Pulsed and continuous measurements of exponentially decaying systems

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.

arXiv comment5 pages, 3 figures

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• On unitary evolution and collapse in Quantum Mechanics
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• The Lee model: a tool to study decays
• Evaluation of Energy Resolution by Changing Angle and Position of Incident Photon in a LYSO Calorimeter
• The experimental observation of $a_0(1710)$: Long awaited from Regge approach
• Nonclassical correlations in decaying systems
• Toward a QFT treatment of nonexponential decay