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Physical Review A

Interferometric six-wave mixing spectroscopy with broadband light: Isomorphism and factorized time correlator diagrams

Jason C. Kirkwood, A. C. Albrecht

Published Mar 7, 2000• 6 citations
Publisher

Abstract

The theory of an interferometric six-wave mixing quasiecho signal from a modeled molecular liquid using broadband (``noisy'') light is reported. The line-shaping function is treated by a standard mixture of a dynamic (homogeneous) dephasing process and a static (inhomogeneous) Bohr frequency distribution. Simulations are presented in either limit of the overall process to demonstrate the rephasing aspects of this nonlinear spectroscopy. The general aspects of the two-dimensional signal are inferred from factorized time correlator (FTC) diagrams. These diagrams pictorially represent the correlation functions of the random noise (associated with the broadband light) that arise upon stochastic averaging at the signal level. The entire set of FTC diagrams is seen to be isomorphic with those that describe a nonecho interferometric noisy light spectroscopy at fifth order, and the third-order electronically resonant four-wave mixing. Similarities between these three very different processes are discussed in terms of this one-to-one correspondence.

DOI
10.1103/physreva.61.043803

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Journal of the Optical Society of America B•May 1, 2005•5 citations
The theory of an interferometric six-wave mixing quasiecho signal from a modeled molecular liquid using broadband (``noisy'') light is reported. The line-shaping function is treated by a standard mixture of a dynamic (homogeneous) dephasing process and a static (inhomogeneous) Bohr frequency distribution. Simulations are presented in either limit of the overall process to demonstrate the rephasing aspects of this nonlinear spectroscopy. The general aspects of the two-dimensional signal are inferred from factorized time correlator (FTC) diagrams. These diagrams pictorially represent the correlation functions of the random noise (associated with the broadband light) that arise upon stochastic averaging at the signal level. The entire set of FTC diagrams is seen to be isomorphic with those that describe a nonecho interferometric noisy light spectroscopy at fifth order, and the third-order electronically resonant four-wave mixing. Similarities between these three very different processes are discussed in terms of this one-to-one correspondence.
The theory for temporally multidimensional, electronically resonant four-wave-mixing (FWM) spectroscopy based on broadband light interferometry is developed. Both homodyne and heterodyne detection are considered. Upon spectrally resolving the signal, the electronic Bohr frequency is seen to be extremely down-converted, even to zero frequency, but only with homodyne detection. These very low frequency fringes, referred to as radiation difference oscillations, are well known in the interferometric coherent Raman broadband light spectroscopies. Such low frequency fringes permit interferometry in the optical region using Nyquist criteria corresponding to far infrared sampling rates. Possible applications are illustrated by simulations of the two-dimensional third order signals from an electronic two-level system in a variety of ``baths.'' It is seen how homogeneous and inhomogeneous line-shaping mechanisms manifest themselves differently and revealingly in the free induction decay, the photon echo decay and their cross term components of the FWM signal.
Coherent Raman scattering using broadband, incoherent (noisy) light (termed I(2)CRS{\mathrm{I}}^{(2)}\mathrm{CRS}I(2)CRS---the I for interferometric and the superscript 2 for twice acting noisy fields) is treated for a multiply resonant, multicomponent mixture of molecules. Both the resonant-resonant and resonant-nonresonant hyperpolarizability contributions to the signal intensity are included in this formalism. The emphasis is on the physical understanding of this spectroscopy. To this end, factorized time correlator (FTC) diagram analysis is used to characterize the I(2)CRS{\mathrm{I}}^{(2)}\mathrm{CRS}I(2)CRS signal. The FTC diagram technique also serves to organize the terms that arise through the stochastic averaging of the noise at the intensity level. In addition to the FTC diagram analysis, a spectral filter analogy is employed to provide further insight into the physics behind I(2)CRS.{\mathrm{I}}^{(2)}\mathrm{CRS}.I(2)CRS.
Summary form only given. Nonlinear techniques using broadband light have been developed and applied for studying dephasing processes, population and orientational dynamics of molecules. These techniques are based on the fact that in wave-mixing processes one may have the time resolution determined by the laser coherence time instead of the laser pulse duration. One limiting factor of the measurement sensitivity is a constant signal (pedestal), which is present even when the delay time between the exciting broadband beams is substantially longer than their coherence time and relaxation time under study. A technique has been developed, which uses not "white" detection, but spectral filtering in field-correlated four-wave mixing, the so called interferometric four-wave mixing (IFWM), which gives a signal that reveals oscillatory modulation, enabling us to discriminate it more easily from the pedestal. The technique allows to determine rather precisely the frequency of a molecular vibration and its dephasing time, as well as to study damped molecular rotations in liquids. We report the first measurements of population relaxation rates affected by stimulated emission in the presence of the pump field applying the IFWM technique.
Degenerate four-wave mixing using broadband, non-transform-limited (incoherent) laser light having a Lorentzian spectral density is treated analytically for a Bloch two-level system. We consider the configuration in which an incoherent beam from a Lorentzian source is split into two beams having distinct k vectors, k and ${\mathit{k}}^{\ensuremath{'}}$. The twin beam along ${\mathit{k}}^{\ensuremath{'}}$ has been subjected to a controllable delay, \ensuremath{\tau}, relative to k. These twin beams, focused into the sample of interest, generate new fourth fields, the signal at ks{\mathit{k}}_{\mathit{s}}ks​=2k-${\mathit{k}}^{\ensuremath{'}}$ being examined here as a function of \ensuremath{\tau}. A set of factorized time correlation (FTC) diagrams is introduced to organize the calculation and to yield both analytic expressions as well as physical insight. Not only is the signal not symmetric in \ensuremath{\tau} but the signal can peak at \ensuremath{\tau}\ensuremath{\ne}0 even in the absence of inhomogeneous broadening. Finally, the physical insights and the use of the FTC diagrams are extended to rationalize several other incoherent light spectroscopies. \textcopyright{} 1996 The American Physical Society.
A nearly degenerate, four-wave mixing (ND4WM) setup with noisy light called I^(2)ND4WM(-) is investigated both experimentally and theoretically through factorized-time-correlation (FTC) diagram analysis. This third order nonlinear signal is of interest because the phenomenon of color-locking appears very directly in the measured signal. Color locking is a fundamental aspect of noisy-light spectroscopies that often plays a critical but subtle role in production of the signal. For I^(2)ND4WM(-), color-locking results in complete cancellation of the spectrally broad noise carried by the noisy light used to create it. When combined with FTC diagram analysis the qualitative features of the I^(2)ND4WM(-) can be understood. In addition to the striking noise cancellation, the qualitative features addressed in this work include the time profile, dynamic range, and polarization dependence of the signal. For comparison the spectrally broad I^(2)ND4WM(+) signal is presented.