Photon Echo Data Research Articles

Three‐Pulse Photon‐Echo Peak Shift Spectroscopy and Its Application for the Study of Solvation and Nanoscale Excitons

An understanding of chemical reactivity begins with an understanding of the dynamics involved regarding system-bath interactions. Spectroscopic studies of these interactions in condensed-phase multichromophoric systems are intricate and contain much information. Photon-echo spectroscopy has proven to be a useful tool for probing these interactions. A description of three-pulse photon-echo peak shift spectroscopy (3PEPS)--theory, experiment, and application--for the study of solvation and dynamics of nanoscale excitons is presented. Also, we discuss how two-dimensional photon-echo spectroscopy (2DPE) relates to 3PEPS and show how 3PEPS data can be extracted from 2D photon-echo data.

Local vibrations in disordered solids studied via single-molecule spectroscopy: Comparison with neutron, nuclear, Raman scattering, and photon echo data

The energy spectrum of low-frequency vibrational modes (LFMs) in three disordered organic solids---amorphous polyisobutylene (PIB), toluene and deuterated toluene glasses, weakly doped with fluorescent chromophore molecules of tetra-tert-butylterrylene (TBT) has been measured via single-molecule (SM) spectroscopy. Analysis of the individual temperature dependences of linewidths of single TBT molecules allowed us to determine the values of the vibrational mode frequencies and the SM-LFM coupling constants for vibrations in the local environment of the molecules. The measured LFM spectra were compared with the ``Boson peak'' as measured in pure PIB by inelastic neutron scattering, in pure toluene glass by low-frequency Raman scattering, in doped toluene glass by nuclear inelastic scattering, and with photon echo data. The comparative analysis revealed close agreement between the spectra of the local vibrations as measured in the present study and the literature data of the Boson peak in PIB and toluene. The analysis has also the important result that weak doping of the disordered matrices with nonpolar probe molecules whose chemical composition is similar to that of the matrix molecules does not influence the observed vibrational dynamics markedly. The experimental data displaying temporal stability on the time scale of a few hours of vibrational excitation parameters in local surroundings was obtained for the first time both for polymer and molecular glass.

Analysis of vibrational coherences in homodyne and two-dimensional heterodyne photon-echo spectra of Nile Blue

We propose a simple model which allows a comprehensive interpretation of the available experimental photon-echo data on Nile Blue. Homodyne signals such as two- and three-pulse photon echo, transient grating and three-pulse peak shift are addressed. An explanation of their time evolution is provided with a single parameter set. A new interpretation of two-dimensional (2D) heterodyne experimental spectra is proposed which emphasizes the strong electron–vibrational coupling of the 590 cm −1 mode of Nile Blue. The model is used for predictions of 2D correlation and relaxation signals monitored with improved resolution (low temperature, short pulse durations). It is argued that such measurements could provide the first experimental detection of the signatures of electron–vibrational coupling in 2D photon-echo spectra.

Appearance of intramolecular high-frequency vibrations in two-dimensional, time-integrated three-pulse photon echo data

An alternative experimental outline to measure homodyne detected three-pulse photon-echo data is presented. The novel experimental approach allowing for online monitoring and correction of experimental timing and stability is discussed in detail using the paradigm system of Nile blue in alcohol solution. It is shown that excellent signal-to-noise ratios together with high reproducibility of the data can be routinely achieved. We report in detail on the appearance of high-frequency intramolecular vibrations in the two-dimensional three-pulse photon-echo data and suggest that besides the conventionally discussed three-pulse photon-echo peak-shift the width of the integrated echo signal as a function of population time contains identical and easily accessible information on high-frequency intramolecular vibrations. A comparison of experimental data with theoretical modeling is performed showing that the observed echo-width oscillations are in line with predictions of the Brownian oscillator model.

Rapid phase-cycled two-dimensional optical spectroscopy in fluorescence and transmission mode

Two dimensional magnetic and optical spectra contain information about structure and dynamics inaccessible to the linear spectroscopist. Recently, phase cycling techniques in optical spectroscopy have extended the capabilities of two-dimensional electronic spectroscopy. Here, we present a method to generate collinear pump/probe pulses at high update rates for two-dimensional electronic spectroscopy. Both fluorescence mode and transmission mode photon echo data from rubidium vapor is presented.

