Phase Correlation in Cascade Spontaneous Emission by a Multilevel System. A Classical Explanation of the Scully-Druhl “Quantum Eraser”

Abstract

An excited multilevel atom can emit radiation spontaneously at more than one frequency, corresponding, respectively, to more than one transition. These emission processes may take place simultaneously or during different time intervals. The phenomenon of quantum beats [1] is an example of simultaneous emission from two (closely spaced) upper levels to the same lower level. A cascade emission process is an example of consecutive spontaneous emission at different frequencies. In the case of quantum beats, an essential aspect of the phenomenon is the coherent superposition of the two upper states, the phase difference of which determines the phase of the quantum beats [1] ; although the spontaneous emission field of each frequency may have random phase, the two phases are correlated, so that their difference has a well defined part. Does an analogous effect exist in a cascade — or consecutive — emission process? If a multilevel atom is excited to a state which is a coherent superposition of the ground state and one of the upper levels (higher than the second), will there be correlation between the phases of the spontaneous emission fields of the intermediate transitions? It turns out that the answer to this question, besides being of fundamental interest in itself, also yields a simple — essentially classical — explanation of the “quantum eraser” proposed in a recent article by Scully and Drühl [2] , who invoke the (nonclassical) role of the observer in quantum-mechanical state reduction in their explanation.