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Physical Review E

Coherent control of stimulated emission inside one-dimensional photonic crystals

Alessandro Settimi, S. Severini, Marco Centini, Concita Sibilia, M. Bertolotti, Anna Napoli, ANTONINO MESSINA

Published Jun 15, 2005• 10 citations
Publisher

Abstract

In this paper, the quasinormal mode (QNM) theory is applied to discuss the quantum problem of an atom embedded inside a one-dimensional (1D) photonic band gap (PBG) cavity pumped by two counterpropagating laser beams. The e.m. field is quantized in terms of the QNMs in the 1D PBG and the atom modeled as a two-level system is assumed to be weakly coupled to just one of the QNMs. The main result of the paper is that the decay time depends on the position of the dipole inside the cavity, and can be controlled by the phase difference of the two laser beams.

DOI
10.1103/physreve.71.066606

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Journal of Optics•Jul 31, 2015•2 citations
In this paper, the quasinormal mode (QNM) theory is applied to discuss the quantum problem of an atom embedded inside a one-dimensional (1D) photonic band gap (PBG) cavity pumped by two counterpropagating laser beams. The e.m. field is quantized in terms of the QNMs in the 1D PBG and the atom modeled as a two-level system is assumed to be weakly coupled to just one of the QNMs. The main result of the paper is that the decay time depends on the position of the dipole inside the cavity, and can be controlled by the phase difference of the two laser beams.
An extension of the second quantization scheme based on the quasinormal-modes theory to one-dimensional photonic band gap (PBG) structures is discussed. Such structures, treated as double open optical cavities, are studied as part of a compound closed system including the electromagnetic radiative external bath. The electromagnetic field inside the photonic crystal is successfully represented by a new class of modes called quasinormal modes. Starting from this representation we introduce the Feynman's propagator to calculate the decay rate of a dipole inside a PBG structure, related to the density of modes, in the presence of the vacuum fluctuations outside the one-dimensional cavity.
We present a quantum theory of a coherently pumped two-level atom in a photonic band gap (PBG), coupled to both a multimode waveguide channel and a high-quality microcavity embedded within a photonic crystal. One mode is engineered to exhibit a sharp cutoff within the PBG, leading to a large discontinuity in the local photon density of states near the atom, and the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence. Another mode of the waveguide channel is used to propagate the pump beam. We derive analytical expressions for the optical amplitude, intensity, second-order correlation functions, and conjugate quadrature variances for the light emitted by the atom into the microcavity. The quantum degree of second-order coherence in the cavity field reveals enhanced, inversionless, nearly coherent light generation when the photon density of states jump between the Mollow spectral components is large. The cavity field characteristics are highly distinct from that of a corresponding high-QQQ cavity in ordinary vacuum. In the case of a vanishing photon density of states on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian, and the cavity field exhibits quadrature coherence.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band gap (PBG) material, with one resonant frequency near the edge of the PBG. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive optical memory device on the atomic scale. The protected electric dipole within the PBG provides a basis for a qubit to encode information for quantum computations. A detailed literature survey on the nature, fabrication and applications of PBG materials is presented to provide context for this research.
The coherent control of cooperative spontaneous emission from two identical non-overlapping three-level atoms in the V-configuration located within a photonic band gap (PBG) material with two resonant frequencies near the upper band edge of the PBG and confined to a region small in comparison to their radiation wavelengths but still greater than their atomic sizes is investigated. The dependencies of cooperative effects in which a photon emitted by one atom is reabsorbed by the other atom on the inter-atomic separation, on the initial state of the two-atom system, on the strength of the driving control laser field, and on the detuning of the atomic resonant frequencies from the upper band edge frequency is analyzed so as to identify the conditions for which these cooperative effects are enhanced or inhibited. Cooperative effects between atoms are shown to be influenced more by the PBG than by the nature of the atomic transitions involved. Excited state populations as well as coherences between excited levels are expressed in terms of time-dependent amplitudes which are shown to satisfy coupled integro-differential equations for which analytic solutions are derived under special conditions. Unlike for the case of one atom in a PBG where the fractional non-zero steady state populations on the excited levels as well as the coherence between the excited levels are constants independent of time, in the case of two atoms in PBG these quantities continuously oscillate as a manifestation of beating due to the continuous exchange between the two atoms of the photon trapped by the PBG. The values of these quantities as well as the amplitudes and frequencies of their oscillations depend of the parameters of the system, providing different ways of manipulating the system. The general formalism presented here is shown to recapture the special results of investigations of similar systems in free space when the non-Markovian memory kernels of the PBG are replaced by delta function dependent Markovian memory kernels.