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Acta Physica Sinica

Spontaneous emission from a V-type three-level atom in a dynamic photonic crystal

Xing Rong, Xie Shuang-Yuan, Xu Jing-Ping, Yang Ya-Ping

Published Jan 1, 2017• 2 citations
Publisher

Abstract

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.

DOI
10.7498/aps.66.014202

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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.
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 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.
Studying the spontaneous emission of a V-type three-level atom embedded in a photonic crystal (PC) by fractional calculus, we found that the atomic excited states in the anisotropic PC can be expressed as a superposition of four dressed states analytically. Through detuning two allowed atomic transition energies with respect to the photonic band edge, the coupling between these two transitions leads to three dynamic regimes, namely non-Markovian decay, damped quantum interference and quantum interference, classified by the numbers of contributed bounded dressed states. From the degree of quantum interference of two atomic transitions, we found the energy exchange between the atom and PC reservoir is the lowest as the excited states become degenerate but with maximum quantum interference when the atom is prepared at one of the excited states. The results also show that excited states prefer to stay out of phase at all detuning energy except for near degenerate. Therefore, we can control the spontaneous emission rate not only by the amount of detuning frequencies but also the relative phase of initial states.
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.
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.
Spontaneous emission from a two-level atom embedded in photonic crystals was investigated in this paper. Due to the photon localization and the quantum interference between the two dressed states, some changes in the radiation field take place: when the excited level moves from the gap to the band, the energy of the localized field is transferred to the propagating field through the diffusion field. If the localized field and the propagating field could coexist, the population evolution in the excited level would exhibit quasi-oscillation behavior. If they could not coexist, there would be no quasi-oscillation. The steady-state trapped atom population in the excited level is changed also. All these characteristics depend not only on the relative position δ of the excited level ω _1 with respect to the band-edge ω _c but also on the photon density of states ρ(ω_k) (or the band-edge smoothing parameter e ) near the band edge.