The Aharonov–Anandan phase and geometric double-quantum excitation in strongly coupled nuclear spin pairs

Abstract

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.