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

Abstract

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.