Real-space topological invariant for time-quasiperiodic Majoranas

• URL: http://arxiv.org/abs/2404.13129v2
• Date: Tue, 18 Jun 2024 05:36:37 GMT
• Title: Real-space topological invariant for time-quasiperiodic Majoranas
• Authors: Zihao Qi, Ilyoun Na, Gil Refael, Yang Peng,
• Abstract summary: We introduce a real-space topological invariant capable of identifying time-quasiperiodic Majoranas by leveraging the system's spectral localizer. Our numerical simulations, focusing on a Kitaev chain driven by two incommensurate frequencies, validate our approach.
• Score: 2.523120849967009
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: When subjected to quasiperiodic driving protocols, superconducting systems have been found to harbor robust time-quasiperiodic Majorana modes, extending the concept beyond static and Floquet systems. However, the presence of incommensurate driving frequencies results in dense energy spectra, rendering conventional methods of defining topological invariants based on band structure inadequate. In this work, we introduce a real-space topological invariant capable of identifying time-quasiperiodic Majoranas by leveraging the system's spectral localizer, which integrates information from both Hamiltonian and position operators. Drawing insights from non-Hermitian physics, we establish criteria for constructing the localizer and elucidate the robustness of this invariant in the presence of dense spectra. Our numerical simulations, focusing on a Kitaev chain driven by two incommensurate frequencies, validate the efficacy of our approach.

Related papers

• Unravelling quantum chaos using persistent homology [0.0]
  Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems. We present a topological pipeline for characterizing quantum dynamics, which draws inspiration from the classical approach.
  arXiv  Detail & Related papers  (2022-11-28T07:33:21Z)
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous [62.997667081978825]
  The impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom. The dynamics of this system is determined in closed analytical form. We observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior.
  arXiv  Detail & Related papers  (2021-11-23T20:25:57Z)
• 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)
• Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
  We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
  arXiv  Detail & Related papers  (2021-09-08T11:18:50Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Detecting non-Bloch topological invariants in quantum dynamics [7.544412038291252]
  Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian systems. We report the dynamic detection of non-Bloch topological invariants in single-photon quantum walks. Our work sheds new light on the experimental investigation of non-Hermitian topology.
  arXiv  Detail & Related papers  (2021-07-30T16:40:30Z)
• Observation of arbitrary topological windings of a non-Hermitian band [2.9564207475274467]
  A key topological feature, unique to non-Hermitian systems, is the non-trivial winding of the energy band in the complex energy plane. Our results open a pathway for the experimental synthesis and characterization of topologically non-trivial phases in non-conservative systems.
  arXiv  Detail & Related papers  (2020-11-29T04:27:21Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Realization of an anomalous Floquet topological system with ultracold atoms [0.879504058268139]
  Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems. Here, we realize a system with bosonic atoms in a periodically-driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections.
  arXiv  Detail & Related papers  (2020-02-23T06:37:33Z)
• 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)
• Topological quantum optical states in quasiperiodic cold atomic chains [0.0]
  Topological quantum optical states in one-dimensional (1D) quasiperiodic cold atomic chains are studied in this work. We propose that by introducing incommensurate modulations on the interatomic distances of 1D periodic atomic chains, the Aubry-Andr'e-Harper model can be mimicked. It is found that the present system indeed supports nontrivial topological states localized over the boundaries.
  arXiv  Detail & Related papers  (2020-01-15T03:53:54Z)

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.