Anomalous commutation relation and modified spontaneous emission inside a microcavity

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Abstract
Usual quantum-optical operator relations for a beam splitter are shown to lead to an anomalous commutation relation inside a microcavity. The physical origin of this anomaly is identified as self-interference of the mode whose coherence length is longer than the round-trip length of the cavity. Altered spontaneous emission of an excited atom is found to be a direct manifestation of this anomalous commutation relation. The anomalous Heisenberg uncertainty relations, which are derived from the commutation relation according to the Schwartz inequality, cannot be detected by probing the internal field with a beam splitter. The anomalous commutation relation, however, can be related to the change in the effecitve reflectivity of the beam splitter. The similarity and difference between an excited atom and a probe beam splitter are discussed.