Dynamics of amorphous polymers in the temperature region 2– [formula omitted] where the standard model of low-temperature glasses begin to fail: studies by single molecule spectroscopy and comparison with photon echo data

Spectra of single tetra-tert-butylterrylene molecules incorporated in purely amorphous polyisobutylene matrix have been measured at 2, 4.5 and 7 K (244, 381 and 187 molecules, correspondingly). This is a temperature region, where the main assumptions of the standard two-level system (TLS) model of low-temperature glasses begin to be not valid. At T=2 K the main parameters of most of the registered spectra were found to be consistent with the standard TLS model. At T=4.5 and 7 K some deviations from predictions of this model were observed. The detailed analysis reveals that increasing of temperature leads to additional, in comparison with the predictions of the standard TLS model, line broadening of spectral peaks. This additional line broadening was attributed to the influence of quasi-local low-frequency modes (LFMs) of the amorphous matrix in system under study at T=4.5 and 7 K . Distributions of single spectral peak widths of the detected spectra (the line width distributions) have been calculated and compared with the line width distributions simulated for the same system. Comparative analysis of experimental and simulated distributions allows to evaluate the value of LFM contribution at 4.5 and 7 K . The single molecule spectroscopy data were compared with the literature values of inverse optical dephasing times, 1/ πT 2, as measured for the same system by photon echo (S.J. Zilker et al., J. Chem. Phys. 109 (1998) 6780).

How Fast Is Excitation Energy Transfer in the Photosystem II Reaction Center in the Low Temperature Limit? Hole Burning vs Photon Echo

The Qy(S1) excitonic structure, excitation energy transfer (EET), and primary charge-transfer separation processes of the isolated photosystem II reaction center (PS II RC) have proven to be formidable problems due, in part, to the severe spectral congestion of the So→Qy absorption spectrum. Recently, Prokhorenko and Holzwarth (J. Phys. Chem. B 2000, 104, 11563) reported interesting femtosecond 2-pulse photon echo data on the RC at 1.3 K for excitation wavelengths between 676 and 686 nm. At times longer than ∼1 ps and λ ≳ 678 nm, the echo decay curves are highly dispersive, which was attributed to a distribution of primary charge separation rates ranging from 2 ps to several hundred ps. A prompt subpicosecond component of the echo decay curves was also observed and suggested to be due to EET occurring in ∼100−200 fs. We present here persistent nonphotochemical hole burned spectra and transient triplet bottleneck hole spectra obtained with burn wavelengths between 680 and 686 nm, which show that the EET time in that wavelength region is no shorter than ∼5−10 ps. It is argued that the prompt component of the echo decay curves is due to relaxation of low-frequency phonons excited by the pump pulse. The argument is based on hole burning spectroscopy being the frequency domain equivalent of 2-photon echo spectroscopy, as well as on published photon echo data for chromophores in amorphous hosts.

The underdamped Brownian oscillator model with Ohmic dissipation: Applicability to low-temperature optical spectra

The multimode Brownian oscillator (MBO) model with Ohmic dissipation has frequently been used to interpret photon echo and spectral data on solvation dynamics of chromophores in liquids at room temperature. We report on the applicability of this model to high-resolution linear electronic absorption spectra of chromophores in solid hosts at low temperatures, where the zero-phonon line (ZPL) is resolved from phonon sideband structure. The results are also relevant to frequency and time domain nonlinear spectra. In the MBO model, active BOs (phonons) are linearly coupled to bath modes. This coupling endows the bath modes with absorption intensity which, with Ohmic dissipation (white light spectrum for the bath modes), results in the bath modes contributing to absorption in the region of the ZPL. Experimental results for a multitude of molecular systems indicate that the ZPL profile is determined by electronic dephasing, which is not accounted for in the MBO model. Thus, it is important to assess the contribution of the MBO bath modes to the ZPL profile. To this end, closed-form, finite temperature expressions for the underdamped MBO (UMBO) model are derived for the linear response function, linear absorption spectrum, and width and Franck–Condon factor of the ZPL. It is proven formally that the UMBO ZPL width is zero at T=0 K. Results of calculations for model systems whose parameter values (BO damping constant, frequency and Huang–Rhys factor) are typical of real systems are presented. It is concluded that Ohmic dissipation leads to unphysically large ZPL widths as well as asymmetric ZPL profiles that appear not to have been observed. Moreover, the ZPL width adds to those of the multi-BO (phonon) transitions. Thus, use of the UMBO model with Ohmic dissipation to interpret data on relaxation dynamics of nuclear modes may result in erroneous conclusions. It is shown that Franck–Condon factors of the ZPL obtained with the UMBO model can differ significantly from those calculated with the conventional formula.

