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Journal of Modern Optics

Quantum beat phenomenon due to polaritons in dispersive and photonic band gap materials

Mahi R. Singh

Published Jan 1, 2003• 11 citations
Publisher

Abstract

The quantum beats phenomenon due to polaritons has been studied in dispersive materials and photonic band gap materials doped with a three-level atom. It is considered that the atom is in top and middle excited states and the spontaneous emission of the radiation field from the top excited state to the ground state and the middle excited state to the ground state is allowed. The following interesting results are found in the present paper. When two excited states of the atom lie outside the band gap of these materials, there is an emission of two polaritons from the upper and the middle excited states to the ground state. These two polaritons interfere and produce the quantum beats effect. But when the upper state lies within the band gap and the middle state lies either within the band gap or outside the band gap, the quantum beat effect disappears.

DOI
10.1080/0950034021000013255

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Quantum electrodynamics of a single two-level atom 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. Despite a nonlocal effective polariton-polariton coupling, the system is proven to be integrable and is diagonalized exactly by means of the Bethe-ansatz technique. Its spectrum consists of bound many-polariton complexes (quantum solitons) and exhibits some unusual features due to the existence of the polaritonic gap. Only solitons containing an even number of polaritons propagate within the gap, while a soliton with an odd number of polaritons is pinned to the atom and forms a many-polariton-atom bound state, in which the radiation and the medium polarization are localized in the vicinity of the atom. The model under consideration has a quite general structure and can also be applied to the case of photonic-band-gap materials. \textcopyright{} 1996 The American Physical Society.

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The quantum beats phenomenon due to polaritons has been studied in dispersive materials and photonic band gap materials doped with a three-level atom. It is considered that the atom is in top and middle excited states and the spontaneous emission of the radiation field from the top excited state to the ground state and the middle excited state to the ground state is allowed. The following interesting results are found in the present paper. When two excited states of the atom lie outside the band gap of these materials, there is an emission of two polaritons from the upper and the middle excited states to the ground state. These two polaritons interfere and produce the quantum beats effect. But when the upper state lies within the band gap and the middle state lies either within the band gap or outside the band gap, the quantum beat effect disappears.
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.
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.
We investigate spontaneous emission and quantum interference effects involving a three-level atom in the vicinity of a photonic band edge beyond the weak-driving-field approximation. We consider two different three-level atoms, each subject to a probe field from the ground state and each embedded within a different photonic crystal (PhC). The first atom has the two excited states separated by a dipole transition in the optical frequency range, with this frequency being close to the surrounding PhC's band edge. The probe field couples the ground state and the highest excited state, and is well outside the PhC band gap. If a coupling field is applied between the two upper levels, electromagnetically induced transparency (EIT) may occur, depending on the position of the band edge. The second atom has the two upper levels each dipole-coupled to the ground state and close enough that the emissions from each can coherently interfere. This atom is embedded within a PhC whose band edge lies near the lower of the two excited states, and a probe field is applied that lies just beyond this band edge. This atom exhibits a quantum interference phenomenon related to EIT called field-induced transparency, again depending on the position of themore » band edge relative to the lower excited state.« less
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.
We investigate spontaneous emission and quantum interference effects involving a three-level atom in the vicinity of a photonic band edge beyond the weak-driving-field approximation. We consider two different three-level atoms, each subject to a probe field from the ground state and each embedded within a different photonic crystal (PhC). The first atom has the two excited states separated by a dipole transition in the optical frequency range, with this frequency being close to the surrounding PhC's band edge. The probe field couples the ground state and the highest excited state, and is well outside the PhC band gap. If a coupling field is applied between the two upper levels, electromagnetically induced transparency (EIT) may occur, depending on the position of the band edge. The second atom has the two upper levels each dipole-coupled to the ground state and close enough that the emissions from each can coherently interfere. This atom is embedded within a PhC whose band edge lies near the lower of the two excited states, and a probe field is applied that lies just beyond this band edge. This atom exhibits a quantum interference phenomenon related to EIT called field-induced transparency, again depending on the position of the band edge relative to the lower excited state.
Quantum electrodynamics of a single two-level atom 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. Despite a nonlocal effective polariton-polariton coupling, the system is proven to be integrable and is diagonalized exactly by means of the Bethe-ansatz technique. Its spectrum consists of bound many-polariton complexes (quantum solitons) and exhibits some unusual features due to the existence of the polaritonic gap. Only solitons containing an even number of polaritons propagate within the gap, while a soliton with an odd number of polaritons is pinned to the atom and forms a many-polariton-atom bound state, in which the radiation and the medium polarization are localized in the vicinity of the atom. The model under consideration has a quite general structure and can also be applied to the case of photonic-band-gap materials. \textcopyright{} 1996 The American Physical Society.