Quantum Zeno effect and adiabatic change

Abstract

We show that the quantum Zeno effect and the adiabatic change have a close connection even though the former means a halt of the dynamics by frequent measurements and the latter is the dynamics by a slowly changing Hamiltonian. We investigate the motion of a spin under stepping magnetic fields in terms of the ~inverse! quantum Zeno effect. The relation between this model and the adiabatic change is studied. Another model is used to integrate the two effects into one formulation which is an extension of the proof of the adiabatic theorem. Despite their good parallelism, the asymptotic behaviors of the transition probability with respect to the total period T have different forms; the former effect shows a T 21 behavior while the latter scales T 22 . @S1050-2947~97!00908-6# PACS number~s!: 03.65.Bz, 42.50.2p The quantum Zeno effect is the suppression or the inhibition of the free dynamics of a system by frequent or continual measurements @1#. The projection associated with measurements effectively destroys the coherence, only through which the transition from one state to another could take place. So the essential ingredient of the Zeno effect is not literal quantum measurement but destruction of coherence, which can be provided by other means such as optical pumping @2#, collisions, noisy external fields, and so on. We even can find classical realizations of the Zeno effect; for example, in a system of two coupled pendulums, we can suppress the excitation transfer from one pendulum by giving strong damping to the other pendulum. The damping accompanies no energy losses. It is very interesting to view the quantum Zeno effect from a rotating frame in which the free dynamics of the system is canceled. In this frame, a series of projections is performed toward slightly different states one after another and the system evolves after these states. This effect was discussed by Aharonov and Vardi @3# and was called the ¯ ,