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Journal of Shaanxi Normal University

Coherent control and quantum shaping with the laser pulse

Li Yongfang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The interaction between the laser pulse with a small-area and a three-level atomic system is investigated.The formation and characterization of the shaped laser pulse are analyzed and the two-photon transition is studied with the shaped laser pulse.The influence of the relaxation of the excited state and the length of the shaping medium on the two-photon absorption is discussed.Based on the dispersion theory the oscillation of the transient twophoton transition is explained.The result indicates that the transition probability of two-photon absorption evolves regularly with the several values of parameters such as the length of medium(l),relaxation time(t2) and bandwidth(Δω).Meanwhile the transition probability appears in the transient oscillation.

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The interaction between the laser pulse with a small-area and a three-level atomic system is investigated.The formation and characterization of the shaped laser pulse are analyzed and the two-photon transition is studied with the shaped laser pulse.The influence of the relaxation of the excited state and the length of the shaping medium on the two-photon absorption is discussed.Based on the dispersion theory the oscillation of the transient twophoton transition is explained.The result indicates that the transition probability of two-photon absorption evolves regularly with the several values of parameters such as the length of medium(l),relaxation time(t2) and bandwidth(Δω).Meanwhile the transition probability appears in the transient oscillation.
Multiphoton transition probability can be manipulated by tailoring the ultrashort laser pulses. In this paper, we theoretically and experimentally investigate the influence of the absorption bandwidth and line shape on the coherent control of two-photon transitions in two-level system by manipulating the femtosecond laser pulse with the $\ensuremath{\pi}$ spectral phase step. A coherent feature with a coherent peak and two coherent dips can be achieved if the absorption bandwidth is less than twice of the laser spectral bandwidth. The absorption bandwidth decides the coherent peak or dip intensity, and the absorption line shape affects the symmetry of the two coherent dips.
Based on the second-order perturbation theory,the two-photon processes in the atom system excited by a shaped chirped-pulse are analyzed.The evolution of the two-photon transition probability is studied under the two cases of non-resonance and resonance.It′s shown that the transition probabilities disappeared at some corresponding frequencies under the non-resonance case,and thus the laser pulse can get through the medium without loss. Meanwhile,the maximum two-photon transition probability is obtained by choosing the best shaping function under the resonance case.
Multiphoton transitions can be reached by many routes through a continuum of virtual levels. We show that the transition probability of two-photon and multiphoton processes can be controlled by tailoring the shape of an ultrashort excitation pulse, so that the many paths leading to the final state interfere to give a desired probability amplitude. We analyze the effect of pulse shapes on N-photon absorption as well as on Raman transitions. We show theoretically that certain tailored dark pulses do not excite the system at all, while other shaped pulses induce transitions as effectively as transform limited pulses, even when their peak amplitudes are greatly reduced. These results are confirmed experimentally for two-photon transitions in atomic cesium.
We show theoretically and experimentally that two-photon coherent control in a VVV-shape three-level system projects a one-photon coherent transient in a simple two-level system. The second- and third-order spectral phase terms of a shaped laser pulse play the roles of time and quadratic spectral phase, respectively, in conventional coherent transients. In a three-pulse coherent control experiment of atomic rubidium, the phase and amplitude of controlled transition probability is retrieved from a two-dimensional Fourier-transform spectral peak. It is hoped that this control scheme may harness coherent control capability on multidimensional Fourier-transform spectroscopy.
The spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level \ensuremath{\Lambda}-type optical medium under coherent population trapping. The general case of unequal oscillator strengths of the transitions is considered. The durations of the probe pulse and the coupling pulse T1,2(T2>T1){T}_{1,2} {(T}_{2}>{T}_{1})T1,2​(T2​>T1​) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schr\"odinger equations and reduced wave equations in the adiabatic limit taking account of the first nonadiabatic correction. The adiabaticity criterion is also discussed taking account of pulse propagation. The dynamics of propagation is found to be strongly dependent on the ratio of the transition oscillator strengths. It is shown that the envelopes of the pulses slightly change throughout the medium length in the initial stage of propagation. This distance can be large compared to the one-photon resonant absorption length. Eventually, the probe pulse is completely reemitted into the coupling pulse during propagation. An effect of localization of the atomic coherence was observed similar to the one predicted by Fleischhauer and Lukin [Phys. Rev. Lett. 84, 5094 (2000)].
Behavioral features of polariton dispersion laws are studied for three-level atoms interacting with two coherent laser radiation pulses with frequencies ω1 and ω2 that are in resonance with optically resolved one-photon transitions between levels 1⇆21 \leftrightarrows 21⇆2 and 2⇆32 \leftrightarrows 32⇆3 , respectively, and with regard to the direct two-photon transition between levels 1 and 3. The approximation of given photon densities of both pulses compared with the densities of atoms is used. It is shown that the dispersion law consists of three branches whose position and shape are determined by the Rabi frequencies of the above three optical transitions and the photon densities in both pulses. The direct consideration of all three optical transitions leads to the dependence of the dispersion law of atomic polaritons on a new quantum parameter—the phase difference between the three Rabi frequencies. The values of the system parameters are found for which the branches of the dispersion law may intersect. The concept of the surface of the dispersion law is introduced in the dependence of the eigenfrequencies of atomic polaritons on the photon wave vectors in both pulses.