Probing the evolution of quantum superposition states in a nuclear spin-5/2 system

Abstract

We report the effects of off-diagonal coupling on eigenstates and eigenvalues of a realistic quantum Hamiltonian, a ^{121}Sb (spin I=5/2) nuclear spin Hamiltonian in an antimony single crystal. In our nuclear resonance experiment, off-diagonal matrix elements are generated and controlled by the angle θ between the directions of the electric field gradient and an external magnetic field. With a very small θ, a two-state-like avoided level crossing is directly probed as a function of an external magnetic field. On the other hand, by increasing θ under a weak magnetic field, we find that the nuclear spin transitions undergo dramatic changes as θ approaches 90^{∘}. All our experimental observations are in excellent agreement with exact diagonalization calculations for the Hamiltonian, demonstrating how superposition states of a multistate quantum system evolve as a function of a well-defined control parameter.