Pulsed and continuous measurements of exponentially decaying systems

TL;DR

This paper investigates how different measurement methods, pulsed and continuous, affect the decay law of quantum systems, revealing differences in the Quantum Zeno effect and challenging the Schulman relation.

Contribution

It demonstrates that pulsed and continuous measurements yield different effects on quantum decay, showing the Schulman relation does not always hold.

Findings

Quantum Zeno effect confirmed with measurements slowing decay

Differences observed between pulsed and continuous measurement outcomes

Schulman relation does not universally apply to measurement types

Abstract

We study the influence of a detector on the decay law of a quantum state whose "undisturbed" survival probability is purely exponential. In particular, we consider a detector with a finite energy band of detection, i.e. it interacts only with decay products having an energy within a certain range of values. In one case, we assume that the detector performs many repeated measurements at short time intervals in all of which a collapse of the wave function occurs (bang-bang or pulsed-type measurements). In the second case, we assume a continuous measurement which preserves unitarity. We confirm the slowing down of the decay in presence of a measuring apparatus, the Quantum Zeno effect, but the outcomes of the detector are in general qualitatively and quantitatively different in the two cases. In turn, this implies that the so-called Schulman relation (the equivalence of pulsed and continuous measurements) does not hold in general and that it is in principle possible to experimentally access how a certain detector performs a measurement.