Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems

• URL: http://arxiv.org/abs/2105.02689v1
• Date: Thu, 6 May 2021 14:09:52 GMT
• Title: Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Authors: Hannes Weisbrich, Gianluca Rastelli, Wolfgang Belzig
• Abstract summary: We propose universal protocols to determine quantum geometric properties in non-Abelian systems. Our schemes suggest a way to prepare eigenstates of the quantum metric.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to access. In non-Abelian systems this accessibility to geometric properties can be even more restrictive due to the degeneracy of the states. We propose universal protocols to determine quantum geometric properties in non-Abelian systems. First, we show that for a weak resonant driving of the local parameters the coherent Rabi oscillations are related to the quantum geometric tensor. Second, we derive that in a Landau-Zener like transition the final probability of an avoided energy crossing is proportional to elements of the non-Abelian quantum geometric tensor. Our schemes suggest a way to prepare eigenstates of the quantum metric, a task that is difficult otherwise in a degenerate subspace.

Related papers

• Entanglement Asymmetry in non-Abelian Anyonic Systems [0.0]
  We show that the information-theoretic characteristics of anyons diverge fundamentally from those of non-anyonic systems. In bipartite anyonic systems, pure states may have different marginal spectra, and mixed states may contain pure marginal states. Our findings significantly advance the understanding of the information-theoretic aspects of anyons and may lead to realizations of quantum communication and cryptographic protocols.
  arXiv  Detail & Related papers  (2024-06-05T18:00:06Z)
• Non-adiabatic holonomic quantum operations in continuous variable systems [2.4060220973816144]
  Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to its potential robustness. Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes.
  arXiv  Detail & Related papers  (2024-02-04T07:06:23Z)
• Particle-Number Threshold for Non-Abelian Geometric Phases [0.0]
  We introduce a particle-number threshold (PNT) that assesses a system's capabilities to perform purely geometric manipulations of quantum states. This threshold gives the minimal number of particles necessary to fully exploit a system's potential to generate non-Abelian geometric phases. We benchmark our findings on bosonic systems relevant to linear and nonlinear quantum optics.
  arXiv  Detail & Related papers  (2023-01-27T21:38:55Z)
• 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)
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata [0.24999074238880484]
  We show how to implement arbitrary translationally invariant quantum cellular automata in any dimension using finite-depth circuits of $k$-local gates. Our results imply that the topological classifications of SPT phases and QCA both collapse to a single trivial phase in the presence of $k$-local interactions.
  arXiv  Detail & Related papers  (2022-12-13T19:00:00Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• 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)
• Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases [55.41644538483948]
  Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control. We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. Our results open new horizons for measurement-enabled quantum control of many-body topological states.
  arXiv  Detail & Related papers  (2021-02-10T19:00:00Z)
• Phase space formulation of the Abelian and non-Abelian quantum geometric tensor [0.0]
  We present a formulation of the Berry connection and the quantum geometric tensor. We show that the quantum metric tensor can be computed using only the Wigner functions. Our results indicate that the developed approach is well adapted to study the parameter space associated with quantum many-body systems.
  arXiv  Detail & Related papers  (2020-11-29T08:23:46Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

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.