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Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics

A theory of nonlinear susceptibility in polaritonic band‐gap materials doped with multi‐level atoms

Debashish Mukherji, Mahi R. Singh

Published May 1, 2005• 0 citations
Publisher

Abstract

We have studied the nonlinear susceptibility in dispersive polaritonic band-gap (DPBG) materials in the presence of five-level impurity atoms. Initially, the atom is prepared in a coherent superposition of two levels |b〉 and |c〉. The levels |b〉 and |c〉 are coupled to the upper level |a〉 with a coherent laser field. The nonlinear susceptibility has been calculated corresponding to transitions |a〉 → |c〉 and |a〉 → |b〉 using the equation of motion for the density matrix. The atomic system is interacting with the polariton reservoir. The effect of atom-polariton reservoir coupling on the imaginary part of the nonlinear susceptibility has been studied when the resonance energy lies in lower band of the polariton spectrum. It is found that by shifting the resonance energy away from the band edge, the system goes to the probe gain state. It is also found that by changing the intensity of the coherent laser field, the system switches from gain to loss state and vice-versa. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssc.200460746

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We have studied the nonlinear susceptibility in dispersive polaritonic band-gap (DPBG) materials in the presence of five-level impurity atoms. Initially, the atom is prepared in a coherent superposition of two levels |b〉 and |c〉. The levels |b〉 and |c〉 are coupled to the upper level |a〉 with a coherent laser field. The nonlinear susceptibility has been calculated corresponding to transitions |a〉 → |c〉 and |a〉 → |b〉 using the equation of motion for the density matrix. The atomic system is interacting with the polariton reservoir. The effect of atom-polariton reservoir coupling on the imaginary part of the nonlinear susceptibility has been studied when the resonance energy lies in lower band of the polariton spectrum. It is found that by shifting the resonance energy away from the band edge, the system goes to the probe gain state. It is also found that by changing the intensity of the coherent laser field, the system switches from gain to loss state and vice-versa. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
A theory of coherent population trapping (CPT) has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials when doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra leading to unusual optical properties. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. The transition between the two lower states of an atom is dipole forbidden. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations are performed for both PBG and DPBG materials with the phase factor between the coherent states chosen such that the number density of the upper state becomes zero when the photon fields have the same intensity. It is found that when the resonance energies lie away from the band edges and within the lower band, the CPT effect is observed in both materials when the fields have identical intensities. Similar results are also found when the resonance energies lie away from the band edges and within the upper band. When one of the resonance energies lies near the lower band edge, the number density vanishes at all intensities of the fields for both materials. This is an effect of the band structure of the materials and is not due to the CPT effect. A similar result is seen when one of the resonance energies lies near the upper band edge of a PBG material. However, for a DPBG material, the number density does not become zero when one of the resonance energies lies near the upper band edge, except due to the CPT effect brought on by the identical intensities of the photon fields. This is a very interesting phenomenon.
A theory of linear susceptibility has been developed in the presence of dipole-dipole interaction for photonic-band-gap (PBG) materials doped with an ensemble of five-level nanoparticles. An external probe laser induces dipole moments in nanoparticles. When the concentration of the particles is high, the induced dipoles interact with one another through dipole-dipole interaction. Mean-field theory is used to include the effect of dipole-dipole interaction in the calculation of susceptibility. Numerical simulations are performed for the real and imaginary susceptibilities and it is found that the system switches between inversionless and noninversionless states. In addition the system switches between absorptionless and nonabsorptionless states. These occur when the resonance energy lies near the valence-band edge of the photonic-band-gap material. The theory also predicts a polarization catastrophe in PBG materials doped with nanoparticles.
A theory for the refractive-index enhancement due to quantum coherence and interference has been developed in dispersive polaritonic and photonic band-gap materials doped with an ensemble of noninteracting three-level atoms. Quantum coherence is introduced by driving the atoms with a coherent monochromatic laser field. The real and the imaginary parts of the susceptibility have been calculated by using the master equation and the Laplace transform methods. It is found that the energy gap in these materials plays an important role in the refractive-index enhancement. Numerical simulations for the real and the imaginary parts of susceptibility are performed for SiC as a function of the probe laser frequency. It is found that there is a giant refractive-index enhancement with vanishing absorption when the resonance frequencies lie near the lower band edge.
We study the dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipole-dipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.
Quantum electrodynamics of two identical two-level atoms placed within a frequency dispersive medium whose polariton spectrum has a gap due to photon coupling to a medium excitation (exciton, optical phonon, etc.) is studied within the framework of the dipole resonance (rotating-wave) approximation. For finite interatomic distances a polariton-atom bound state lying within the polaritonic gap is shown to be split into a doublet due to an effective atom-atom interaction. Evaluating the splitting as a function of the interatomic separation, we estimate a width of a polariton-impurity band when a system of spatially correlated atoms is present. The results obtained for the case of two atoms are then generalized to the case of an atomic chain (a one-dimensional atomic lattice). The equations describing a propagation of a band polariton are derived and the expressions for the band polariton spectrum and its effective mass are obtained. The model under consideration has quite a general structure and is applied to the case of photonic-band-gap materials as well. Numerical calculations are presented for SiC semiconductors.