TY - JOUR

T1 - Control of the Geometric Phase and Nonequivalence between Geometric-Phase Definitions in the Adiabatic Limit

AU - Zhu, Xiaosong

AU - Lu, Peixiang

AU - Lein, Manfred

N1 - Funding Information: This work was supported by the National Key Research and Development Program of China under Grant No. 2019YFA0308300, the Deutsche Forschungsgemeinschaft, the National Natural Science Foundation of China under Grants No. 11774109, No. 12174134, No. 12021004, and No. 11627809, and the Alexander von Humboldt Foundation.

PY - 2022/1/20

Y1 - 2022/1/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85123703548&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.128.030401

DO - 10.1103/PhysRevLett.128.030401

M3 - Article

C2 - 35119895

AN - SCOPUS:85123703548

VL - 128

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

IS - 3

M1 - 030401

ER -