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Physical Review A

Effect of counter-rotating terms on the spontaneous emission in an anisotropic photonic crystal

Shuai Yang, M. Al-Amri, Shi‐Yao Zhu, Muhammad Suhail Zubairy

Published Mar 15, 2013• 10 citations
Publisher

Abstract

The spontaneous emission of a two-level atom in a anisotropic photonic crystal is investigated without making use of the rotating wave approximation (RWA). Similar to the RWA case, there exist two characteristic atomic transition frequencies which separate the radiation field from the localized and propagated fields. Unlike the RWA calculation, these two characteristic frequencies are shifted due to a full calculation of the energy shifts.

DOI
10.1103/physreva.87.033818

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The spontaneous emission of a two-level atom in a anisotropic photonic crystal is investigated without making use of the rotating wave approximation (RWA). Similar to the RWA case, there exist two characteristic atomic transition frequencies which separate the radiation field from the localized and propagated fields. Unlike the RWA calculation, these two characteristic frequencies are shifted due to a full calculation of the energy shifts.
We investigate the spontaneous radiation from a two-level atom embedded in a three-dimensional anisotropic photonic crystal with two bands. The properties of the spontaneous emission are dependent strongly on the position of the upper level. The faster and slower decay components can occur in the emitted field, but it does not mean the existence of both accelerated and inhibited components for the atomic population decay. The radiation spectrum is dependent on the location of the observer. We also study the influence of the existence of the two bands on spontaneous emission, Lamb shift, the emitted field, and the radiation spectrum.
The spontaneous emission field and spectrum of a two-level atom, located in an isotropic photonic crystal with dynamic band edges, are investigated by means of numeric calculation. The investigation is expected to help comprehend the characteristics of the atomic spontaneous emission in the dynamic photonic crystal, and provide a possible way to control dynamically the spontaneous emission in photonic crystal. The expression of the spontaneous radiation field is obtained without using the far-zone approximation and the Weisskopf-Wigner approximation, and expected to be applicable in other relevant researches. In the investigation, the spontaneous radiation field and spectrum are calculated when the band edge frequency is unmodulated, or modulated by a step function or triangle function. In the unmodulated situation, the radiation field intensity tends to a constant which is equal to the intensity of the localized field component. The radiation field pulse presents a wave packet behavior as propagation distance increases. The components of the radiation field correspond one-to-one to the peaks in the spontaneous radiation spectrum. When the band edge frequency is modulated by step function, the radiation field intensity tends to a steady-state value after the modulation has happened. And the steady-state intensity is affected by the time when the modulation happens. The components of the non-localized field and the frequency of the localized field after modulation depend on the atomic transition frequency and the band edge frequency, and are identical to those in the unmodulated situation with the same parameters. When the band edge frequency is modulated by a triangle function, the field intensity presents a decaying quasi-periodic oscillation after a long enough time. The modulation frequency determines the frequency of the oscillation, and influences the decay rate. The radiation energy becomes sharp peaks around a set of the discrete frequencies which are evenly spaced with the modulation frequency. The central frequency of these frequencies depends on the atomic transition frequency and the value range of the band edge frequency. The modulation initial phase affects the intensity of the radiation field emitted in an initial period of time.
The spontaneous emission properties of a Λ_type atom embedded in anisotropic photonic crystals are investigated. We find that the dynamical properties of the atom and the propagating characteristics of the radiation field are obviously influenced by the relative position of the upper level from the forbidden gap and the space between the two lower levels. With the help of numerical calculation and theoretical analysis, we plot the evolution of the total radiation field and its components with the time. Furthermore, we also study the influence of photonic crystals on radiative properties of the atom by means of spontaneous emission spectrum.
Spontaneous emission in photonic crystals with anisotropic three-dimensional dispersion relation is studied. If the upper level is below a characteristic frequency omega(1), or above omega(2), or between omega(1) and omega(2), the radiation is a localized field with a frequency in the band gap, or a propagating field with a frquency in the band, or a diffusion field, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is small compared to that in an ordinary vacuum or in one- or two-dimensional photonic crystals due to lower density of states.
We investigate the spontaneous-emission properties of a two-level atom embedded in a three-dimensional anisotropic photonic crystal. In addition to the modified density of states, the atom is driven by a coherent intense low-frequency field (LFF), which creates additional multiphoton decay channels with the exchange of two low-frequency photons and one spontaneous photon during an atomic transition. Due to the low frequency of the applied field, the various transition pathways may interfere with each other and thus give rise to a modified system dynamics. We find that even if all the atomic (bare and induced) transition frequencies are in the conducting band of the photonic crystal, there still may exist a photon–atom bound state in coexistence with propagating modes. The system also allows us to generate narrow lines in the spontaneous-emission spectrum. This spectrum is a function of the distance of the observer from the atom due to the band gap in the photonic crystal. The system properties depend on three characteristic frequencies, which are influenced by quantum interference effects. Thus these results can be attributed to a combination of interference and band-gap effects.
We theoretically investigate the spontaneous emission light of an excited three-level atom embedded in an anisotropic photonic crystal with two asymmetric bands. The property of spontaneous emission relating to the atomic position in a unit cell of the crystal is described with a position-dependent phase difference. The atomic transition in free space can be manipulated by the other associated transition coupling to photonic crystal. The result shows that the spontaneous emission spectra are effectively shifted and tuned by the atomic position-dependent phase, which results in the asymmetric distribution of the photonic density of states between two bands, and the increasing band can push the emitted light towards the other band. The physical process can be further illuminated through analyzing the emitted field in photonic crystal. The result perhaps offers an interesting route towards tunable photonic devices.