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Chinese Physics B

Effect of atomic initial phase difference on spontaneous emission of an atom embedded in photonic crystal

Bing Zhang, Sun Xiu-Dong, Jiang Xiang-Qian

Published Aug 1, 2010• 1 citation
Publisher

Abstract

We investigate the effect of initial phase difference between the two excited states of a V-type three-level atom on its steady state behaviour of spontaneous emission. A modified density of modes is introduced to calculate the spontaneous emission spectra in photonic crystal. Spectra in free space are also shown to compare with that in photonic crystal with different relative positions of the excited levels from upper band-edge frequency. It is found that the initial phase difference plays an important role in the quantum interference property between the two decay channels. For a zero initial phase, destructive property is presented in the spectra. With the increase of initial phase difference, quantum interference between the two decay channels from upper levels to ground level turns to be constructive. Furthermore, we give an interpretation for the property of these spectra.

DOI
10.1088/1674-1056/19/8/083201

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We investigate the effect of initial phase difference between the two excited states of a V-type three-level atom on its steady state behaviour of spontaneous emission. A modified density of modes is introduced to calculate the spontaneous emission spectra in photonic crystal. Spectra in free space are also shown to compare with that in photonic crystal with different relative positions of the excited levels from upper band-edge frequency. It is found that the initial phase difference plays an important role in the quantum interference property between the two decay channels. For a zero initial phase, destructive property is presented in the spectra. With the increase of initial phase difference, quantum interference between the two decay channels from upper levels to ground level turns to be constructive. Furthermore, we give an interpretation for the property of these spectra.
The spontaneous emission from a V-type three-level atom embedded in an isotropic photonic crystal with dynamic photonic band edge is studied. We consider the situation where the atom interacts with all possible radiation modes, and calculate numerically the evolution of atomic population without using Markov approximation. The calculation method can be used in related researches. In the present paper, we mainly discuss the effects of modulation parameters and the quantum interference on spontaneous emission when the band edge is modulated with step function or triangle function. We hope that the results can contribute to the applications in the dynamic photonic crystal environment in controlling the spontaneous emission via the quantum interference. The results show that in the step-modulated situation, the number of the photon-atom bound dressed states after the modulation has happened depends on atomic transition frequencies and the band edge frequency at that time, and is identical to the one in the unmodulated situation with the same parameters. The long-time evolution of the atomic population is affected by the time when the modulation happens. Depending on the system initial state, after the modulation has happened, the quantum interference can weaken the probability amplitude components corresponding to the photon-atom bound dressed states, and cause the upper-level population to decay quickly from a great value to a value near zero; or on the contrary, it can strengthen the bound dressed states, and make the upper levels retain a high population. In the modulated situation with trigonometric functions, after long enough time, the total upper-level population presents a decaying quasi-periodic oscillation behaviour. And the evolution of the total upper-level population tends to synchronize with the modulation, so the frequency of the quasi-periodic oscillation is approximately equal to the modulation frequency. But, the quantum interference can destroy the synchronization under some conditions. The decay rate of the total upper-level population is affected by the modulation frequency, and also by the initial state of the system and the angle between two dipole moment because of the quantum interference.
Spontaneous emission from two two-level atoms within an anisotropic photonic crystal is investigated when direct dipole-dipole interaction is taken into account. The radiation properties of the present two atoms system are similar to that of a V-type three-level atom embedded in an anisotropic photonic crystal. The direct dipole-dipole interaction can enhance or depress the spontaneous emission depending on the relative position of the upper levels from the band edge of the photonic crystals. Owing to quantum interference and the dipole-dipole interaction, the spontaneous emission spectra are complicated non-Lorentzian shapes and depend strongly on the relative position of the upper levels from the bandgap and the initial state of the system.
Spontaneous emission from a V-type three-level atom in a photonic crystal is investigated. Quantum interference between the two atomic transitions affects the constructor of dressed states, and leads to an interesting behavior of the populations in the two upper levels: antitrapping, periodic oscillation, and no population inversion. Those properties depend strongly on the relative position of the upper levels from the forbidden gap and the initial state of the atom, and differ from that of a two-level atom in a photonic crystal. The emitted field, which is composed of localized mode(s) and propagating mode(s), is also studied. Quantum interference can enhance or reduce the energy of the localized field.
The two models of three-level (one upper level and two lower levels, or two upper levels and one lower level) atom embedded in a double-band photonic crystal are adopted. The atomic transitions from the upper levels to the lower levels are assumed to be coupled by the same reservoir which are respectively the isotropic photonic band gap (PBG) modes, the anisotropic PBG modes and the free vacuum modes. The effects of the fine structure of the atomic ground state levels in the model with one upper level and two lower levels and the quantum interferences in the model with two upper levels and one lower level on the spontaneous emission spectrum of an atom are investigated in detail. Most interestingly, it is shown that new spontaneous emission lines are produced from the fine splitting of atomic ground state levels in the isotropic PBG case. The quantum interferences induce additional narrow spontaneous lines near the transition from the empty upper level to the lower level.
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.