Quantum theory of spontaneous emission from a two-level atom in a one-dimensional cavity with output coupling

A nonperturbative fully quantum-theoretical analysis describing the transient spontaneous emission of an initially excited two-level atom in a one-dimensional cavity with output coupling is presented. A delay-differential equation for the probability amplitude of the upper atomic state is strictly derived from the Schrodinger equation. With this equation, both the time evolution of the atomic state and the emission spectrum are calculated. Furthermore, the mode function makes the calculations of emitted fields both inside and outside the cavity possible. The calculated result of the vacuum Rabi oscillation in an underdamped cavity and the result of enhanced spontaneous emission rate in an overdamped cavity are presented. A retardation-governed revival of the upper atomic state is predicted. The calculated results also show the inhibition of spontaneous emission by detuning or by setting the atom at a node.>