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Physical Review Letters

Realization of a Time-Domain Fresnel Lens with Coherent Control

J. Degert, Wendel Wohlleben, B. Chatel, Marcus Motzkus, B. Girard

Published Oct 29, 2002• 58 citations
Publisher

Abstract

Perturbative chirped pulse excitation leads to oscillations of the excited state amplitude. These coherent transients are governed by interferences between resonant and off-resonant contributions. Control mechanisms in both frequency and time domain are used to modify these dynamics. First, by applying a phase step in the spectrum, we manipulate the phase of the oscillations. By direct analogy with Fresnel zone lenses, we then conceive highly phase-amplitude modulated pulse shapes that slice destructive interferences out of the excitation time structure and enhance the final population.

DOI
10.1103/physrevlett.89.203003

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Perturbative chirped pulse excitation leads to oscillations of the excited state amplitude. These coherent transients are governed by interferences between resonant and off-resonant contributions. Control mechanisms in both frequency and time domain are used to modify these dynamics. First, by applying a phase step in the spectrum, we manipulate the phase of the oscillations. By direct analogy with Fresnel zone lenses, we then conceive highly phase-amplitude modulated pulse shapes that slice destructive interferences out of the excitation time structure and enhance the final population.
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Chirped biphotons generated via spontaneous parametric down-conversion in chirped quasi-phase-matched nonlinear crystals have ultrabroadband frequency spectra, while their correlation times are not ultranarrow, due to the nonlinear frequency dependence of the phase factor. Based on the idea of Fresnel zone lenses, we propose a Fresnel-inspired binary phase-shaping scheme for tailoring broadband biphoton spectra. By applying binary phase masks to the biphoton spectrum, a Fresnel zone lens was produced in the frequency domain, compressing the broadband temporal wave packets of the chirped biphotons to the Fourier-transform limit due to the effective removal of the quadratic phase. Furthermore, biphoton correlation trains can also be generated by properly shaping the biphoton spectrum with this scheme. This provides a method for biphoton compression and shaping, which avoids the length dependence and the impact of higher-order dispersion in a dispersive medium by using the phase compensation method. Our results could prove useful in quantum metrology, lithography, and coding of entangled photons.
The effects of coherent excitation of a two-level system with a linearly chirped pulse are studied theoretically and experimentally [in Rb (5s-5p)] in the low field regime. The coherent transients are measured directly on the excited state population on an ultrashort time scale. A sharp step corresponds to the passage through resonance. It is followed by oscillations resulting from interferences between off-resonant and resonant contributions. We finally show the equivalence between this experiment and Fresnel diffraction by a sharp edge.
The second harmonic generation (SHG) process is investigated theoretically using the quantum mechanics method of coherent control. Based on the extremum conditions for the SHG intensity at the center frequency, a Fresnel-inspired binary phase shaping scheme is proposed for tailoring the fundamental pulse. The SHG spectrum can be compressed into a narrowband signal with lower background by modulating the relative phases between the frequency components within the fundamental pulse, inducing constructive interference at the center frequency and destructive interference elsewhere. Multipeak second harmonic signals can also be obtained by properly modulating various interference pathways. These results have potential applications in high resolution nonlinear spectroscopy, microscopy, and information coding.
Mechanisms and optimal experimental conditions in coherent control still intensely stimulate debates. In this work, a phase-only control mechanism in an open quantum system is investigated experimentally and numerically. Several parameterizations for femtosecond pulse shaping (combination of chirp and multipulses) are exploited in transient absorption of a prototype organic molecule to control population and vibrational coherence in ground and excited states. Experimental results are further numerically simulated and corroborated with a four-level density-matrix model, which reveals a phase-only control mechanism based on the interaction between the tailored phase of the excitation pulse and the induced transient absorption. In spite of performing experiment and numerical simulations in the linear regime of excitation, the control effect amplitude depends non-linearly on the excitation energy and is explained as a pump-dump control mechanism. No evidence of single-photon control is observed with the model. Moreover, our results also show that the control effect on the population and vibrational coherence is highly dependent on the spectral detuning of the excitation spectrum. Contrary to the popular belief in coherent control experiments, spectrally resonant tailored excitation will lead to the control of the excited state only for very specific conditions.