The Geometric Phase in Quantum Systems

Arno Böhm

Xu-Ying Lou, Yu-Shi Cheng, P. Z. Zhao +1 more

With the growing interest in non-Hermitian quantum systems, the concepts of geometric phase such as Berry phase, adiabatic non-Abelian geometric phase, and nonadiabatic Abelian geometric phase have been gradually extended from Hermitian to non-Hermitian quantum systems. However, extending the most general form, the nonadiabatic non-Abelian geometric phase, to non-Hermitian systems has remained an open problem. In this paper, we address this issue by proposing a formalism of the nonadiabatic non-Abelian geometric phase in non-Hermitian quantum systems. Our formalism is consistent with the previous extensions in non-Hermitian quantum systems, and can also naturally revert to the concepts of geometric phase in Hermitian quantum systems. It provides a general formulation of geometric phase for both Hermitian and non-Hermitian quantum systems.

At Wien

Da-Wei Luo, J. Q. You, Hai-Qing Lin +2 more

Geometric phases have been shown to be feasible in implementing quantum gates to perform quantum information processing. For all the realistic applications, the environmental influence on the geometric phase and decoherence such as memory effects must be properly considered in order to achieve the required precision in geometric quantum computation. In this paper, we study the geometric phase for a generic open quantum system based on a microscopic model. A remarkable feature of the open system's geometric phase obtained from our theoretical formulation is that the geometric phase can be obtained regardless of the existence of the master equations, while the environmental noise features such as memory effects are fully accounted for. We demonstrate that the geometric phases for a general open quantum system can be fundamentally modified by its non-Markovian environments.

J H Hannay

Ali Mahdifar, Parvin Rahimi, Ehsan Amooghorban +1 more

In this paper, with respect to the advantages of geometric phase in quantum computation, we calculate the geometric phase of the optomechanical systems. This research can be considered as an important step toward using the optomechanical systems in quantum computation with utilizing its geometric phase.