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arXiv:1603.01219 · Physical Review A

Experimental observation of fractional echoes

Γαβριήλ Καρράς, E. Hertz, Franck Billard, B. Lavorel, Guillaume Siour, Jean‐Michel Hartmann, O. Faucher, Erez Gershnabel, Yehiam Prior, Ilya Sh. Averbukh

Published Sep 6, 2016• 33 citations
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Abstract

We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes, which appear periodically at delays which are integer multiples of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of ${\mathrm{CO}}_{2}$ molecules excited by a pair of femtosecond laser pulses.

DOI
10.1103/physreva.94.033404

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We report the observation of fractional echoes in a double-pulse excited nonlinear system. Unlike standard echoes, which appear periodically at delays which are integer multiples of the delay between the two exciting pulses, the fractional echoes appear at rational fractions of this delay. We discuss the mechanism leading to this phenomenon, and provide experimental demonstration of fractional echoes by measuring third harmonic generation in a thermal gas of CO2{\mathrm{CO}}_{2}CO2​ molecules excited by a pair of femtosecond laser pulses.
The effect of temporal coherent control on the two-photon resonant third-harmonic generation in the continuum of ionization of an atomic system is experimentally investigated by means of a pair of partially incoherent, identical laser pulses. The evidence of quantum interference in the third-harmonic generation, as a function of delay between pulses, is reported. The transition from a resonant to a nonresonant case is also shown. The results agree with the predictions of a recently published theoretical model showing that the onset of quantum interference appears to be related to the coherence time of the laser radiation that is much shorter than the pulse duration.
Photon echoes, observed recently in ruby and in NH2{\mathrm{NH}}_{2}NH2​D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.
The effect of temporal coherent control on the two-photon-resonant third-harmonic generation and multiphoton ionization into the continuum states of an atomic system is experimentally and theoretically investigated by means of a pair of partially incoherent, identical laser pulses. The evidence of quantum interference as a function of the delay between the pulses is reported. The transition from the resonant to the nonresonant case is also shown. The obtained results agree with the prediction of a theoretical model showing that the onset of quantum interference appears to be related to the coherence time of the laser radiation, which is much shorter than the pulse duration.
In femtosecond degenerate four-wave mixing experiments in sodium vapor, quantum beats are observed at the wavelength of the third harmonic when the fundamental beams are three-photon resonant. The period of beating, which corresponds to fine structure energy-level splitting, does not change with the atomic number density, buffer gas pressure, or laser intensity. Surprisingly, the third-harmonic signal is observed only at negative time delays for the transient grating pulse sequence. We relate this to the well-known interference effect between excitation pathways involving the fundamental and the third-harmonic fields, which leaves atoms virtually unexcited and prevents formation of population grating.
We report the application of third-harmonic generation (THG) to study photon-echo-associated coherent molecular states. Two temporally separated circularly polarized laser pulses are focused into a cell containing I(2) vapor to create the coherent dipole moments. A delayed oppositely circularly polarized pulse is then focused into the same region to generate the third harmonic. Since no THG can be produced by any individual pulse, correlated THG may easily be measured without using any fast detection scheme.