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| The diagram below represents a schematic of the three pulse photon echo peak shift experiment. Three femtosecond optical pulses, which are resonant with the electronic transition of the chromophore and incident on the sample in a boxcars geometry, result in the formation of two echo signals. The intensity of the echo signals are measured with two detectors. The temporal delay between the maxima of the two echo signals (the "peak shift"), is measured as a function of the delay between k1 and k2 (the coherence time), for fixed k2-k3 delay (population time). A measurement of peak shift as a function of population time comprises a 3PEPS data set. The timescales and amplitudes of the decay components in the 3PEPS scan reveals the frequencies and amplitudes of protein motions coupled to the electronic transition of the bound ligand. |
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Here's a second way to think about the experiement. As shown above, a sequence of three laser pulses, each with a slightly different propagation direction, are applied to the sample. The laser pulse frequency is in resonance with the transition frequency between the ground state and excited state of the solute. The first pulse creates a coherent superposition between the ground and excited states, and the ensemble of absorbing molecules subsequently dephases. The second pulse creates a population, either in the ground or excited state, and no further dephasing occurs. The third pulse again creates a superposition of states, and the ensemble may rephase and emit the echo signal. In competition to rephasing, molecules may relax by a free-induction decay (FID) process. |
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| The time delay between the first and second pulse is called coherence time, τ; the time delay between the second and third pulse is called population time, T. These are illustrated in the figure, above. The intensity of the time-integrated signal originating from both rephasing and FID, when plotted as a function of τ (for a fixed T), has a maximum at positive τ. The position of the maximum is called the peak shift and is plotted as a function of T. Environmental fluctuations, namely vibrations of the chromophore and protein, that occur during the coherence or population periods, induce random phase changes, which prevent rephasing of the affected transition dipoles but do not affect the FID signal. Consequently, with longer T, proportionally more molecules relax by FID, causing an apparent shift of the peak position of the time-integrated signal toward shorter τ (i.e., a decay of the peak shift). |