Minimal distance between chromophore and two-level systems in amorphous solids: effect on photon echo and single molecule spectroscopy data

We investigated the possible effect of the existence of minimal cutoff distance between two-level system (TLS) and chromophore molecule in glasses on the low-temperature photon echo (PE) and single molecule spectroscopy (SMS) data. Our analysis was based on the tunneling TLS and sudden jump models of glasses. The PE data were considered using the stochastic model of PE in low-temperature glasses as modified by us. Analysis of SMS data was based on the theory of SM line shapes developed by Geva and Skinner [J. Phys. Chem. 101 (1997) 8920]. It was shown that the existence of a minimal approach distance between TLS and chromophore centers results in noticeable changes of the calculated PE and SMS data. These changes increase with increasing of temperature.

Optical dephasing in doped polymers and the soft potential model: analysis of photon echo in doped PMMA

The approach for description of the optical dephasing in doped amorphous solids in the framework of the soft-potential model (SPM) was developed. A procedure for calculation of the homogeneous line width at low temperatures within this model was suggested. The temperature dependencies of the optical dephasing for two amorphous systems, polymethimetacrylate doped with tetra-tert-butylterrylene and zinc-tetraphenylporphine were calculated. Calculations were performed using the parameters known from the literature. The results were compared with the photon echo data for these systems, measured in the broad temperature range. It was found that the SPM describes the temperature behavior of the homogenous line width qualitatively correctly. At temperatures below 2 K, where the main contribution to optical dephasing is associated with tunneling two-level systems, the predicted line width values agree well with the experimental data. At higher temperatures, some difference between the prediction and experimental data was observed and attributed to the effect of impurity on the formation of quasilocal oscillations of the matrix.

Unusual vibrational dynamics of the acetic acid dimer

The vibrational relaxation of the C=O stretching mode of the CH3CO2H cyclic dimer, the CH3CO2D cyclic dimer, and CH3CO2CH3 were measured in CCl4 solution at room temperature. The population relaxation of the v=1 state of the C=O mode is nonexponential, modeled with a biexponential decay having a fast time constant in the subpicosecond regime and a slow time constant of a few picoseconds. For the cyclic dimers of the acetic acids, the fast component dominates the population decay, whereas the slow component dominates the decay of the CH3CO2CH3, the model compound for the monomeric acetic acid. Deuteration of the dimer increases the relaxation time constant. The non-hydrogen-bonding monomer methyl acetate also has a subpicosecond decay constant. The pump–probe anisotropy decay reveals that the orientational dynamics of these molecules also occurs on the subpicosecond time scale and is reasonably well described by rotational diffusion in the slip hydrodynamic limit. Stimulated infrared photon echo decay experiments reveal that the correlation function of the frequency fluctuations of the cyclic acid dimer has a motionally narrowed process described by a 4 ps pure dephasing time and process with a 2.1 ps correlation time, comparable to a solvent response time. The dephasing dynamics is dominated by the population relaxation. In analyzing the photon echo data, the contribution from the rotational diffusion is incorporated by approximating the cyclic acid dimer as a symmetric top diffuser with its transition dipole located in the molecular plane but not parallel to any of the principal axes. General formulas, which will be useful in other applications, for incorporation of the diffusive dynamics of the symmetric top into the third order response functions are obtained. Nonexponential fast vibrational relaxation of C–CO2–X moiety is not adequately described by the anharmonic coupling with the nearby combination and overtone bands. In the regime where the rotational, vibrational, and dephasing times are all comparable, the solvent memory effects may play a role in vibrational dynamics, causing unusually rapid nonexponential population decay.

