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The Journal of Chemical Physics

Laser phase coherence effects in time-delayed multiphoton transitions: A modified collisional time-correlation function method

Deepak Srivastava

Published Oct 15, 1994• 0 citations
Publisher

Abstract

A recently proposed collisional time-correlation function method for resonance laser–target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field and molecular target dipole/susceptibility correlation functions. The first and second order laser field correlation functions, also known as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser–target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump–probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.

DOI
10.1063/1.468395

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Physical Review A•May 1, 1988•47 citations
A recently proposed collisional time-correlation function method for resonance laser–target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field and molecular target dipole/susceptibility correlation functions. The first and second order laser field correlation functions, also known as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser–target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump–probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.
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The spectral and dynamic effects associated with a non-zero difference, d, between the permanent dipole moments of two molecular states involved in a transition, are investigated for a variety of electromagnetic field-molecule interactions. Both analytical and exact numerical techniques are used to solve the time-dependent Schrodinger equation and to obtain the temporal populations of the molecular states and the associated absorption spectra, for molecular interactions with a Gaussian pulsed, or one or two continuous wave (CW), laser(s).;Analytical rotating wave approximation results are derived for a single CW laser interacting with a two-level d {dollar}\\ne{dollar} 0 molecule with an excited state lifetime, and for a two-level d {dollar}\\ne{dollar} 0 molecule interacting with two CW lasers. A symmetry-adapted Riemann product integral method for exact calculations of pulsed laser-molecule interactions is developed and applied to specific problems. The Floquet technique for the treatment of periodic Hamiltonians is extended to accommodate the interaction of a molecule with two CW lasers.;The one-field RWA results are used to predict and interpret the effects of permanent dipoles on the temporal behaviour of the molecular states for a decaying two-level system interacting with a CW laser, and for a non-decaying two-level system interacting with a pulsed laser. It is shown that the excited state lifetime and the pulse duration can act as internal and external probes, respectively, of the temporal effects of permanent dipoles, relative to the often-studied d = 0 problem. The two-field analytical RWA solutions are used to help discuss and predict the effects of permanent dipole moments in two-laser multi-photon transitions. Several examples of multi-photon, two-colour, two-level resonance profiles, calculated in the RWA and by using exact Floquet techniques, are used to demonstrate how particular multi-photon transitions can be optimized, and to help quantify the conditions for the validity of the two-colour RWA. The effects of neighbouring energy levels on the transition of interest, for both probe and pump-probe laser-molecule interactions, are investigated using a series of three- to seven-level model molecular systems.
In this paper we examine the conditions for the erosion of coherence effects in the multiphoton excitation of a collision-free sparse molecular level structure driven by a laser field, which is characterized by a stabilized amplitude and a fluctuating phase. The stochastic equations of motion for the molecule excited by a phase-diffusing laser field were solved within the framework of second-order cumulant expansion. The kinetic master equation was found to be valid for the description of the dynamics of the multiphoton excitation process provided that the correlation time of the laser phase is considerably shorter than the relevant molecular time scales and that the rate of the slow diffusion of the laser phase considerably exceeds the Rabi frequencies. We conclude that the experimental observation of the celebrated fluence dependence of the efficiency of high-order multiphoton excitation in isolated molecules may sometimes originate from the fluctuations in the laser field rather than from intramolecular vibrational energy redistribution.
An expression for the probability of time-resolved three-photon ionization via coherently excited resonant states of a molecular system is derived in the perturbative density matrix formalism with the aid of the Liouville space Feynman diagram. It is shown how the time evolution of the molecular coherence in the first resonant state can be detected as a function of the delay time between the pumping and probing lasers through the probing two-photon ionization process. The three-photon ionization process consists of the simultaneous and sequential processes which are classified by the Liouville space Feynman diagrams. The possibility of appearance of quantum beats in the pump–probe three-photon ionization is discussed by performing model calculations of the probability of ionization. The role of the direct and redistributed processes is discussed. The redistributed process is induced by intramolecular processes in the resonant state. The theoretical treatment is applied to the (1+2) three-photon ionization of pyrazine observed by Knee et al. It is demonstrated that the fast decay component (110 ps) of the pyrazine spectra originates from the intramolecular dephasing of the vibronic coherence created by the pumping pulse laser, and this component appears only when the redistributed process (the ionization process through triplet levels) is absent.
As a succession of two pulses propagates through a medium which exhibits a resonance (single or multiphoton), the resonant parts of the susceptibility will depend on the relative phase of the two pulses, provided the delay between the pulses is shorter than the phase relaxation time of the interaction. As a result of this "coherent interaction", the reradiation of the sample (the fluorescence, the absorption and the generation of harmonics) will be a periodic function of the phase difference and delay between the two pulses of the sequence 1. The study of these coherent effects is important, because one expect to find conditions under which the maximum harmonic conversion to much shorter wavelengths can be greatly enhanced 2. The presence of the multiphoton resonance enhances the nonlinear susceptibility responsible for the harmonic generation, but reduces also the maximum achievable conversion efficiency because of resonant losses (depletion of the fundamental by multiphoton absorption). The latter effect can be eliminated by a judicious choice of the pulse sequencing and phasing. In addition to demonstrating, for the first time, coherent interaction enhancement in harmonic generation, the data of third harmonic versus relative phase of the pulse sequences enable us to measure the phase angle of the third order susceptibility (hence the contribution of the continuum relative to that of the resonance).
The dependence of the electronic absorption spectrum of a dye molecule on the time of delay between the excitation of the molecule by a pump-laser pulse and the probing of the absorption by a test-laser pulse is studied. The effect of dephasing of the molecular transition arising from the interaction with dissipative systems is described by a stochastic modulation of the electronic transition frequency. It is shown that in the case when the two laser pulses are short compared with the correlation time of the frequency modulation and when the spectral linewidth of the pump-laser light is smaller than the bandwidth of the equilibrium absorption spectrum, hole burning appears although the molecules have equal mean transition frequencies. This effect arises from non-Markovian correlations between the dephasings of the molecule during the actions of the pump- and the test-laser pulse. With increasing delay time the holes are smoothed out and disappear when the delay time exceeds the correlation time. Such effects were found in recent femtosecond absorption experiments by Shank et al. [in Ultrafast Phenomena V, dited by G. R. Fleming and A. E. Siegman (Springer, Berlin, 1986), p. 179].