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The Journal of Chemical Physics

Photon echoes and related four-wave-mixing spectroscopies using phase-locked pulses

Minhaeng Cho, Norbert F. Scherer, Graham R. Fleming, Shaul Mukamel

Published Apr 15, 1992• 150 citations
Publisher

Abstract

The use of phase-locked pulses in various spectroscopic techniques related to the third-order polarization P(3) is analyzed. Using correlation function expressions for the nonlinear response function, we clarify the interrelationship among several photon echo, pump–probe, and spontaneous light emission techniques, without alluding to any specific model for the material system. By combining phase-locked pulses and heterodyne detection it becomes possible to probe separately the real and imaginary parts of the nonlinear response function. Combining two phase-locked pulse excitation with time-resolved detection of the spontaneous light emission allows direct separation of the Raman and fluorescence contributions.

DOI
10.1063/1.462686

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The use of phase-locked pulses in various spectroscopic techniques related to the third-order polarization P(3) is analyzed. Using correlation function expressions for the nonlinear response function, we clarify the interrelationship among several photon echo, pump–probe, and spontaneous light emission techniques, without alluding to any specific model for the material system. By combining phase-locked pulses and heterodyne detection it becomes possible to probe separately the real and imaginary parts of the nonlinear response function. Combining two phase-locked pulse excitation with time-resolved detection of the spontaneous light emission allows direct separation of the Raman and fluorescence contributions.
The recently demonstrated technique of optically phase-locked pulse-pair (PLPP) excited spontaneous emission is described by a third-order perturbative density matrix approach. A nonlinear polarization description shows how PLPP spectroscopy depends on all the relevant material dephasing time scales. The time and frequency integrated resonance spontaneous emission consists entirely of resonance fluorescence, and is derived exclusively from excited-state population decay terms, i.e., diagonal second-order density-matrix elements. These third-order polarization results are proportional to the previously derived linear polarization expressions found to describe the observed PLPP I2 vapor emission. The nonlinear treatment allows a comparison of this technique to other forms of ultrafast pump–probe spectroscopies such as transient absorption and photon echo techniques. The role of impulsively prepared coherences is clearly described by this analysis. The effect of pulse duration, relative to material dephasing times, is explored for relaxation given by the optical Bloch equations. The most significant differences between a linear and nonlinear polarization treatment occur for pulse durations greater than the optical dephasing time or when excited state population and coherence decays are of the order of rovibrational periods. A fluorescence line narrowing effect, due to short pulse excitation, is predicted.
The present work is devoted to the description of a nonperturbative treatment of anharmonic effect and mode-mode coupling taking place in molecular vibrational systems. The information is obtained from the four-wave-mixing signal detected in the usual photon-echo phase-matched direction, termed 4WM photon-echo, using heterodyne detection to test separately the real and the imaginary parts of the third-order polarization. This approach allows a complete redistribution of the relaxation, dephasing, and transition constants on account of the magnitude of the coupling strength. In addition, our analytical approach accounts for the contributions provided by the various possible chronological orderings of the field interactions. The high sensitivity of the signal with both the energy shifts induced by the internal couplings and off-resonant energy parameter of the laser excitation is properly analyzed in the framework of our analytical description.
We demonstrate coherent control over interference between different Liouville-space pathways that describe the generation of the nonlinear optical polarization in a stimulated photon echo. This control was exercised by phase-locking of the excitation pulses and observed in the heterodyne detected echo signal. A theoretical analysis of the effect is presented and found to be in good agreement with the obtained results. The relation between this novel time-domain interference effect and the pressure-induced extra resonance in four-wave mixing spectroscopy is discussed.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.