Induced and Spontaneous Emission

Abstract

The problem of induced and spontaneous emission is investigated for an atomic two‐level system with incident beams of radiation which are either in a coherent state or in a stationary state (contain a definite number of photons). The treatment is fully quantum‐mechanical, and is confined to the case where the frequency spectrum of the incident beam is narrow compared to the natural linewidth of the system. It is shown that, under such conditions, the spontaneous emission for frequencies within the narrow band of the incident radiation is sharply reduced compared to the prediction of the natural lineshape. It is shown that a hole is burned in the natural lineshape within the narrow frequency band, thus effectively quenching the spontaneous emission at some frequency within the band. This effect is shown to occur both for the coherent and stationary beams. Quantities proportional to the induced and spontaneous probability amplitudes and the lifetimes are computed for times comparable to and long compared to the free lifetime of the state. An expression is found for the spectrum of the emergent radiation in terms of these quantities. Its physical meaning is briefly discussed. The density operator of the field for all times is given.