Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

Whether quantum state transitions occur by instantaneous jumps (a la Bohr) or deterministic dynamics (Schrödinger's preference) has been intensely debated. Recent experimental measurements of shelved electrons have reignited the debate. We examine aspects of the time-dependent numerical solutions of the Schrödinger equation in quantum systems with two and three levels perturbed by a sinusoidal field. A geometrical construction involving quantum state phase differences illuminates the role of interstate phase differences in a deterministic, rather than random, process of multiphoton absorption. Alternate halves of the Rabi cycle exhibit phase reversals much like the classical beats of coupled oscillators. For non-zero detuning, population inversion does not occur because the exciting field drifts out of the proper phase before inversion is complete. A close correspondence with classical, coupled oscillator beats offers insights for interpretation of deterministic quantum dynamics and suggests an experimental test for the correctness of this picture depending on the long-time phase stability of exciting fields.