Rotational invariance from gauge invariance in adiabatically changing systems

K. T. Hecht

Zhenyu Wang

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic evolution with geometric phases is provided and we determine that in the adiabatic evolution, while the eigenstates are slowly varying, the eigenenergies and degeneracy of the Hamiltonian can change rapidly. We exemplify this result by the example of the adiabatic evolution driven by parametrized pulse sequences. For driving fields that are rotating slowly with the same average energy and evolution path, fast modulation fields can have smaller nonadiabatic errors than obtained under the traditional approach with a constant amplitude.

R. Shankar

Zhen-Yu Wang, Martin Bodo Plenio

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic evolution with geometric phases is provided, and we determine that in the adiabatic evolution, while the eigenstates are slowly varying, the eigenenergies and degeneracy of the Hamiltonian can change rapidly. We exemplify this result by the example of the adiabatic evolution driven by parametrized pulse sequences. For driving fields that are rotating slowly with the same average energy and evolution path, fast modulation fields can have smaller nonadiabatic errors than obtained under the traditional approach with a constant amplitude.

Carlos Martín-Fernández, Gloria Platero, Sigmund Kohler

Periodically time-dependent quantum systems have Floquet solutions. They consist of a phase factor and a Floquet mode which shares the periodicity of the driving. Consequently, any such solution possesses a non adiabatic geometric phase known as the Aharonov-Anandan (AA) phase. It is gauge-invariant and, therefore, is experimentally accessible. We propose a protocol for the measurement of AA phases based on the adiabatic change of the phase of the non-adiabatic driving. We argue that the experimental requirements of the protocol are those of previous measurements of adiabatic phases.

Huazhong Li

We show that non-Abelian gauge fields arise in a nongauged quantum system in the adiabatic approximation by working out a model of N-dimensional rotational symmetry. The induced gauge fields are symmetric under N-dimensional rotations accompanied by compensating gauge transformations of the group SO(N).