Spectroscopic photon echoes

Recently, modem ultrafast spectroscopic methods have opened a new experimental window on the molecular dynamics of water, examining the OH-stretch dynamics for the experimentally convenient aqueous system of HOD diluted in D2O using ultrafast infrared (IR) [1-6], IR-Raman [7], or photon echo [8] spectroscopy. 

When deciding to study the dynamics of electronic excitation energy transfer in molecular systems by conventional spectroscopic techniques (in contrast to those based on non-linear properties such as photon echo spectroscopy) one has the choice between time-resolved fluorescence and transient absorption. This choice is not inconsequential because the two techniques do not necessarily monitor the same populations. Fluorescence is a very sensitive technique, in the sense that single photons can be detected. In contrast to transient absorption, it monitors solely excited state populations this is the reason for our choice. But, when dealing with DNA components whose quantum yield is as low as 10-4, [3,30] such experiments are far from trivial. 

The relationship between spectroscopic and statistical functions has been exploited for a variety of phenomena related in different ways to the dynamical response of the medium. We cite as examples spectral line broadening, photon echo spectroscopy and phenomena related to TDFSS we are examining here. A variety of methods are used for these studies and we add here methods based on ab initio CS. The basic model is actually the same for all the methods in use ab initio CS has the feature, not yet implemented in other methods, of using a detailed QM description of the solute properties, allowing a description of effects due to specificities of the solute charge distribution. 

We are beginning to develop a detailed understanding of these methods (18,21,30,33,34,37-40,42,44,47-49), many of which are described in this book. We have recently demonstrated a series of novel nonlinear all-IR spectroscopic techniques (IR-pump-IR-probe, IR-three-pulse photon echoes, IR-dynamic hole burning, IR-2D spectroscopy), all of them utilizing intense femtosecond IR pulses, with the intention to develop new multidimensional spectroscopic tools to study the structure and the dynamics of proteins (30,31,41,42,50-53). We shall summarize in this contribution our work, its underlying principles, and its applications. 

We have presented two types of nonlinear IR spectroscopic techniques sensitive to the structure and dynamics of peptides and proteins. While the 2D-IR spectra described in this section have been interpreted in terms of the static structure of the peptide, the first approach (i.e., the stimulated photon echo experiments of test molecules bound to enzymes) is less direct in that it measures the influence of the fluctuating surroundings (i.e., the peptide) on the vibrational frequency of a test molecule, rather than the fluctuations of the peptide backbone itself. Ultimately, one would like to combine both concepts and measure spectral diffusion processes of the amide I band directly. Since it is the geometry of the peptide groups with respect to each other that is responsible for the formation of the amide I excitation band, its spectral diffusion is directly related to structural fluctuations of the peptide backbone itself. A first step to measuring the structural dynamics of the peptide backbone is to measure stimulated photon echoes experiments on the amide I band (51). 

In agreement with this conclusion, the Bloch picture applied here to derive Equation (30) does not predict a decay of the first moment, since the Bloch description omits spectral diffusion processes. Nevertheless, it is possible to understand the existence of a peak shift within the Bloch description, and this suggests a qualitative interpretation for its decay. As we have seen from photon echo experiments on spectroscopic probes... 

Jimenez R, Mourik F, Yu JY, Fleming GR. Three-pulse photon echo measurements on LH1 and LH2 complexes of Rhodobacter sphaeroides nonlinear spectroscopic probe of energy transfer. J Phys Chem B 1997 101 7350-7359. 

Besides various detection mechanisms (e.g. stimulated emission or ionization), there exist moreover numerous possible detection schemes. For example, we may either directly detect the emitted polarization (oc PP, so-called homodyne detection), thus measuring the decay of the electronic coherence via the photon-echo effect, or we may employ a heterodyne detection scheme (oc EP ), thus monitoring the time evolution of the electronic populations In the ground and excited electronic states via resonance Raman and stimulated emission processes. Furthermore, one may use polarization-sensitive detection techniques (transient birefringence and dichroism spectroscopy ), employ frequency-integrated (see, e.g. Ref. 53) or dispersed (see, e.g. Ref. 54) detection of the emission, and use laser fields with definite phase relation. On top of that, there are modern coherent multi-pulse techniques, which combine several of the above mentioned options. For example, phase-locked heterodyne-detected four-pulse photon-echo experiments make it possible to monitor all three time evolutions inherent to the third-order polarization, namely, the electronic coherence decay induced by the pump field, the djmamics of the system occurring after the preparation by the pump, and the electronic coherence decay induced by the probe field. For a theoretical survey of the various spectroscopic detection schemes, see Ref. 10. 

Note that the application of the convolution scheme in the simple form (44) requires that the nonlinear polarization contains only a single interaction with the probe laser field. Apart from the transient transmittance spectrum considered above, this condition is also fulfilled for related detection schemes such as time-resolved fluorescence, ionization, and excited-state absorption. Coherent spectroscopic signals such as the photon-echo, on the other hand, contain two interactions with the probe laser field, thus requiring the calculation of the full three-time response function, followed by a double convolution. 

In the last chapter, we used a steady-state treatment to relate the shape of an absorption band to the dynamics of relaxations in the excited state. Because a period on the order of the electronic dephasing time will be required to establish a steady state, Eqs. (10.43) and (10.44) apply only on time scales longer than this. We need to escape this limitation if we hope to explore the relaxation dynamics themselves. Our first goal in this chapter is to develop a more general approach for analyzing spectroscopic experiments on femtosecond and picosecond time scales. This provides a platform for discussing how pump-probe and photon-echo experiments can be used to probe the dynamics of structural flucmations and the transfer of energy or electrons on these short time scales. 

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