Aharonov-Anandan quantum phase for relativistic spin polarized protons

Tiezheng Qian, Zhao-Bin Su

We show the existence of a nonadiabatic geometric phase, i.e., an Aharonov-Anandan (AA) phase, in the Aharonov-Casher (AC) topological interference effect in one-dimensional mesoscopic rings. We find the AC phase is the phase accumulated by the spin wave function during a cyclic evolution, and show it is the sum of a geometric AA phase and a dynamical phase. In the adiabatic limit, the AA phase becomes the spin-orbit Berry phase introduced by Aronov and Lyanda-Geller. By solving exactly the model of a quasi-one-dimensional ring formed by the 2DEG on a semiconductor heterostructure, we discuss the observability of the AA phase in the AC effect.

Indrani Bose, S. Chatterjee

Société française de physique

Christian Bengs, Mohamed Sabba, Malcolm H. Levitt

The Aharonov-Anandan phase is a contribution to the phase acquired by the cyclic evolution of a quantum state, which depends only on the geometric properties of its trajectory. We report the study and the exploitation of the Aharonov-Anandan phase by nuclear magnetic resonance interferometry techniques in homonuclear spin-1/2 pairs in the near-equivalence limit. We introduce a new method for engineering effective zero-quantum Hamiltonians with an arbitrary phase in the transverse plane. We use this method to generate a variety of cyclic zero-quantum paths, enabling direct study of the geometric Aharonov-Anandan phase to probe the rotational characteristics of the zero-quantum subspace. We show that the geometric Aharonov-Anandan phase may be used for efficient double-quantum excitation in strongly coupled spin pairs. We find that geometric double-quantum excitation outperforms the standard method by a factor of 2 in experiments performed on a typical case involving near-equivalent spin pairs.

Mai-Lin Liang, Shun-Lin Shu, Bing Yuan

Aharonov–Anandan (AA) phases for two coupled spins in a rotating magnetic field are obtained. The conditions for the adiabatic limit are also derived. It is found that if the rotating field is confined to a plane and the total spin is an integer, the adiabatic phase or the Berry phase will be zero, but the AA phase will not. Unlike adiabatic evolution, the AA phase is not the sum of geometric phases for the subsystems.

Scott Roger Shepard