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.%研究了动态各向同性光子晶体中Ⅴ型三能级原子的自发辐射,主要讨论了光子晶体能带带边频率受到阶跃调制和三角函数周期调制两种情况下,调制参数对占据数演化的控制作用,以及此过程中量子相干效应带来的影响.结果表明,阶跃调制时,调制发生后原子上能级劈裂出来的束缚缀饰态数目只取决于原子的跃迁频率和此时的带边频率,且与具有相同参数条件的静态情形下的相同.调制发生时刻对其后原子上能级占据数的长时演化情况有影响.随系统初态的不同,量子相干效应既可导致调制之后占据数迅速衰减,也可使原子上能级保留较多的占据数.三角函数周期调制时,原子上能级总占据数在足够长的时间之后随时间做频率近似等于调制频率的有衰减的准周期振荡.衰减率与调制频率有关,也因量子相干效应而受系统初态以及偶极矩夹角的影响.
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