Three-pulse photon echo of an excitonic dimer modeled via Redfield theory

A time-nonlocal quantum master equation coupled with a perturbative scheme to evaluate the third-order polarization in the phase-matching direction k(s) = -k(1) + k(2) + k(3) is used to efficiently simulate three-pulse photon-echo signals. The present method is capable of describing photon-echo peak shifts including pulse overlap and bath memory effects. In addition, the method treats the non-Markovian evolution of the density matrix and the third-order polarization in a consistent manner, thus is expected to be useful in systems with rapid and complex dynamics. We apply the theoretical method to describe one- and two-color three-pulse photon-echo peak shift experiments performed on a bacterial photosynthetic reaction center and demonstrate that, by properly incorporating the pulse overlap effects, the method can be used to describe simultaneously all peak shift experiments and determine the electronic coupling between the localized Q(y) excitations on the bacteriopheophytin (BPhy) and accessory bateriochlorophyll (BChl) in the reaction center. A value of J = 250 cm(-1) is found for the coupling between BPhy and BChl.

The energies of 1s states inside and outside the quantum well of a CdSe/ZnS quantum-dot quantum well (QDQW) and the transition dipole moment between these two states have been calculated by effective mass approximation. By using the calculation results, the longitudinal and transversal relaxation times of CdSe/ZnS have been approximated. We obtain a three-pulse photon echo (TPE) signal on the basis of the two states using the optical Bloch equations. We find that there should be four echoes in TPE from our theoretical calculation. In particular, the effects of the variation in core radius and shell thickness have been studied. It has been shown from the numerical calculation that the TPE signal is strongly dependent on the size and structure of the QDQW, and is dominated by relaxation time, which is also dependent on the size and structure.

The temperature dependence of the optical dephasing mechanism in an organic polymer glass, polymethylmethacrylate (PMMA), was studied from 300 K to 30 K using the dye IR144 as a probe. Transient grating and three pulse photon echo measurements were made, and the three pulse photon echo peak shift (3PEPS) was recorded as a function of temperature. The peak shift data reveal time constants of ∼6 fs and ∼60 fs, along with vibrational beats and a long-time constant value for the peak shift. The 6 fs component is attributed to intramolecular vibrations and the 60 fs component to librational degrees of freedom of the PMMA itself. This contribution appears slightly underdamped and the fitted spectral density matches well with the Raman spectrum of PMMA. The two ultrafast decays are insensitive to temperature. For temperatures above 80 K the long-time peak shift increases linearly as temperature decreases but at 80 K the shift levels off and decreases for temperatures between 80 and 30 K. Fit values for the inhomogeneous width (500 cm−1) and the reorganization energy (378 cm−1) describe the initial value of the peak shift, its decay, the absorption spectrum, and the three-pulse photon echo signal quite well at both high and low temperature. We were not very successful in describing the temperature dependence of the long-time peak shift, although the insensitivity of the dynamics to temperature could be qualitatively accounted for. At low temperature the imaginary portion of the line shape function, which is temperature independent, contributes significantly to the response, while at high temperature the dephasing is dominated by the real part of the line shape function. A more sophisticated model is required to quantitatively describe the data.

The decay of three-pulse photon echo signals from a solute in a liquid solvent is sensitive to the solute’s transition frequency fluctuations, as characterized by its two-point time correlation function, otherwise known as the solvation correlation function. The most widely used method for determining this solvation correlation function from photon echo data involves the three-pulse photon echo peak shift (3PEPS) method. Using this method the long-time decay of the solvation correlation function can be obtained directly, but the determination of the short-time decay requires a difficult numerical fitting procedure. In this study we propose several alternative approaches to determining the solvation correlation function from echo data, the most promising and straightforward of which we call the S3PE (short-time slope of the three-pulse photon echo) method. The accuracy and efficacy of this approach is illustrated by extracting the solvation correlation function from “experimental” data obtained from classical molecular dynamics computer simulations.

