papers  (2021-07-21T12:48:39Z)
• Floquet dynamical quantum phase transitions in periodically quenched systems [0.685316573653194]
  Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. In this work, we explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry.
  arXiv  Detail & Related papers  (2020-10-31T06:19:31Z)
• Unified theory to characterize Floquet topological phases by quench dynamics [6.496235214212858]
  We propose a unified theory based on quantum quenches to characterize generic $d$-dimensional ($d$D) Floquet topological phases. For a $d$D phase which is initially static and trivial, we introduce the quench dynamics by suddenly turning on the periodic driving. This prediction provides a simple and unified characterization, in which one can not only extract the number of conventional and anomalous Floquet boundary modes, but also identify the topologically protected singularities in the phase bands.
  arXiv  Detail & Related papers  (2020-04-29T08:18:22Z)
• Bulk detection of time-dependent topological transitions in quenched chiral models [48.7576911714538]
  We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction. This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
  arXiv  Detail & Related papers  (2020-01-16T17:44:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.