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Acta Physica Sinica

Enhancement and suppression of the spontaneous emission of a two-level atom in a photonic crystal with a state-conservative photonic pseudogap

Xiaodong Liu, Wang Yi-Quan, Xu Xing-Sheng, Bingying Cheng, Daozhong Zhang, (1)中国科学院物理研究所光物理实验室，北京 100080; (2)中国科学院物理研究所光物理实验室，北京 100080;大连民族学院机电信息工程系，大连 116600

Published Jan 1, 2004• 2 citations
Publisher

Abstract

It is shown that there exist a conservation rule of the number of states in a photonic crystal with pseudogaps in the whole frequency regime, and a local conservation rule of the number of states in a photonic crystal with completely photonic band gaps in every band regime. These conservation rules state that, relative to the photonic density of states (DOS) in the effective medium of a photonic crystal, if a valley of the DOS in the photonic crystal appears in some range of frequencies, it must be compensated for by the increases over some other ranges. In this paper, using a model DOS with a state-conservative photonic pseudogap, we obtain naturally the enhancement and suppression of spontaneous emission of a two-level atom in a photonic crystal, and a DOS-induced suppression, enhancement, narrowing and redshift or blueshift of spontaneous emission spectra. Our theory will be especially appropriate in the problem of the spontaneous emission of a collection of dependently emitting atoms or molecules with essentially random dipole orientations in a photonic crystal with a photonic pseudogap.

DOI
10.7498/aps.53.125

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It is shown that there exist a conservation rule of the number of states in a photonic crystal with pseudogaps in the whole frequency regime, and a local conservation rule of the number of states in a photonic crystal with completely photonic band gaps in every band regime. These conservation rules state that, relative to the photonic density of states (DOS) in the effective medium of a photonic crystal, if a valley of the DOS in the photonic crystal appears in some range of frequencies, it must be compensated for by the increases over some other ranges. In this paper, using a model DOS with a state-conservative photonic pseudogap, we obtain naturally the enhancement and suppression of spontaneous emission of a two-level atom in a photonic crystal, and a DOS-induced suppression, enhancement, narrowing and redshift or blueshift of spontaneous emission spectra. Our theory will be especially appropriate in the problem of the spontaneous emission of a collection of dependently emitting atoms or molecules with essentially random dipole orientations in a photonic crystal with a photonic pseudogap.
We have investigated the analytical forms of the photonic density of states (DOS) in a photonic crystal in the interested frequency regime according to the rule of state conservation in a photonic crystal with pseudogaps, which states that, if a valley of the DOS appears in some range of frequencies, it must be compensated for by increasing over some other ranges. By using a model DOS with a state-conservative photonic pseudogap, we have also investigated the enhancement and suppression of spontaneous emission of two-level atoms with different frequency positions and widths of emission spectra in a state-conservative electromagnetic reservoir; and the DOS-induced suppression, enhancement, narrowing and redshifting or blueshifting of spontaneous emission spectra are naturally obtained.
We show that the total number of states in a photonic crystal in the entire allowed frequency regime will be conserved, and it is equal to that of its corresponding effective medium, i.e., if the density of states (DOS) has a valley(s) in some range(s) of frequencies, it must be compensated for by increases over some other range(s). This rule is of importance in developing a model pseudogap in order to describe the mean emission characteristics of the system when there is a collection of dependently emitting atoms or molecules with essentially random dipole orientations in a large volume and the spectrum of the active atoms is wide enough. This is because, with this rule, the states-conservative model always results in DOS-induced suppression, absolute enhancement, narrowing, spectrum splits, and redshift or blueshift of spontaneous-emission spectra.
The spontaneous emission from a microwave-driven four-level atom embedded in an anisotropic photonic crystal is studied. Due to the modified density of state (DOS) in the anisotropic photonic band gap (PBG) and the coherent control induced by the coupling fields, spontaneous emission can be significantly enhanced when the position of the spontaneous emission peak gets close to the band gap edge. As a result of the closed-loop interaction between the fields and the atom, the spontaneous emission depends on the dynamically induced Autler–Townes splitting and its position relative to the PBG. Interesting phenomena, such as spectral-line suppression, enhancement and narrowing, and fluorescence quenching, appear in the spontaneous emission spectra, which are modulated by amplitudes and phases of the coherently driven fields and the effect of PBG. This theoretical study can provide us with more efficient methods to manipulate the atomic spontaneous emission.
The spontaneous emission spectrum of a two-level atom in a one-dimensional (1D) anisotropic photonic crystal with symmetry of double helix is investigated using Laplace transform. Properties of spectrum of the radiation modes are discussed in detail under different values of detuning of atomic resonant frequency from a band-edge. Since spontaneous emission is proportional to the density of states (DOS), it is suppressed within the reflection band, corresponding to vanishing of the DOS. However, it is enhanced at the band edge. Therefore, spontaneous emission spectrum of the system is influenced at the edge of the stop band rather than at its centre.
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 consider the spontaneous emission of a two-level quantum emitter, such as an atom or a quantum dot, in a modulated time-dependent environment with a photonic band gap. An example of such an environment is a dynamical photonic crystal or any other environment with a band gap whose properties are modulated in time, in the effective mass approximation. After introducing our model of a dynamical photonic crystal, we show that it allows new possibilities to control and tailor the physical features of the emitted radiation, specifically its frequency spectrum. In the weak-coupling limit and in an adiabatic case, we obtain the emitted spectrum and we show the appearance of two lateral peaks due to the presence of the modulated environment, separated from the central peak by the modulation frequency. We show that the two side peaks are not symmetric in height, and that their height ratio can be exploited to investigate the density of states of the environment. Our results show that a dynamical environment can give further possibilities to modify the spontaneous emission features, such as its spectrum and emission rate, with respect to a static one. Observability of the phenomena we obtain is discussed, as well as relevance for tailoring and engineering radiative processes.