Control of the Geometric Phase and Nonequivalence between Geometric-Phase Definitions in the Adiabatic Limit

Xiaosong Zhu, Peixiang Lu, and Manfred Lein
Phys. Rev. Lett. 128, 030401 – Published 20 January 2022
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Abstract

If the time evolution of a quantum state leads back to the initial state, a geometric phase is accumulated that is known as the Berry phase for adiabatic evolution or as the Aharonov-Anandan (AA) phase for nonadiabatic evolution. We evaluate these geometric phases using Floquet theory for systems in time-dependent external fields with a focus on paths leading through a degeneracy of the eigenenergies. Contrary to expectations, the low-frequency limits of the two phases do not always coincide. This happens as the degeneracy leads to a slow convergence of the quantum states to adiabaticity, resulting in a nonzero finite or divergent contribution to the AA phase. Steering the system adiabatically through a degeneracy provides control over the geometric phase as it can cause a π shift of the Berry phase. On the other hand, we revisit an example of degeneracy crossing proposed by AA. We find that, at suitable driving frequencies, both geometric-phase definitions give the same result and the dynamical phase is zero due to the symmetry of time evolution about the point of degeneracy, providing an advantageous setup for manipulation of quantum states.

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  • Received 30 September 2019
  • Accepted 18 November 2021

DOI:https://doi.org/10.1103/PhysRevLett.128.030401

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Xiaosong Zhu1,2,3, Peixiang Lu2,3,*, and Manfred Lein1,†

  • 1Leibniz University Hannover, Institute of Theoretical Physics, 30167 Hannover, Germany
  • 2Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
  • 3Optics Valley Laboratory, Hubei 430074, China

  • *lupeixiang@hust.edu.cn
  • lein@itp.uni-hannover.de

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Issue

Vol. 128, Iss. 3 — 21 January 2022

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