On the Theory of Quantum Jumps

Abstract

According to quantum mechanics, a measurement can only produce single eigenvalues of the measured observable, as if the system always exists in an eigenstate. For discrete states, this leads to the idea of a quantummechanical system executing jumps at random instants between eigenstates. DEHMELT [1] suggested to observe these jumps as the switching on and off of the fluorescent emission of a single ion or atom when a metastable state is weakly coupled to a strongly driven transition. This suggestion has led to several experiments [2–5] and even more theoretical treatments [6–10], Most theoretical papers focus on the evaluation of the intensity correlation function f(t), which is the probability density for photon emission at time t, provided that another photon was emitted at time zero. Two papers [9,10] argue that the relevant quantity is rather the waiting-time distribution w(t), defined as the probability distribution for the time lapse t one has to wait for the first emitted photon after an earlier emission at time zero. Furthermore, the various treatments consider different special cases with regard to the level scheme, the degree of saturation and the degree of coherence of the driving light.