The mechanism of energy transfer in the antenna of photosynthetic purple bacteria

The mechanism of energy transfer in the antenna system of purple bacteria is investigated by combination of photon echo spectroscopy and disordered exciton theory. In the B800 component of light harvesting complex 2 (LH2), a picture of incoherent hopping between monomers provides an excellent description of the photon echo data recorded as a function of excitation wavelength. In the B850 pigments of LH2, and to a somewhat greater extent in the B875 pigments of light harvesting complex 1 (LH1), the excitation is delocalized over several pigments. The observed dynamics correspond to relaxation between exciton states as a result of exciton–phonon coupling. Nonetheless, a picture of “hopping” between small groups of molecules provides a crude description of the motion of the excitation in B850, and B875. The electronic coupling required to simulate the experimental absorption spectrum and photon echo data is larger in LH1 than in LH2 (B850).

Determining the solvation correlation function from three-pulse photon echoes in liquids

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.

Exciton Dynamics in the Chlorosomal Antennae of the Green Bacteria Chloroflexus aurantiacus and Chlorobium tepidum

The energy transfer processes in isolated chlorosomes from green bacteria Chlorobium tepidum and Chloroflexus aurantiacus have been studied at low temperatures (1.27 K) by two-pulse photon echo and one-color transient absorption techniques with ∼100 fs resolution. The decay of the coherence in both types of chlorosomes is characterized by four different dephasing times stretching from ∼100 fs up to 300 ps. The fastest component reflects dephasing that is due to interaction of bacteriochlorophylls with the phonon bath, whereas the other components correspond to dephasing due to different energy transfer processes such as distribution of excitation along the rod-like aggregates, energy exchange between different rods in the chlorosome, and energy transfer to the base plate. As a basis for the interpretation of the excitation dephasing and energy transfer pathways, a superlattice-like structural model is proposed based on recent experimental data and computer modeling of the Bchl c aggregates (1994. Photosynth. Res. 41:225–233.) This model predicts a fine structure of the Q y absorption band that is fully supported by the present photon echo data.

Photon-echo amplification and regeneration for optical data storage and processing

Optical data storage devices and erasable memories with storage densities in the range of terabits/cm 2, all-optical devices for communication like optical bit-rate converters, routers and image processors can become a reality with photon-echo-based frequency-selective materials. In photon-echo-based optical data storage and data processing the photon-echo-output intensity generally is about 0.1–1% of the input intensity. Many devices, such as processors would require that the photon-echo output is used as an input to a new photon-echo process and hence the amplification of photon-echo signals is necessary. In this paper we describe the development of a fibre amplifier for amplifying photon-echo data. Requirements and performance for the fibre amplifier are discussed. Some examples of our initial experiments, where photon-echoes amplified by the fibre amplifier are used to generate secondary photon-echoes, are also presented.

Nonphotochemical hole burning in Zn-TBP/PMMA. Unusual burning kinetics and very narrow holewidth limit

Nonphotochemical hole burning (NPHB) kinetics was investigated on PMMA samples doped with Zn-TBP molecules. The combination of a very low triplet state saturation threshold of Zn-TBP and a large dispersion of NPHB quantum efficiencies produces very specific hole burning kinetics. The most interesting effects are: (a) very high sensitivity of hole width and burning quantum efficiency to burning power; (b) narrow persistent hole width limit as compared to transient hole burning and 3-pulse photon echo data. The experimental results are interpreted in terms of a kinetic hole burning model which includes a broad distribution of the NPHB quantum efficiencies, the triplet state saturation effect, and the influence of spectral diffusion.