A series of π-extended cyclic thiophene oligomers of 12, 18, 24, and 30 repeat units have been studied using methods of ultrafast time-resolved absorption, fluorescence upconversion, and three-pulse photon echo. These measurements were conducted in order to examine the structure-function relationships that may affect the coherence between chromophores within the organic macrocycles. Our results indicate that an initial delocalized state can be seen upon excitation of the cyclic thiophenes. Anisotropy measurements show that this delocalized state decays on an ultrafast time scale and is followed by the presence of incoherent hopping. From the use of a phenomenological model, we conclude that our ultrafast anisotropy decay measurements suggest that the system does not reside in the Förster regime and coherence within the system must be considered. Three-pulse photon echo peak shift experiments reveal a clear dependence of initial peak shift with ring size, indicating a weaker coupling to the bath (and stronger intramolecular interactions) as the ring size is increased. Our results suggest that the initial delocalized state increases with ring size to distances (and number of chromophores) comparable to the natural light-harvesting system.

Three-pulse photon echo peak shift in optically dense samples

A theoretical description of the three-pulse photon echo peak shift for model reaction systems is presented. An electronic two-state system with a finite upper-state lifetime and a three-state system in which electronic transitions can occur are considered. A probabilistic argument is employed to incorporate the incoherent transitions. New pathways describing the transition of electronic population are introduced and the nuclear propagator in the electronic population state is written by a convolution integral between those of the nonreactive two-state system weighted by some factors for the electronic transition. The response functions are given by multitime correlation functions and are analyzed by the cumulant expansion method. Some numerical calculations are presented and the influence of incoherent reactions on the peak shift is discussed. Comparison with experimental data confirms the existence of the effects predicted here.

The role of weakly chirped pulses (time bandwidth product, DeltanuDeltatau<0.61) on three-pulse photon echo signals has been systematically studied. Pulses with varying chirp were characterized with frequency resolved optical gating (FROG) and used to measure spectrally resolved three-pulse photon echoes of a dye in solution. The weakly chirped pulses give rise to markedly different echo signals for population times below approximately 100 fs. The chirped pulses can decrease or enhance spectral signatures of an excited state absorption transition in the echo signal. Furthermore, the observed dephasing dynamics depend on the phase of the electric fields. Simulations based on a three-level model and the electric fields retrieved from the FROG traces give a good agreement for photon echo experiments with both transform limited and chirped pulses. The simulations also allow for a numerical investigation of effects of chirp in two-dimensional spectroscopy. For a two-level system, the chirped pulses result in nonelliptical two-dimensional spectra that can erroneously be interpreted as spectral heterogeneity with frequency dependent dephasing dynamics. Furthermore, chirped pulses can give rise to "false" cross peaks when strong vibrational modes are involved in the system-bath interaction.

The immune system is remarkable in its ability to produce antibodies (Abs) with virtually any specificity from a limited repertoire of germ line precursors. Although the contribution of sequence diversity to this molecular recognition has been studied for decades, recent models suggest that protein dynamics may also broaden the range of targets recognized. To characterize the contribution of protein dynamics to immunological molecular recognition, we report the sequence, thermodynamic, and time-resolved spectroscopic characterization of a panel of eight Abs elicited to the chromophoric antigen 8-methoxypyrene-1,3,6-trisulfonate (MPTS). Based on the sequence data, three of the Abs arose from unique germ line Abs, whereas the remaining five comprise two sets of siblings that arose by somatic mutation of a common precursor. The thermodynamic data indicate that the Abs recognize MPTS via a variety of mechanisms. Although the spectroscopic data reveal small differences in protein dynamics, the anti-MPTS Abs generally show similar levels of flexibility and conformational heterogeneity, possibly representing the convergent evolution of the dynamics necessary for function. However, one Ab is significantly more rigid and conformationally homogeneous than the others, including a sibling Ab from which it differs by only five somatic mutations. This example of divergent evolution demonstrates that point mutations are capable of fixing significant differences in protein dynamics. The results provide unique insight into how high affinity Abs may be produced that bind virtually any target and possibly, from a more general perspective, how new protein functions are evolved.

