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Conference on Lasers and Electro-Optics

Coherent phenomena in two band photonic crystals

Dimitris G. Angelakis, Emmanuel Paspalakis, P. L. Knight

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. The majority of studies of quantum optical processes occurring in atoms interacting with modified reservoirs, such as microcavities and photonic band gap materials, have concentrated on spontaneous emission dynamics. In this paper we report our recent theoretical results on absorption and dispersion dynamics of a A-type system where one transition spontaneously decays in a two band photonic reservoir. The coupling to this modified reservoir leads to a non-Markovian spontaneous decay of the atomic state, which in return influences the dispersion and absorption properties of a probe laser pulse coupling to the other atomic transition.

DOI
10.1109/iqec.2000.907894

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Journal of Physics B Atomic Molecular and Optical Physics•Jun 30, 2006•14 citations
Summary form only given. The majority of studies of quantum optical processes occurring in atoms interacting with modified reservoirs, such as microcavities and photonic band gap materials, have concentrated on spontaneous emission dynamics. In this paper we report our recent theoretical results on absorption and dispersion dynamics of a A-type system where one transition spontaneously decays in a two band photonic reservoir. The coupling to this modified reservoir leads to a non-Markovian spontaneous decay of the atomic state, which in return influences the dispersion and absorption properties of a probe laser pulse coupling to the other atomic transition.
We study the spontaneous emission, absorption, and dispersion properties of a \ensuremath{\Lambda}-type atom where one transition interacts near resonantly with a double-band photonic crystal. Assuming an isotropic dispersion relation near the band edges, we show that two distinct coherent phenomena can occur. First the spontaneous emission spectrum of the adjacent free-space transition obtains ``dark lines'' (zeros in the spectrum). Second, the atom can become transparent to a probe laser field coupling to the adjacent free-space transition.
In this paper, the probe absorption spectrum of a four-level atom in photonic crystals has been investigated. A model is used, which assumes the transitions from the two upper levels to one of the lower levels coupled to the modes of the modified reservoir (photonic band gap) and transitions from the two upper levels to the other lower level coupled to the free vacuum modes. The effect of quantum interference in spontaneous emissions from the two upper levels to the lower levels on the absorption spectrum of an atom is investigated in detail. Most interestingly, it is shown that the atom becomes transparent to a probe laser field coupled to the free space transition only in situations where complete quantum interference takes place in both the free space transitions and the modified reservoir transitions.
Considering a three-level $\ensuremath{\Lambda}$-type atom with both transitions coupled to a single photonic-band-gap reservoir, we investigate the upper-state population and spontaneous emission spectra by using the resolvent operator for the isotropic dispersion model, and give their analytical solutions. For the case of two transitions coupled to the same reservoir, the upper-state population always displays an oscillatory behavior and finally reaches a steady-state value. For atomic transition frequencies in the vicinity of the band-gap edge or inside the gap, the spontaneous emission spectra become strongly non-Lorentzian.
We investigate the dispersive property of a A-type atomic system embedded in photonic band gap structures. The atomic coherence is established by the structured reservoir which consists of a double-band photonic band gap (PBG) and defect modes. With an atomic density of 7×10^15 atoms/cm^3, the group velocity of a probe laser being detuned far away from the gap is shown to be reduced to 3×10^2 m/s near the transparency window associated with the PBG edges and 6×10^3 m/s at the transparency window associated with the defect modes, without using any deriving field. The influence of the smoothness of the density of modes and the decay rate of the second ground state of atoms are analysed.
In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored" electromagnetic vacuum of a photonic band gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption lineshapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
The probe absorption–dispersion spectra of a driven three-level atom in a double-band photonic crystal have been investigated. We use the model which assumes the upper levels of the atomic transitions coupled via a classical driving field. One of the transitions interacts with the free vacuum modes, and the other transition couples to the modes of the modified reservoir (photonic band gap). The effect of the classical driving field on the absorption–dispersion spectra of an atom is investigated in detail. Most interestingly, it is shown that the atom becomes transparent to a probe laser field coupled to the free space transition, and slow group velocities are obtained near the transparency window.