Comparison of photon echo, hole burning, and single molecule spectroscopy data on low-temperature dynamics of organic amorphous solids

A joint analysis of spectroscopic data obtained at liquid–helium temperatures by three line-narrowing techniques, photon echo (PE), persistent hole burning (HB), and single molecule spectroscopy (SMS), is presented. Two polymer systems, polyisobutylene (PIB) and polymethylmethacrylate (PMMA), doped with tetra-tert-butylterrylene (TBT) were studied via PE and HB techniques and the results are compared with literature data [R. Kettner et al., J. Phys. Chem. 98, 6671 (1994); B. Kozankiewicz et al., J. Chem. Phys. 101, 9377 (1994)] obtained by SMS. Both systems behave quite differently. In TBT/PIB a rather strong influence of a dispersion of the dephasing time T2 was found which plays only a minor role in TBT/PMMA. We have also measured the temperature dependence of T2 for both systems in a broad temperature range (0.4–22 K). Using these data we separated the two different contributions to the optical dephasing — due to an interaction with two-level systems and due to coupling with local low-frequency modes. The data are compared with calculations using a numerical and a semianalytical model in the presence of a large dispersion of the single molecule parameters. Furthermore, we discuss the differences of the linewidths as measured by different experimental methods.

Dephasing and diffusional linewidths in spectra of doped amorphous solids: Comparison of photon echo and single molecule spectroscopy data for terrylene in polyethylene

Abstract The concept of “homogeneous” spectral linewidths in doped amorphous solids and some possibilities to separate the linewidth parts related to the optical dephasing and spectral diffusion (SD) are discussed. The results of the model calculations of the photon echo (PE) decay under conditions of a large dispersion of homogeneous linewidths are presented. The deviations of the PE decay from an exponential due to this dispersion are discussed. The experimental data on incoherent PE in the terrylene/polyethylene system are presented and compared with literature single molecule spectroscopy (SMS) data. It is shown that in this case the dephasing time dispersion plays an important role for the linewidth distribution in SMS. A simple method for separation of the dephasing and SD linewidths in the SMS, based on intensity saturation effects, is considered. The facilities of this method using some SMS data are demonstrated.

Influence of laser phase and frequency fluctuations on photon-echo data erasure

Erasure of data stored by use of photon echoes has been investigated as a function of data writing time and data storage time. The results clarify the requirements on laser phase and frequency stability for performing photon-echo data erasure. The analysis of phase and frequency stability of a light source by the photon-echo erasure process is illustrated. A theoretical analysis emphasizing the physical processes that affect the erasure efficiency as well as an extensive discussion of possible error sources are given. Finally, an approach to bit-selective photon-echo data erasure that is insensitive to laser phase and frequency fluctuations is suggested.

Electronic spectral diffusion in glasses: The influence of coupling to the medium on experimental observables

The theory of electronic dephasing in low temperature glasses is extended to include the possibility that the strength of coupling of the chromophore to the solvent medium depends on the nature of the bath dynamical processes and the nature of the chromophore and, therefore, the chromophore-bath coupling can vary as a function of the rate of the dynamics of the medium. In the context of the sudden jump two-level system (TLS) model of low temperature glasses, this theory is used to reconcile the apparent contradiction implied by differences observed in spectral diffusion data for cresyl violet and metal-porphyrins in deuterated ethanol glass at 1.5 K. Previously, the coupling strength of a chromophore to the TLS has been assumed to be independent of rate of the transition between TLS states. Within the context of this approximation, spectral diffusion data yield, Pi(R), the intrinsic TLS fluctuation rate distribution. With the inclusion of the rate dependent coupling, C(R), it is shown that the spectral diffusion observables actually yield Pi(R)C(R). Therefore, the observed lack of spectral diffusion for a particular chromophore over some range of times can imply C(R) is zero rather than the current interpretation that Pi(R) is zero. To illustrate the importance of C(R), a hueristic model is analyzed. A fluctuation rate distribution is introduced that consists of the sum of three log-normal functions each associated with a specific class of dynamics occurring over three overlapping ranges of rates. The uncharged and nonpolar metal porphyrins is taken to couple to TLS strain dipoles, while the charged and polar cresyl violet also couples to TLS electric dipoles. By taking one of the types of TLS dynamics to only give rise to electric dipole fluctuations, it is possible to fit all of the experimental data in deuterated ethanol with a single intrinsic distribution of TLS fluctuation rates. This analysis of previously reported data is supported by the presentation of new stimulated photon echo data on both cresyl violet and zinc meso-tetraphenyl porphine in deuterated ethanol.