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Acta Physica Sinica

Propagation property of ultra-short laser pulses in multi-level quantum system

Lu Jian-Qing, Xiangyun Zhang, Zhang Shi-An, Jia Tian-Qing, Zhenrong Sun, Zugeng Wang, (1)华东师范大学数学系，应用数学和交叉学科研究中心，上海 200062; (2)华东师范大学物理系，精密光谱科学与技术国家重点实验室，上海 200062

Published Jan 1, 2009• 1 citation
Publisher

Abstract

The propagation property of an ultrashort pulse in multi-level quantum system has been investigated with numerical method. A strong absorption is observed and its degree depends on the characteristic time of quantum system. For rather weak laser field, the self-induced transparency can still be observed with proper pulse area of the input ultrashort laser. When the ultrashort laser pulse becomes stronger, it will be split, and its basic split unit （i.e. the minimum area of a stably propagating laser pulse） A0 is not the same as that of two-level quantum system, which depends on the number of the excited states and their dipoles. Furthermore, after a rather long propagating distance, there only remains a shorter but more intense sub-pulse with an area of A0.

DOI
10.7498/aps.58.8212

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Journal of Physics B Atomic and Molecular Physics•Feb 21, 1975•10 citations
The propagation property of an ultrashort pulse in multi-level quantum system has been investigated with numerical method. A strong absorption is observed and its degree depends on the characteristic time of quantum system. For rather weak laser field, the self-induced transparency can still be observed with proper pulse area of the input ultrashort laser. When the ultrashort laser pulse becomes stronger, it will be split, and its basic split unit （i.e. the minimum area of a stably propagating laser pulse） A0 is not the same as that of two-level quantum system, which depends on the number of the excited states and their dipoles. Furthermore, after a rather long propagating distance, there only remains a shorter but more intense sub-pulse with an area of A0.
Here, I discuss the propagation of an ultrashort pulse through a collection of harmonic multilevel systems. In the limit of weak excitation and a large number of excited states, I show that the amplitude of the input driving pulse decays exponentially with propagation distance. The absorption coefficient associated with this decay is determined by the characteristic time of the manifold of excited states, instead of the polarization decay time as in the conventional absorption coefficient of a two-level atom. The input ultrashort pulse creates in the excited states a wave packet, which oscillates emitting secondary pulses in the process. Analytic solutions are obtained that describe the propagation of individual wave-packet re-emission pulses, and it is shown that their phase depends on the detuning of the input pulse.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
In this paper, I numerically investigate the propagation of ultrashort pulses through an extended collection of multilevel systems under the condition of electromagnetically induced transparency. The transparency of a weak probe pulse is induced by a much stronger coupling pulse. In the limit of a weak probe excitation and a large number of excited states, I show that the free-induction decay signal that would naturally follow the excitation pulse is strongly suppressed, and the envelope of the probe pulse suffers a distortion in its temporal profile as the pulse propagates into the medium. This distortion is characterized by a stronger absorption of the leading edge of the pulse than that of its trailing edge. The temporal phase of the pulse, however, remains constant throughout propagation.
The effect of pulse width on propagation characteristics of the femtosecond ultrashort laser pulse in V-type three-level atomic media with different densities is investigated by using the numerical solution,which is obtained by PC-FDTD method for the full Maxwell-Bloch equation.It is shown that the effect of the pulse width on propagation characteristics of the pulse is different for different atomic density cases.When the ultrashort pulse propagates in the dilute medium with smaller atomic density,the pulse is not easy to split.When the pulse doesn't split,the pulse amplitude will decrease obviously with the pulse width increasing.When the ultrashort pulse propagates in the medium with very large atomic density,the pulse is easy to split,and the number of sub-pulses increases with the pulse width increasing Moreover the increase of the pulse width accelerates the pulse splitting.
Femtosecond-pulse propagation in resonantly excited semiconductors is investigated by numerically solving the semiconductor Maxwell-Bloch equations for plane waves. For excitation at the exciton resonance, it is shown that the pulse absorption exhibits a strongly nonlinear dependence on the input pulse area. Very long propagation distances for strong pulses are observed, but even when all dephasing processes have been neglected, no lossless propagation (self-induced transparency) was found. The influence of the electron-hole many-body effects, nonequilibrium carrier relaxation, and optical dephasing on the pulse-propagation dynamics is studied. The exchange interaction in the electron-hole plasma is shown to support large propagation distances. For excitation of the continuum states, the dependence of the absorption on the intensity of the input pulse is reduced due to the rapid carrier relaxation into quasiequilibrium distributions.
For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.