Coherence versus incoherence: Collapse and revival in a simple quantum model

TLDR

The study examines irreversibility in an exactly solvable, loss‑free quantum model. The authors aim to describe the temporal behavior of the dynamic elements of this model. They analyze a single two‑level atom coupled to a single radiation mode in the dipole approximation, deriving new long‑time numerical and closed‑form analytic solutions for the atomic dipole moment, population difference, and dipole‑dipole correlation function under the rotating‑wave approximation. They find that the loss‑free system exhibits collapse—episodic nonexponential damping of atomic inversion and dipole moment—and two distinct revival types that nearly recover the initial state, providing analytic expressions for the collapse function, revival times, and envelope of revival maxima, all without semiclassical or decorrelation approximations.

Abstract

We describe the temporal behavior of the dynamic elements of an exactly soluble quantum model. The model consists of a single two-level atom or spin interacting with a single mode of the quantized radiation field in the dipole approximation, the mode being initially in an arbitrary coherent state of excitation. We give new long-time numerical and closed-form approximate analytic solutions for the expectation values of the atomic dipole moment and the difference in population of the two atomic levels in the rotating wave approximation. The atomic dipole-dipole correlation function is calculated. All of the results are obtained without semiclassical or decorrelation approximations. Unusual features found in the temporal behavior of this lossless model problem are "collapse," i.e., episodic nonexponential damping of both the atomic inversion and dipole moment, and two kinds of "revival" or partial recorrelation, in the dynamic evolution, during which the initial state is nearly recovered. We give analytic formulas for the collapse function, for both of the revival times, and for the envelope of the revival maxima. Some remarks are made about the nature of irreversibility in this exactly soluble and loss-free model.