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The Journal of Chemical Physics

Semiclassical Green function calculation of four wave mixing in polarizable clusters and liquids

Jan Adriaan Leegwater, Shaul Mukamel

Published Nov 1, 1994• 20 citations
Publisher

Abstract

A theory for the nonlinear optical response of an assembly of four level atoms representing an s–p transition, with dipole–dipole interactions is developed. Simulation results for two-pulse ultrafast four wave mixing measurements in atomic clusters and in liquids demonstrate that the electronic density of states can be obtained by combining absorption and four wave mixing experiments. We show that a sensitive direct probe for interatomic interactions and correlations is provided by reversing the pulse time ordering in a photon echo sequence. The effect of nuclear motions on the linear absorption spectrum is investigated.

DOI
10.1063/1.468297

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The Journal of Chemical Physics•Mar 1, 1983•63 citations
A theory for the nonlinear optical response of an assembly of four level atoms representing an s–p transition, with dipole–dipole interactions is developed. Simulation results for two-pulse ultrafast four wave mixing measurements in atomic clusters and in liquids demonstrate that the electronic density of states can be obtained by combining absorption and four wave mixing experiments. We show that a sensitive direct probe for interatomic interactions and correlations is provided by reversing the pulse time ordering in a photon echo sequence. The effect of nuclear motions on the linear absorption spectrum is investigated.
Transient four-wave mixing experiments with 100 fs pulses in a dense potassium vapor probe the electronic energy fluctuations that lead to optical decoherence. Echo-peak shift experiments yield a biexponential two-time correlation function of energy level fluctuations. Molecular dynamics simulations show that the slow component is a many-body excitonic contribution arising from long-range resonant interactions. The decay of the correlation function occurs on comparable time scales in theory and experiment.
Considering an electronic two-level system coupled to vibrational degrees of freedom and driven by short and intense non-overlapping laser pulses, we introduce the concept of nonperturbative response functions. These response functions are expressed in terms of effective electronic transition dipole moments which depend on the strength of the field-matter coupling and on the pulse durations. It is shown that the nonlinear polarization representing four-wave-mixing signals can elegantly be expressed in terms of these nonperturbative response functions to all orders in the field-matter coupling. The nonperturbative response functions generalize the interpretative power of the familiar third-order response functions to four-wave-mixing experiments with intense laser pulses.
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.
The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].
We present a theory of the four-wave-mixing (FWM) spectroscopy for the multilevel system coupled to the bath with arbitrary time scale, in contrast to most previous work that assumes the fast bath dynamic limit (motionally narrowed limit). Exact quantum mechanical expressions for the relevant nonlinear response tensor and the nonlinear polarization vector are obtained for a model Hamiltonian. Effects of molecular rotation and the polarization directions of the input radiation fields are also fully taken into account. The results show how the cross correlation as well as the autocorrelation functions of the fluctuations in the energy-gaps or transition frequencies between eigenstates contribute to the FWM spectroscopy. The result is applied to three-pulse echo spectroscopy. We examine the results for a variety of model spectral density functions, and recover the results of the previously reported theories as limiting cases.
The effects of intense laser pulse trains in coupled multilevel systems (such as pure or mixed molecular crystals) are analyzed by calculating exact density matrix evolutions. It is shown that two-level approximations are inadequate. The contributions of exchange couplings, inhomogeneous broadening, permanent multipole interactions and transition multipole interactions to absorption and photon echo line shapes are calculated. The absorption line shape of 1,4-dibromonaphthalene (DBN) is shown to be predominantly an isotopic substitution effect, as our Monte Carlo results give quantitative agreement with experiment for this model. Average t-matrix approximations to the Green’s function, which have been used to propose a different mechanism for the DBN line shape are shown to be qualitatively inadequate. Dipole–dipole interactions are shown to be an important photon echo decay mechanism in mixed crystals, with the relative importance of permanent and transition multipole interactions dependent on the resonance frequency distribution. Multiple pulse trains, including multiple pulse echoes and optical multiple-quantum sequences, are shown to be capable of distinguishing different types of interactions in the molecular Hamiltonian and reducing optical density effects. Specific pulse sequences are proposed and their effects are calculated.