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Physical Review A

Coherent control of two-photon transitions in a two-level system with broadband absorption

Shian Zhang, Hui Zhang, Tianqing Jia, Zugeng Wang, Zhenrong Sun

Published Oct 2, 2009• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.80.043402

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ 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.
In this paper, we study theoretically and experimentally the coherent control of non-resonant two-photon transition in a molecular system (Perylene dissolved in chloroform solution) by shaping the femtosecond pulses with simple phase patterns (cosinusoidal and π phase step-function shape). The control efficiency of the two-photon transition probability is correlated with both the laser field and the molecular absorption bandwidth. Our results demonstrate that, the two-photon transition probability in a molecular system can be reduced but not completely eliminated by manipulating the laser field, and the control efficiency is minimal when the molecular absorption bandwidth is larger than twice the laser spectral bandwidth.
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.
A femtosecond laser pulse can be tailored to control the two-photon transitions using the ultra-fast pulse-shaping technique. This paper theoretically and experimentally demonstrates that two-photon transitions in molecular system with broad absorption line can be effectively controlled by square phase-modulation in frequency domain, and the influence of all parameters characterizing the square phase-modulation on two-photon transitions is systemically investigated and discussed. The obtained results have potential application in nonlinear spectroscopy and molecular physics.
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 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.
With femtosecond laser spectral phase shaping technique and polarization modulation technique,the coherent control of two-photon fluorescence(TPF)in Rhodamine B solution is studied.By shaping the femtosecond pulse with simple phase patterns(cosinusoidal andπphase step-function shape),two-photon fluorescence intensity of Rhodamine B can be controlled effectively.Theoretical simulation and calculation show that the variation of twophoton fluorescence intensity for Rhodamine B solution is ascribed to the constructive and destructive interference of various quantum paths in two-photon transitions.TPF of Rhodamine B solution displays periodical change by polarization modulation.TPF decreases when the laser polarization changes from linear through elliptical to circular.These experimental results are theoretically confirmed to be caused by the variation of laser polarization.