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CRC Press eBooks

O A Simple Theory on the Effect of Dephasing of Vacuum Fields on Spontaneous Emission in a Microcavity

Yong Lee

Published Jul 9, 2020• 0 citations
Publisher

Abstract

This chapter presents simple theoretical models which take into account the effect of dephasing of the vacuum fields on the spontaneous emission in a microcavity. This would be necessary to evaluate the limit of the capability of microcavity-based solid-state optical devices. The dephasing of the quantized fields, i.e., the vacuum fields, which is our main concern, results from the energy exchange between fields and medium polarizations interacting with phonon reservoirs, that is, from the dispersion. A symmetric structure of the system allows us to use the one-way time-evolution of field b, in order to obtain a motion equation of the field, which is in general derived from a round-trip time-evolution of the field. The alteration of the spontaneous emission in a microcavity can be viewed as a manifestation of the self-interference of the quantized fields, which are vacuum fields.

DOI
10.1201/9780138738938-2

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This chapter presents simple theoretical models which take into account the effect of dephasing of the vacuum fields on the spontaneous emission in a microcavity. This would be necessary to evaluate the limit of the capability of microcavity-based solid-state optical devices. The dephasing of the quantized fields, i.e., the vacuum fields, which is our main concern, results from the energy exchange between fields and medium polarizations interacting with phonon reservoirs, that is, from the dispersion. A symmetric structure of the system allows us to use the one-way time-evolution of field b, in order to obtain a motion equation of the field, which is in general derived from a round-trip time-evolution of the field. The alteration of the spontaneous emission in a microcavity can be viewed as a manifestation of the self-interference of the quantized fields, which are vacuum fields.
We present a simple theory on the effect of optical dephasing on the spontaneous emission (SE) rate in a microcavity containing (absorbing) dispersive dielectric media based on a photon Green's-function formalism in which the reservoir damping of medium polarizations is included in a phenomenological way. The theory yields the well-known result that the SE rate in free space is modified by the real part of the refractive index at the transition frequency of an atom in a bulk dielectric. On the other hand, it turns out that the degree of the alteration of the SE rate in a high-Q microcavity with dispersive media is affected not only by the real part of the refractive index but also by the imaginary part of the refractive index that is associated with the dephasing of the photon field due to the reservoir damping, i.e., the destruction of self-interference of the photon field.
The theory of spontaneous emission in dielectric media is extended to take proper account of dispersion and local field corrections. For the case of spontaneous emission in a plasma or radiative electron-hole recombination in a semiconductor, there are effectively no local field corrections. A shift of emission lines due to a dispersive host medium is predicted and interpreted. The corrections to spontaneous and stimulated emission due to dielectric interfaces in microcavity lasers are discussed.
The optical processes of a single-atom model in the phonon field have been studied. To deal with the quantum electrodynamics phenomena in condensed matter microcavities, the influence of electron-phonon interactions has to be taken into account. As a clear picture, the effect of the lattice's oscillation on the optical transition in condensed matter microcavities is reduced to a model of a single atom in a phonon field. We deduce that in the case with a phonon participating, the Bloch equation is still satisfied. In the process of spontaneous emission for an electron interacting with a phonon, we derive the Rabi oscillation for the simple atom in the phonon field.
Abstract Chapter 15 derived the fundamental theory and eigenstates for the quantized radiation field and then showed how the quantum vacuum gives rise to spontaneous emission. This chapter now goes more deeply into the meaning and implications of the quantized field. The polarization of a photon can be used as a qubit and the photonic qubit is called a flying qubit. It enables transmission of information from one node to another. Spontaneous emission is shown to enable creation of an entangled state between a photonic qubit and the spin of an electron. Spontaneous emission can also degrade the performance of some device designs and in other devices it can enhance performance such as for a single photon emitter. In this we show how to engineer the vacuum to control spontaneous emission.
In this chapter, the authors develop a consistent theory of spontaneous emission in an optical micro cavity from a broadened atom. They derive the atomic broadening from first principles by assuming the presence of reservoirs coupled to the atoms. The simplest model of the atom is the so-called two-level atom, which has only two energy levels, the excited and the ground level. However, realistic atoms are surrounded by media that affect the atoms, giving them homogeneous or inhomogeneous broadening. The important parameter of coupling ratio of spontaneous emission to a desired quasi mode cannot be exactly treated by the present mathematical model of the cavity, although it is easily seen qualitatively that the ratio will decrease with increasing atomic broadening. The authors assume that each atom emits independently and ignored the possible interaction among atoms during spontaneous emission. Solving the master equation for the density matrix elements, the readers have derived formulas for spontaneous emission rate and emission spectrum.
This chapter gives an overview of the field as it stands at the time of writing in mid 1995. It shows how the picture radically changes when there is more than one atom in the cavity. The simplest light-atom interaction one can think of is the coupling between a single atom and a single mode of the electromagnetic field. This system provides considerable insight into the fundamental physics of the light-atom coupling but the reader is warned that the more general many mode-many atom interactions are much richer in their dynamics. An atom in free space couples not only to one, but to a continuum of modes. The mathematics of the Weisskopf-Wigner theory of spontaneous emission tends to obscure the relatively simple physics of the emission process. An alternative, shorter way of calculating the single atom spontaneous emission rate is to use Fermi’s Golden rule, which is a prescription for calculating general transition rates to first order in perturbation theory.