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Journal of Modern Optics

Thermally induced decay of the atom in a photonic bandgap reservoir

Martin Konôpka

Published Jan 1, 1999• 6 citations
Publisher

Abstract

We investigate thermally induced partial decay of a two-level atom into a photonic bandgap reservoir in regimes when the atomic transition is tuned in the forbidden gap or at the band edge. The atom decays into a quasi-equilibrium state different from those given by the Boltzmann statistical distribution. We take values of physical parameters typical for Rydberg atoms and currently existing photonic crystals. We show that specific thermally induced transitions can be significant for such Rydberg atoms even at bandgap frequencies provided that there is a peak in the density of modes at the band edge. We point out a temperature sensitivity of microwave quantum optics devices based on photonic band structures due to temperature-dependent transitions and level shifts in regimes when important quantum transitions occur at energies near to band-edge frequencies.

DOI
10.1080/09500349908231252

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We investigate thermally induced partial decay of a two-level atom into a photonic bandgap reservoir in regimes when the atomic transition is tuned in the forbidden gap or at the band edge. The atom decays into a quasi-equilibrium state different from those given by the Boltzmann statistical distribution. We take values of physical parameters typical for Rydberg atoms and currently existing photonic crystals. We show that specific thermally induced transitions can be significant for such Rydberg atoms even at bandgap frequencies provided that there is a peak in the density of modes at the band edge. We point out a temperature sensitivity of microwave quantum optics devices based on photonic band structures due to temperature-dependent transitions and level shifts in regimes when important quantum transitions occur at energies near to band-edge frequencies.
We investigate spontaneous emission from a two-level atom embedded in photonic crystals. Due to the photon localization and the quantum interference between the two dressed states, some changes of the radiation field happen, and the energy is transferred among the excited atom, the localized field, the propagating field and the diffusion field. If there is a localized field, it appears quasi-oscillation behaves of the population evolution in the excited level. If there isn't a localized field, it appears no quasi-oscillation. Moreover, there have some steady-state trapped atom populations in the excited level, and the spontaneous emission spectrum near the forbidden gap edge is different from that in the vacuum. All these characteristics depend not only on the relative position of the excited level from the band-edge but also on the photon density of states (or the band-edge smoothing parameter) near the band edge.
We present a comprehensive quantum electrodynamical analysis of the interaction between a continuum with photonic band gaps (PBGs) or frequency cut-off and an excited two-level atom, which can be either ‘bare’ or ‘dressed’ by coupling to a near-resonant field mode. A diversity of novel features in the atom and field dynamics is shown to arise from the non-Markovian character of radiative decay into such a continuum of modes. Firstly the excited atom is shown to evolve, by spontaneous decay, into a superposition of non-decaying single-photon dressed states, each having an energy in a different PBG, and a decaying component. This superposition is determined by the atomic resonance shift, induced by the spontaneously emitted photon, into or out of a PBG. The main novel feature exhibited by the decaying excited-state component is the occurrence of beats between the shifted atomic resonance frequency and the PBG cut-off frequencies, corresponding to a non-Lorentzian emission spectrum. Secondly the induced decay of a resonantly driven atom into such a continuum exhibits a cascade of transitions down the ladder of dressed states, which are labelled by decreasing photon numbers of the driving mode. Remarkably, this cascade is terminated at the dressed-state doublet, from which all subsequent transitions to lower doublets are forbidden because they fall within the PBG. This doublet then becomes an attractor state for the populations of higher-lying doublets. As a result, the photon-number distribution of the driving mode becomes strongly sub-Poissonian.
Using the response formula of photonic crystals and Bloch equations, we analyzed the coherent emission in a two-level atom embedded in an arbitrary photonic crystal. We derived a formula for the transient emission expressed by the photon density of states (DOS), the Rabi frequency, and the background decay. Near the band edge, when the ratio of the Rabi frequency to the decay rate is a proper value, a transient gain occurs and the sharp structures of the DOS near the band edge lead to a drastic enhancement of the emission and the oscillation of the emission.
The spontaneous emission of a two-level atom, located in an isotropic photonic crystal with dynamically modulated photonic band edge, has been studied. When the photonic band edge is modulated with step functions or triangle functions, the evolution of atomic population on the upper level has been discussed. When the photonic band edge is modulated with step functions, the dynamics of atomic population depends not only on the detuning value of the atomic transition frequency from the band edge, but also on the time point of stepping. With the different time point of stepping, the dynamics of atomic population after stepping is different. When the photonic band edge is modulated with triangle functions, the atomic population oscillates quasi-periodically while decaying in general. The oscillation frequency, peak and valley values, and the decaying rate of oscillation can be modulated by choosing the frequency and initial phase of triangle functions.
A method of laser control of absorption and dispersion of two-level quantum system (atoms, ions, quantum dots) embedded into photonic band gap (PBG) material via variation of intensity and frequency of an external laser field is proposed. It is shown that in order to provide an effective control, the frequency of atomic transition should be located at the photonic band edge near the bottom of the PBG. The method is based on the laser induced Mollow splitting of the atomic energy levels and strong dependence of the decay rates of the so-called dressed states on the frequency of the Mollow splitting due to photonic band edge. This enables us to control absorption and dispersion of a signal laser field, which is near-resonant to the quantum transition of dopant.