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Related Experiment Video

Updated: Apr 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops.

Atushi Tanaka¹, Sang Wook Kim², Taksu Cheon³

¹Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 16, 2014

Summary

This study links exotic quantum holonomy in Hermitian systems to exceptional points in non-Hermitian quantum theory. It reveals how quantum kicked tops exhibit higher-order exceptional points and their stability under perturbations.

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Area of Science:

Quantum Physics
Non-Hermitian Quantum Mechanics
Quantum Chaos

Background:

Exotic quantum holonomy arises in families of Hermitian cycles.
Exceptional points (EPs) are critical points in non-Hermitian systems where eigenvalues and eigenvectors coalesce.
Quantum kicked tops are a paradigmatic model for studying quantum chaos.

Purpose of the Study:

To investigate the correspondence between exotic quantum holonomy and exceptional points in quantum kicked tops.
To derive explicit expressions for adiabatic parameter dependencies of quasienergies and stationary states.
To analyze the behavior of higher-order EPs under perturbations and their relation to holonomy stability.

Main Methods:

Analysis of quantum kicked tops under specific conditions.
Derivation of adiabatic parameter dependencies for quasienergies and stationary states.
Investigation of complexified adiabatic parameters and perturbation theory to study EP behavior.

Main Results:

An explicit expression for adiabatic parameter dependencies of quasienergies and stationary states, exhibiting anholonomies, was obtained.
Quantum kicked tops with complexified adiabatic parameters were shown to possess higher-order EPs.
These higher-order EPs bifurcate into lower-order EPs under small perturbations, demonstrating the stability of exotic holonomy against such bifurcation.

Conclusions:

A direct link between exotic quantum holonomy and exceptional points in non-Hermitian quantum theory is established within the quantum kicked top model.
The study provides insights into the nature and stability of exceptional points and their connection to topological properties of quantum systems.
The findings contribute to understanding the interplay between topology, non-Hermiticity, and chaos in quantum mechanics.