Decay of an Excited Atom under Imperfect Photon Counting Measurement

Abstract

We investigate the decay of an excited two-level atom under a situation where the emitted photon is detected by the conventional photon counting measurement. We discuss an imperfect measurement with finite probability of failing in counting the emitted photon. By analyzing the extended quantum system including the measurement apparatus, we have calculated the survival probability of the excited atom, as well as the response of the apparatus and the errors in the measurement. The decay rate under the measurement is obtained in a simple form. It is shown that not only the response time of the detector but also the measurement error play crucial roles in modification of the decay rate. The conditions to observe the quantum Zeno effect and the anti-Zeno effect are also clarified for the case of Lorentzian form factor.