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Quantum jumps in a three-level system

Juha Javanainen

Published Jun 9, 1986• 0 citations
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Abstract

According to the usual interpretation of quantum mechanics, measurement of an observable yields its eigenvalue. Extrapolation of classical reasoning then suggests that at every instant of time the quantum system actually is in one of the eigenstates of the observable, and as time goes on it executes random jumps between the states. In this spirit, Cook and Kimble1 have recently elaborated Dehmelt’s suggestion2 that fluorescence from a laser-driven two-level system weakly coupled to a third state may turn on and off when the atom jumps between the active two-level system and the inactive third state.

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Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
According to the usual interpretation of quantum mechanics, measurement of an observable yields its eigenvalue. Extrapolation of classical reasoning then suggests that at every instant of time the quantum system actually is in one of the eigenstates of the observable, and as time goes on it executes random jumps between the states. In this spirit, Cook and Kimble1 have recently elaborated Dehmelt’s suggestion2 that fluorescence from a laser-driven two-level system weakly coupled to a third state may turn on and off when the atom jumps between the active two-level system and the inactive third state.
We compare the statistics of photon counts of the light scattered by a laser-driven two-level system weakly coupled to a third metastable state with the statistics of a dichotomic Markov process. The fluorescence is found to turn abrubtly off and on, as if the atom executed quantum jumps to and from the metastable state. Moreover, the jumping nature of the fluorescence over long time scales survives even though the atom cannot be treated with rate theory and the picture of instantaneous quantum jumps is not strictly justified.
We calculate from the quantum regression theorem the entire photon-counting statistics for the fluorescence from a laser-driven two-level system weakly coupled to a metastable third level, and compare the result with the statistics of a dichotomic Markov process. The comparison shows, that at least in the limit of an infinite intensity of the laser in a single experiment the sequence of photon counts should display randomly alternating periods with no counts and a nonzero counting rate as if the atom executed ``quantum jumps'' to and from the metastable state.
The observation of quantum jumps in a Dehmelt electron-shelving scheme was made two years ago.1 Prior to these experiments considerable theoretical discussion was addressed to the question of whether the turn-on and turn-off of fluorescence, as described by Cook and Kimble,2 would actually occur. This discussion focused on photon statistics. It was taken to be self-evident that a prolonged cessation of fluorescence from the strong transition implied that the atom had jumped and now resided in the shelved state. This is surely correct but with some qualification. What observational information leads to the conclusion that the electron is shelved? It is the appearance of an abnormally long time interval without recording a single photoelectron at the detector monitoring the strong fluorescence. But how long is abnormally long? What is the time resolution of our quantum jump? I calculate the reduced atomic state following a photoelectric detection event, conditioned on the requirement that no subsequent photoelectron has been observed. For sufficiently long times without recording a subsequent photoelectron the atomic state collapses to the shelved state with high (but not unit) probability. The waiting time required for a confident judgment that the atom is in the shelved state is calculated as a function of transition rates and detector efficiency.