The excited-state dynamics of a branched octupolar molecule (tris-4,4‘,4‘ ‘-(4-nitrophenilethynyl)triphenylamine (T-NPTPA)) with charge-transfer character is investigated by complementary measurements of time-resolved fluorescence, transient absorption, and three-pulse photon echo peak shift. The data are compared with those obtained for the linear molecule dimethylnitroaminotolane (DMNAT) representing a linear building block of the octupolar system. Time-resolved fluorescence as well as transient absorption experiments showed the presence of an intermediate C3 symmetry state for the trimer with a depolarization time faster than ∼50 fs. Three-pulse photon echo peak shift measurements for the trimer revealed a large initial fast component of the peak shift decay. The initial peak shift during the first 100 fs was found to be much higher for the trimer as compared to the linear building block. This is in accordance with the time-resolved anisotropy results suggesting a different character of the initial excitation of the trimer. The higher peak shift value for the trimer suggests a smaller total coupling of electronic transition frequency to the nuclear motions, which may be the result of the delocalized character of this initial excited state. A residual peak shift (∼2 fs) at long population times was also observed and was interpreted as an indication of the residual static inhomogeneity (inhomogeneous broadening) in the system.

Three-pulse photon echo induced by the optical transition of excitons in core–shell CdSe/ZnS nanocrystal quantum dots

Here we report results obtained using two-dimensional photon echo spectroscopy (2DPE) to study ultrafast dynamics in CdTe/CdSe heterostructured quantum dots. From these measurements we are able to extract “peak shift” information usually obtained by homodyne three-pulse photon echo peak shift measurements. Additionally we are able to observe how absorptive features in the 2DPE spectrum beat in an anticorrelated fashion at the frequency of the LO phonon modes of the nanocrystal.

Three-pulse photon echo peak shift spectroscopy as a probe of flexibility and conformational heterogeneity in protein folding

The origins of electronic spectral broadening in solutions, glasses and proteins are discussed via three pulse stimulated echo peak–shift measurements. Spectral densities for dye molecules in polar solutions are presented and discussed in terms of molecular models for the dynamics. The breakdown of the harmonic bath picture at low frequencies is presented. Finally, echo measurements on light harvesting complexes of purple bacteria are presented and it is shown that the energy transfer timescale can be obtained from peak–shift measurements.

We report a detailed study of ultrafast exciton dephasing processes in semiconducting single-walled carbon nanotubes employing a sample highly enriched in a single tube species, the (6,5) tube. Systematic measurements of femtosecond pump-probe, two-pulse photon echo, and three-pulse photon echo peak shift over a broad range of excitation intensities and lattice temperature (from 4.4 to 292 K) enable us to quantify the timescales of pure optical dephasing (T(2)(*)), along with exciton-exciton and exciton-phonon scattering, environmental effects as well as spectral diffusion. While the exciton dephasing time (T(2)) increases from 205 fs at room temperature to 320 fs at 70 K, we found that further decrease of the lattice temperature leads to a shortening of the T(2) times. This complex temperature dependence was found to arise from an enhanced relaxation of exciton population at lattice temperatures below 80 K. By quantitatively accounting the contribution from the population relaxation, the corresponding pure optical dephasing times increase monotonically from 225 fs at room temperature to 508 fs at 4.4 K. We further found that below 180 K, the pure dephasing rate (1/T(2)(*)) scales linearly with temperature with a slope of 6.7 ± 0.6 μeV/K, which suggests dephasing arising from one-phonon scattering (i.e., acoustic phonons). In view of the large dynamic disorder of the surrounding environment, the origin of the long room temperature pure dephasing time is proposed to result from reduced strength of exciton-phonon coupling by motional narrowing over nuclear fluctuations. This consideration further suggests the occurrence of remarkable initial exciton delocalization and makes nanotubes ideal to study many-body effects in spatially confined systems.