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Coherent control of a three-level atom in a photonic crystal

We demonstrate coherent control of the population and polarization of a two-level subsystem consisting of the two upper levels of a three-level atom in the V-configuration placed inside the structured reservoir of a photonic crystal. One of the excited state transition frequencies is located deep within the photonic band gap and the other transition is near the photonic band edge. Using the method of generalized-Laplace transforms, we study the population and polarization of the two-level subsystem of the three-level atom in the Born approximation without making the Markov approximation. The generalized-Laplace transform technique allows us to solve the Langevin equation for the operators and the correlation function of operators rather than the Schrodinger equations of motion. Coherent control of the population and the polarization dynamics of the two-level subsystem is demonstrated in the structured electromagnetic density of states of a photonic crystal. We demonstrate the tunability of the fractionalized steady-state population and the residual coherence in the photon–atom bound state by varying the Rabi frequency and the phase of the driving laser field.