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Acta Physica Sinica

Control of evolutionary atomic system of excited atom by using ideal photonic band-gap model

Siqi Zhang, Lu Jing-Bin, Xiaojing Liu, Jiping Liu, Li Hong, Liang Yu, Xiaoru Zhang, Han Liu, Wu Xiang-Yao, Guo Yi-Qing

Published Jan 1, 2018• 0 citations
Publisher

Abstract

The evolution of two-level atomic system, in which the initial state is excited state, is investigated by adjusting the structural parameters of the dynamic and static ideal photonic band-gap environment reservoir. In a static state (no modulation), we study the effects of half width, center resonant frequency, and specific gravity on the evolution of energy level population. The results show that when the half width or the specific gravity decreases, in the atomic system there happens decoherence, and the energy dissipation to the outside becomes slower. When the center resonant frequency increases, there exists no resonance between the library central resonant frequency and the atom transition frequency, then the attenuation suppression effect occurs, and the time of atomic attenuation to ground state is longer. An actual quantum system is not isolated, so it is inevitable that it interacts with its ambient environment. Owing to the influence of environment, in the system there appears an irreversible quantum decoherence phenomenon. Therefore, how to effectively suppress the decoherence of quantum system becomes an important problem in quantum information science. Linington and Garraway (2008 Phys. Rev. A 77 033831) pointed out that the evolution process of a two-level atom quantum state can be manipulated by a dynamic dissipative environment. So, we use the dynamic cavity environment to control the evolution of spontaneous emission from an excited two-level atom. The dynamic modulation form for the center resonant frequency of the ideal photonic band-gap environment reservoir includes the rectangular single pulse, rectangular periodic pulse, and slow continuous period. Owing to the periodic modulation, the atoms are affected by different environments. On this basis, the influence of dynamic modulation form on the atomic population evolution is discussed. It is found that no matter what form the dynamic modulation is in, the attenuation inhibition in the evolution of atomic system is evident. These conclusions make the idea of using the environmental change to modulate the coherent evolution of atomic system become true.

DOI
10.7498/aps.67.20172050

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The evolution of two-level atomic system, in which the initial state is excited state, is investigated by adjusting the structural parameters of the dynamic and static ideal photonic band-gap environment reservoir. In a static state (no modulation), we study the effects of half width, center resonant frequency, and specific gravity on the evolution of energy level population. The results show that when the half width or the specific gravity decreases, in the atomic system there happens decoherence, and the energy dissipation to the outside becomes slower. When the center resonant frequency increases, there exists no resonance between the library central resonant frequency and the atom transition frequency, then the attenuation suppression effect occurs, and the time of atomic attenuation to ground state is longer. An actual quantum system is not isolated, so it is inevitable that it interacts with its ambient environment. Owing to the influence of environment, in the system there appears an irreversible quantum decoherence phenomenon. Therefore, how to effectively suppress the decoherence of quantum system becomes an important problem in quantum information science. Linington and Garraway (2008 Phys. Rev. A 77 033831) pointed out that the evolution process of a two-level atom quantum state can be manipulated by a dynamic dissipative environment. So, we use the dynamic cavity environment to control the evolution of spontaneous emission from an excited two-level atom. The dynamic modulation form for the center resonant frequency of the ideal photonic band-gap environment reservoir includes the rectangular single pulse, rectangular periodic pulse, and slow continuous period. Owing to the periodic modulation, the atoms are affected by different environments. On this basis, the influence of dynamic modulation form on the atomic population evolution is discussed. It is found that no matter what form the dynamic modulation is in, the attenuation inhibition in the evolution of atomic system is evident. These conclusions make the idea of using the environmental change to modulate the coherent evolution of atomic system become true.
In the paper, we theoretically discuss the use of dynamic cavity environment to realize controlling of the evolution of spontaneous emission from an excited two-level atom. It is found that cyclical changes in cavity environment leads to the interaction betwcen the electromagnetic modes, resulting in the redistribution of the electromagnetic modes density; both the frequency of energy exchange and the energy dissipation rate between atom and environment are affected. When the frequency of environment change is relatively accordant with the process of energy exchange between the atom and environment, the decay rate is obviously inhibited and a stable coherence evolution can be obtained. Thus the evolution of coherent states can be modulated by using dynamic environment changes.
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.
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.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band-gap structure with one resonant frequency near the edge of the photonic band gap. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This nonzero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field-atom interaction exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive, optical memory device on the atomic scale. The protected electric dipole within the photonic band gap provides a basis for a qubit to encode information for quantum computations.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band gap (PBG) material, with one resonant frequency near the edge of the PBG. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive optical memory device on the atomic scale. The protected electric dipole within the PBG provides a basis for a qubit to encode information for quantum computations. A detailed literature survey on the nature, fabrication and applications of PBG materials is presented to provide context for this research.
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.