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.   The present paper discusses the stimulated emission, in strong coupling  regime, of an atom embedded inside a one dimensional (1D) Photonic Band Gap  (PBG) cavity which is pumped by two counter-propagating laser beams. Quantum  electrodynamics is applied to model the atom-field interaction, by  considering the atom as a two level system, the e.m. field as a  superposition of normal modes, the coupling in dipole approximation, and the  equations of motion in Wigner-Weisskopf and rotating wave approximations. In  addition, the Quasi Normal Mode (QNM) approach for an open cavity is adopted, interpreting the local density of states (LDOS) as the local density of  probability to excite one QNM of the cavity; and therefore rendering this  LDOS dependent on the phase difference of the two laser beams. In this paper  we demonstrate that the strong coupling regime occurs at high values of the  LDOS. In accordance with the results of the literature, the emission  probability of the atom decays with an oscillatory behaviour, so that the  atomic emission spectrum exhibits two peaks (Rabi splitting). The novelty of  this work is that the phase difference of the two laser beams can produce a  coherent control of both the oscillations for the atomic emission  probability and, as a consequence, of the Rabi splitting in the emission  spectrum. Possible criteria to design active delay lines are finally  discussed.

Coherent control of stimulated emission inside one dimensional photonic crystals: strong coupling regime