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Journal of Foshan University

Effect of the chirped pulse shape on population in the two-level atom system

Xiangyang Yu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

According to the semi-classical theory of lightmatter interaction,by appling an accurate and efficient fourth-order Runge-Kutta method,we solved the modified Bloch equations with chirped terms.The numerical results show that the chirp and pulse area of different pulse shape have different modulation effects.The different shape chirped pulse controlled the reversion population by adjusting chirp and pulse area.

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According to the semi-classical theory of lightmatter interaction,by appling an accurate and efficient fourth-order Runge-Kutta method,we solved the modified Bloch equations with chirped terms.The numerical results show that the chirp and pulse area of different pulse shape have different modulation effects.The different shape chirped pulse controlled the reversion population by adjusting chirp and pulse area.
According to the semi-classical theory of light-matter interaction,the Bloch equations with chirped terms were established in a dense two-level medium,and an accurate and efficient fourth-order Runge-Kutta method was applied for solving the equations.After numerical simulation,the interactions between a chirped ultra-short pulse and dense resonant two-level medium were investigated,and the influences of local-field effects and chirp on Bloch vectors were gained.The numerical results show that,the evolutions of Bloch vectors and the final state of inversion are strongly modulated by the local-field effects correction coefficient and chirp parameter,which provides a method to achieve stable population inversion of control by adjusting the linear chirp parameter and local-field correction coefficient.
The excitation of a two-level system by a chirped laser pulse is analyzed using an analytical approach (in the perturbation-theory limit) that involves the modified rotating-wave approximation and the numerical solution to the Bloch equation. The dependence of the population of the upper energy level on the chirp is studied for various radiation intensities and pulse durations. An exact solution is compared with the result obtained using the modified rotating-wave approximation and the perturbation theory. It is demonstrated that, for a certain range of parameters, the excitation probability of a two-level system can be effectively controlled via a variation in the chirp.
It is shown that, when two femtosecond chirped Gaussian pulses with equal pulse area and same size but opposite sign of the chirp coefficient, which will be simply called as double pulses, overlap and propagate in the three-level Λ-type atomic medium, both coherence between the double pulses and interaction between the double pulses and the atomic medium arise. Adjusting size of the chirp coefficient can change shape, i.e. field distribution, of the composite pulse of the double pulses, at the same time affect the interaction between the composite pulse field and atoms, and thereby control oscillation process and value of the atomic population. By selecting suitable size of the chirp coefficient, we can make the atoms at the lowest level exciting completely to the higher level; moreover the new population distribution is stationary. It is also show that, for the double pulses with any area, efficient and stable population transfer always can be realized by adjusting size of the chirp coefficient. And this conclusion doesn't vary with the pulse width or the medium density varying.
We investigate propagation of femtosecond chirped Gaussian laser pulse in a dense three-level Λ-type atomic medium by using the numerical solution of the full Maxwell-Bloch equations without the slowly varying envelope and the rotating-wave approximations, and the solution is obtained by PC-FDTD method. It is shown that, variation of the sign and size of the chirp coefficient has considerable effect on pulse propagation property, and the effect is closely relative to size of the pulse area. When the area of chirped pulse is smaller than 4π, splitting doesn’t occur and the chirped pulse evolves gradually to an approximate normal Gaussian pulse (C=0), and this characteristic doesn’t vary with the chirp coefficient varying. However, variation of the chirp coefficient will changed the amplitude and group velocity of the pulse. For the positive chirp(C>0), amplitude and group velocity of the pulse decrease with chirp coefficient increasing, for the negative chirp(CC increasing. Both the chirped pulses with area equal to larger than 4π will split into sub-pulses of different numbers and shapes, the time and number of the pulse splitting will be determined by the sign and size of the chirp coefficient. But in the two cases, the pulse splitting patterns are much different, and the effects of the coefficient are also different. When the pulse area equals 4π, larger chirp coefficient will lead to increased sub-pulse number, but when the pulse area is larger than 4π, larger chirp coefficient will lead to decreased sub-pulse number. In addition, regardless of pulse area being larger or smaller, changing sign and size of the chirp coefficient always produces obvious effect on the atomic population.
The temporal evolution of atomic transition in a two-level system under the frequency-chirped pulse field and its dynamic analysis are discussed respectively by means of the density matrix equation and the method of Bloch vector model.The result shows that the population probability oscillates in time domain under the effects of frequency-chirped pulse.The dynamic evolution process of the Bloch vector indicates that the oscillation of the population probability reflects the physical transformation process among the population transfer,dispersion and absorption in the system.