Stimulated photon echo

Morsink, J.B.W., Hesselink, W.H., and Wiersma, D.A. (1982) Photon echoes stimulated from long-lived ordered populations in multi-level systems. The effect of intersystem crossing and optical branching. Chem. Phys., 71, 289. 

Figure B2.1.10 Stimulated photon-echo peak-shift (3PEPS) signals. Top pulse sequence and iuterpulse delays t and T. Bottom echo signals scaimed as a fiinction of delay t at tluee different population periods T, obtained with samples of a tetrapyrrole-containing light-harvesting protein subunit, the a subunit of C-phycocyanin.

Homoelle B J, Edington M D, Diffey W M and Beck W F 1998 Stimulated photon-echo and transientgrating studies of protein-matrix solvation dynamics and interexciton-state radiationless decay in a phycocyanin and allophycocyanin J. Phys. Chem. B 102 3044-52... 

In a homodyne detection scheme, such as in the stimulated photon echo experiments described in the next paragraph, the detector measures the t-integrated intensity of the square of the third-order polarization... 

C. Comparison of Stimulated Photon Echoes of Vibrational and Electronic Transitions... 

Figure 3 (a) Time sequence of the (stimulated) three-pulse photon echo experiment. The times ti, t2, and t3 represent the time coordinates used in the response functions [Equations (7)—(12)] while r, T, and t measure the delay times with respect to the peak positions of the light pulses. For 5-shaped light pulses, both sets of times would be equivalent, (b) The so-called box configuration, (101) which allows the spatial separation of the third-order polarization generated in the —ki + k2 + kj and the +ki — k2 + k3 phase matched directions. 

Figure 5 (a) Stimulated photon echo signal of the azide ion (N3 ) in D2O at 2043 cm-1 as a function of r and T for the — kj + k2 + k3 (gray surface) and the +ki — k2 + k3 (white surface) phase matching directions, (b) Representative traces for four selected values of T. The solid lines represent a global fit of all the scans to the model correlation function Equation (20). (From Ref. 41.)... 

Figure 9 Stimulated photon echoes from various test molecules in different enzymes CaN-j (azide bound to carbonic anhydrase), Hb-lSb- (azide bound to hemoglobin), and Hb-CO (carbon monoxide bound to hemoglobin). The signal is plotted against delay time r for selected delay times T together with global fits (solid lines). The oscillatory part in the experimental data, which is not reproduced by these fits, reflects the anharmonicity of the transition and is due to interference between fifth and third order nonlinear polarization term (52). (From Ref. 31.)...

Figure 11 The initial decay of the transition frequency fluctuation correlation function ( oio(t)< io(0)) obtained from global fits of the stimulated photon echo data of azide dissolved in D2O (solid line, same data as in Fig. 6), CA-N3- (dashed line) I Ib-N3 (dashed-dotted line), and Hb-CO (dashed-double-dotted line).

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). 

The result of such an experiment on the de novo cyclic penta peptide, which has been introduced previously in this paragraph, is shown in Fig. 20. Qualitatively, the results are very similar to the results of the stimulated photon echo system on isolated test molecules embedded to proteins. As a function of T, the signal decays on a time scale corresponding to vibrational relaxation of the amide I states Tx/2 = 600 fs. As a function of r, on the other hand, a significant peak shift is again obtained. As in the previous case, the peak shift, represented in Fig. 20 by the normalized first moment Mi (T), slightly decays within the first ps, which is the time window accessible to these experiments in the moment. Similar results are obtained for apamin (51). 

Figure 20 The stimulated (three-pulse) photon echo signal of the amide I band of cyc/o-Mamb-Abu-Arg-Gly-Asp as function of delay time r and T (see Fig. 3) and its normalized first moment. The first moment decays with time (T) due to...

Figure 21 The Feynman diagrams, which have to be taken into account to model the rephasing part of the stimulated photon echo system of a excitonically coupled system of vibrations. The i and k +1 are states of the one-exciton and two-exciton manifold, respectively.

Figure 22 (a) Model calculation for the stimulated photon echo signal of the cyclic model peptide (cydo-Mamb-Abu-Arg-Gly-Asp) based on its known structures. The same coupling constants were employed as in the model simulations of the 2D-IR spectrum in Fig. 16. The parameters for homogeneous broadening (T2 = 0.7 ps), vibrational relaxation (Tj = 1.2 ps), and inhomogeneous broadening (diagonal disorder 20 cm-1) were also the same. The pulse duration of the laser pulses was set to 120 fs. (b) The same calculation as in (a), but with -shaped laser pulses and neglecting the inhomogeneous broadening. A sharp coherence spike now occurs at T = r = 0, which is not seen experimentally.

Hamm P, Lim M, DeGrado WF, Hochstrasser RM. Stimulated photon echoes from amide I vibrations. J Phys Chem 1999 103 10049-10053. 

S. A. Passing, Y. Nagasawa, G. R. Fleming, Three Pulse Stimulated Photon Echo Experiments as a Probe of Polar Solvation Dynamics Utility of Harmonic Bath Modes, J. Chem. Phys. 107, 6094 (1997). 

The dephasing time, T2, can be measured by the photon echo technique or determined from the homogeneous width of saturation spectroscopy, which is a Fourier transform of the former, as easily seen from Eq. (5.35). When a sample is irradiated with three consecutive laser pulses at times, 0, t2, and f3, an echo pulse is emitted at time, t2 + t. This is called stimulated photon echo. Several additional echo techniques have been proposed. 

The accumulated 3-pulse stimulated photon-echo method " was used in order to monitor vibrational relaxation times of the first excited electronic state of pentacene. Two amplified dye lasers were used to perform ps photon-echo measurements on pentacene and naphthalene samples, which established that pseudo-local photon scattering was responsible for optical dephasing in vibronic transitions. A mode-locked cavity-dumped synchronously pumped dye laser system was used to demonstrate long coherence times for the delocalized optical excitation of dimer states, by ps photon-echo spectroscopy. ... 

Using three optical excitation pulses a so-called stimulated photon echo (3PSE) may be generated at a time after the third pulse which is identical to the splitting between the first two excitation pulses. The phase-match... 

Fig. 34. Intensity of the stimulated photon echo of triphenyhnethyl in triphenylamine at 1.5 K vs second-third pulse delay in zero field and in a magnetic field of 1.57. The time separation between the first and second pulse was 40 ns.

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