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 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.
In this thesis, we study light-matter interaction in the contexts of coherent population trapping (CPT) and the ac Stark effect in nanoparticles embedded (doped) in two important classes of reservoirs -- photonic crystals and dispersive materials. These materials have gaps in their energy spectra and are studied widely due to their unusual optical properties and potential for novel applications. We consider that the reservoirs are doped with an ensemble of five-level nanoparticles, each with a single Λ core (consisting of a lower doublet and an upper energy level), which interact with both the host reservoir and external radiation fields. We have also included studies of cases where the nanoparticles interact with each other as well via dipole-dipole interaction (DDI), which is included in the mean field approximation. This only happens when the doping concentration is high (~ 1018 per cubic meter).\nIn studying CPT, we have developed a novel technique of optical switching by devising a system whereby the doped nanoparticles become stable against absorption from the radiation field(s) i.e. they switch to their ground states. We have confirmed the occurrence of CPT in both types of reservoir and have also identified a number of important contrasting features which have markedly different utilities. Most significantly, we have found that the strength of the DDI between the nanoparticles plays a very important role in determining the conditions required for CPT in both materials. In studying the ac Stark effect in photonic crystals, we have used an ensemble of five-level nanoparticles, each with a single cascade core [ladder configuration], both with and without DDI. We found that, in the ac Stark regime, resonance tuning of the transitions within the nanoparticles, in relation to the band structure of these crystals, offers a new mechanism for switching the nanoparticle system from an inverted to a non-inverted state. Specifically, a doped nanoparticle can effectively become transparent to any radiation field tuned to the probed transition. Under DDI, we found that the absorption in the system decreases with increasing DDI strength. These findings have very exciting potential for applications in optical switching.
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.
Numerical simulations are performed on the narrowing of transient linewidths of the absorption peaks of an ensemble of four-level atoms doped in a dispersive band-gap material. The atoms do not interact with each other. They are, however, interacting with a reservoir, due to which, the top two levels of the atoms decay to a pair of lower levels. A probe laser field is applied to study the absorption characteristics of the system. The density matrix method is used to calculate the photon yield for the absorption peak in order to observe linewidth narrowing. Numerical simulations are performed for SiC which is a dispersive polaritonic band-gap material. We have observed the occurrence of linewidth narrowing in SiC when the resonance energies lie within the bands. But when the resonance energy lies near the lower band edge of the polaritonic crystal, the narrowing disappears. On the other hand, when the resonance energy lies near the upper band edge, the narrowing of the linewidth remains as pronounced as before. Moreover, we have found that the photon yield is very sensitive to the locations of the resonance energies within the band. These unusual properties can be used to make new types of photonic devices such as switches, gates, etc. Similar results are also found in photonic band-gap materials.
Summary form only given. Unlike semiconductors which facilitate the coherent propagation of electrons, photonic band gap (PBG) materials execute their novel functions through the coherent localization of photons. When a PBG material is doped with impurity atoms which have an electronic transition that lies within the gap, spontaneous emission of light from the atom is inhibited. Inside the gap, the photon forms a bound state to the atom. Outside the gap, radiative dynamics in the colored vacuum is highly nonMarkovian. I discuss the influence of these memory effects on laser action. When spontaneous emission is absent, the next order radiative effect (resonance dipole-dipole interaction between atoms) must be incorporated, leading to anomalous nonlinear optical effects which occur at a much lower threshold than in ordinary vacuum. I describe the collective switching of two-level atoms near a photonic band edge, by external laser field, from a passive stare to one exhibiting population inversion. This effect is forbidden in ordinary vacuum. Finally, I discuss the prospects for a phase sensitive, single (3-level) atom quantum memory device, onto which information may be written by an external laser pulse. By scattering polarized photons (flying qubit) this system may execute certain quantum logic operations.