Geometric contribution to adiabatic amplification in non-Hermitian systems

• URL: http://arxiv.org/abs/2409.13595v1
• Date: Fri, 20 Sep 2024 15:49:47 GMT
• Title: Geometric contribution to adiabatic amplification in non-Hermitian systems
• Authors: Tomoki Ozawa, Henning Schomerus,
• Abstract summary: We experimentally measure the non-Hermitian analog of the Berry phase for adiabatic processes. In non-Hermitian systems, the Berry phase can have an imaginary part, which contributes to the amplification or decay of the total wave intensity. We list classes of non-Hermitian Hamiltonians where this path independence is guaranteed by suitable symmetries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as encountered in optics, classical mechanics, and metamaterial design. Recently, the non-Hermitian analog of the Berry phase for adiabatic processes has been experimentally measured. In non-Hermitian systems, the Berry phase can have an imaginary part, which contributes to the amplification or decay of the total wave intensity. When the imaginary part of the Berry curvature is zero, this geometric amplification factor is determined solely by the initial and final points of the adiabatic path in parameter space, and does not depend on how these points are connected by the path. We list classes of non-Hermitian Hamiltonians where this path independence is guaranteed by suitable symmetries, and find that, for some of these classes, the amplification factor can be written only in terms of the Petermann factors of the initial and final points. Our result can, in turn, be used to experimentally obtain the Petermann factor by observing how the norm of the wavefunction changes under adiabatic processes. We validate our theory using a couple of concrete examples of physical relevance.

Related papers

• Geometrical Amplitude factors in the the adiabatic evolution [0.0]
  In a quantum system initially in the n-th eigenstate, an adiabatic evolution of the Hamiltonian ensures that the system remains in the corresponding instantaneous eigenstate while acquiring a phase factor.<n>In this work, we explore the concept of geometric amplitudes in the context of a Hermitian Hamiltonian with imaginary eigenvalues.
  arXiv  Detail & Related papers  (2025-05-05T18:33:26Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Observation of non-Hermitian bulk-boundary correspondence in non-chiral non-unitary quantum dynamics of single photons [31.05848822220465]
  In non-Hermitian systems, preserved chiral symmetry is one of the key ingredients, which plays a pivotal role in determining non-Hermitian topology.<n>We theoretically predict and experimentally demonstrate the bulk-boundary correspondence of a one-dimensional (1D) non-Hermitian system with chiral symmetry breaking.
  arXiv  Detail & Related papers  (2025-04-07T09:43:43Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Non-Bloch edge dynamics of non-Hermitian lattices [2.2852725150656603]
  We investigate the time evolution of waves around the edge of non-Hermitian lattices. The non-Hermitian skin effect tends to localize the wave to the edge. Our work provides a coherent theory for characterizing the real-time edge dynamics of non-Hermitian lattices.
  arXiv  Detail & Related papers  (2025-03-17T19:22:35Z)
• General theory of slow non-Hermitian evolution [1.3810901729134184]
  Non-Hermitian systems are widespread in both classical and quantum physics. Here we develop a general theory for slow evolution of non-Hermitian systems.
  arXiv  Detail & Related papers  (2025-02-06T16:55:40Z)
• Implementation and topological characterization of Weyl exceptional rings in quantum-mechanical systems [1.877600262062263]
  We report the first quantum-mechanical implementation of Weyl exceptional rings (WERs)<n>We demonstrate the topological transition triggered by shrinking the size of the manifold.
  arXiv  Detail & Related papers  (2024-07-01T02:08:58Z)
• A numerical study of the Bose-Einstein condensates in a double-well trap using finite differences [0.0]
  We study some of their quantum properties and their dependency on the strength of the boson-boson interaction. We observe a deviation in the critical parameters associated with a behavior change in both the energy distribution and the eigenstates of the system.
  arXiv  Detail & Related papers  (2024-02-08T15:11:03Z)
• Wave-packet dynamics in non-Hermitian systems subject to complex electric fields [0.0]
  Berry phases have long been known to significantly alter the properties of periodic systems. In non-Hermitian systems, generalizations of the Berry connection have been proposed and shown to have novel effects on dynamics and transport. We show that the non-Hermiticities of both the band Hamiltonian and the external potential give rise to anomalous weight rate and velocity terms.
  arXiv  Detail & Related papers  (2024-02-02T11:06:46Z)
• Geometric Phase of a Transmon in a Dissipative Quantum Circuit [44.99833362998488]
  We study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.
  arXiv  Detail & Related papers  (2024-01-22T16:41:00Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Quantum Lyapunov exponent in dissipative systems [68.8204255655161]
  The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. We study the interplay between these two processes. The OTOC decay rate is closely related to the classical Lyapunov.
  arXiv  Detail & Related papers  (2022-11-11T17:06:45Z)
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model [44.58985907089892]
  How the property of quantum many-body system especially the phase transition will be affected by the non-hermiticity remains unclear. We show that there is a continuous phase transition induced by the non-hermiticity in QCP. We observe that the order parameter and susceptibility display infinitely even for finite size system, since non-hermiticity endows universality many-body system with different singular behaviour from classical phase transition.
  arXiv  Detail & Related papers  (2022-09-22T01:11:28Z)
• Measuring the Adiabatic Non-Hermitian Berry Phase in Feedback-Coupled Oscillators [0.0]
  The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase.
  arXiv  Detail & Related papers  (2022-05-05T15:12:03Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Quantum Hall admittance in non-Hermitian systems [0.0]
  We give the complex Berry curvature and Berry phase for the two-dimensional non-Hermitian Dirac model. The imaginary part of the complex Berry phase induces the quantum Hall susceptance. We analyze the complex energy band structures of the two-dimensional non-Hermitian Dirac model.
  arXiv  Detail & Related papers  (2021-01-01T13:35:14Z)
• Probing non-Hermitian phase transitions in curved space via quench dynamics [0.0]
  Non-Hermitian Hamiltonians are relevant to describe the features of a broad class of physical phenomena. We study the interplay of geometry and non-Hermitian dynamics by unveiling the existence of curvature-dependent non-Hermitian phase transitions.
  arXiv  Detail & Related papers  (2020-12-14T19:47:59Z)
• On the complex behaviour of the density in composite quantum systems [62.997667081978825]
  We study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We prove that it is a non-perturbative property and we find out a large/small coupling constant duality. Inspired by the proof of KAM theorem, we are able to deal with this problem by introducing a cut-off in energies that eliminates these small denominators.
  arXiv  Detail & Related papers  (2020-04-14T21:41:15Z)

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.