Quantum self-induced transparency in frequency gap media

– We study quantum effects of light propagation through an extended absorbing system of two-level atoms placed within a frequency gap medium (FGM). Apart from ordinary solitons and single-particle impurity band states, the many-particle spectrum of the system is shown to contain massive pairs of confined gap excitations and their bound complexes—gap solitons. Quantum gap solitons propagate without dissipation, and should be associated with self-induced transparency pulses in a FGM. The self-induced transparency (SIT) pulses, predicted and observed in the pioneering work of McCall and Hahn [1], may be regarded as solitons of the Maxwell-Bloch model [2], describing classical radiation propagating in a single direction and coupled to an extended system of two-level atoms. The model is completely integrable [3] and the time evolution of an arbitrary radiation incident on an atomic system is described [4, 5] by the inverse scattering method [6]. In the case of a high-intensity pulse in ordinary vacuum, quantum corrections are negligibly small. Therefore the quantum version of the classical model—quantum Maxwell-Bloch (QMB) model—has been studied [7] only in the context of the superfluorescence phenomenon where quantum effects play a crucial role [8]. But the situation is drastically changed for frequency gap media (FGM), such as a frequency-dispersive medium [9], a photonic bandgap (PBG) material [10, 11], and a one-dimensional Bragg reflector [12], where classical, linear wave propagation inside a frequency gap is excluded [13, 14]. In this letter, we demonstrate the existence of nonclassical light propagation through an extended homogeneous [15] system of two-level atoms placed within a FGM. These light pulses are highly correlated quantum many-body states and are distinct from single-photon hopping conductivity [16] through the photonic impurity band created by the atoms. Because of a nonlocal polariton-atom coupling, an extension of the Bethe ansatz method [17] from the case of a single atom embedded in FGM [13, 14] to the case of an extended many-atom system requires a thorough analysis. The QMB model generalized to the case of FGM exhibits hidden integrability [13], provided that the characteristic times of the interatomic resonance dipole-dipole interaction (RDDI) and other collisional dephasing effects are much longer than () Also with Landau Institute for Theoretical Physics, Moscow, Russia.