Electronic Dephasing Research Articles

Electronic and vibrational coherence effects in broadband transient absorption spectroscopy with chirped supercontinuum probing

The theory of transient absorption with chirped supercontinuum probing is developed for electronic excitation of a vibronic four-level scheme. Dephasing is modeled as homogeneous in the Bloch approximation together with inhomogeneous broadening. The time correction routine for transient spectra is shown to be identical to that of the nonresonant case which was treated previously. Contributions from sequential and coherent terms are calculated and compared to each other. The simulated data reveal how electronic and vibrational dephasing, detuning, and inhomogeneous broadening manifest themselves in the coherent component of femtosecond transient absorption spectra.

Femtosecond photoelectron imaging of pyridazine: S1 lifetime and (3s(n−1),3p(n−1)) Rydberg state energetics

The first real-time study on pyridazine in the S1(n,π*) state is presented. The S1 state is found to dephase with a time constant of 323±17 ps at its origin, and the electronic dephasing mechanism is attributed to the S1–S0 internal conversion. The S1 lifetime is found to decrease rather sharply as the internal energy increases. The 3s (n−1) and 3p (n−1) Rydberg states of pyridazine are clearly identified in angle- and energy-resolved photoelectron images obtained in the (1+2′) photoionization scheme, providing their respective term values of 5.68±0.03 and 6.28±0.04 eV.

Two-Dimensional Analysis of Integrated Three-Pulse Photon Echo Signals of Nile Blue Doped in PMMA

The integrated three-pulse photon echo signal of Nile blue doped in poly(methyl methacrylate) (PMMA) was measured two-dimensionally by varying the first coherence period and the subsequent population period. The electronic dephasing time was in the femtosecond time range even at low temperatures, whereas rephasing and echo formation were still possible even when the population period was extended to >100 ps. Oscillation was present in the echo signal even when population period was extended to longer values than the dephasing time of the vibrational coherence. Echo peak shift measurement indicated a presence of small spectral diffusion in the picosecond time range. A computer simulation was carried out from a model spectral density. The phonon mode of PMMA was represented by a Brownian oscillator centered at ∼116 cm-1, and it reproduced the temperature dependence of the echo signal surprisingly well.

Effects of anharmonicity and electronic coupling on photoinduced electron transfer in mixed valence compounds

We develop a semigroup model of electron transfer (ET) dynamics in mixed valence compounds. This model is useful for investigating the effects of anharmonicity in inner sphere nuclear modes, as well as the dependence of the electronic dynamics on the nature of the electronic coupling. Two effective “subsystem” nuclear vibrations are treated explicitly in the model, to account for the rapid electronic energy gap fluctuations induced by the inner sphere vibrations. The essentially Markovian effects of the remaining “bath” modes are approximated by semigroups. We find that including the anharmonicity in inner sphere vibrations leads to a very small increase in the rate of ET. This effect is due to the change in reactant and product vibronic states when anharmonicity is included, as well as the rapid electronic dephasing induced by the bath. An assumption of strong electronic coupling is found to be sufficient to explain experimentally observed ET rates, but the possible role of conical intersections in ultrafast ET reactions is also noted.

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.

Pump–probe polarization anisotropy study of doubly degenerate electronic reorientation in silicon naphthalocyanine

Measurements with 26 fs pulses that cover the Q(0–0) band of silicon 2,3-naphthalocyanine bis(trihexylsilyloxide) yielded an initial anisotropy of 0.40 that decayed to 0.12 over 200 fs. This contradicts theories predicting anisotropy decay from 7/10 to 1/10. Including ground state bleaching and excited state absorption, anisotropy decay from 2/5 to 1/10 is predicted for degenerate electronic reorientation and dephasing.

Scattering matrix approach to electronic dephasing in long-range electron transfer

Based on the Büttiker dephasing model, we propose an analytical scattering matrix approach to the long-range electron transfer phenomena. The present efficient scheme smoothly interpolates between the superexchange and the sequential hopping mechanisms. Various properties such as the drastic dephasing-assisted enhancement and turnover behaviors are demonstrated in good agreement with those obtained via the dynamical reduced density-matrix methods. These properties are further elucidated as results of the interplay among the dephasing strength, the tunneling parameter, and the bridge length of the electron transfer system.

Resonance Raman and ab Initio Studies of the Electronic Transitions of Aqueous Azide Anion

Resonance Raman spectra and absolute cross sections have been measured for the azide anion (N3-) in dilute aqueous solution at excitation wavelengths of 246, 228, 223, 218, and 208 nm, on resonance with the longest-wavelength UV absorption bands. The spectra are dominated by the fundamental of the 1343 cm-1 symmetric stretch, with much lower intensities in the first overtone of the symmetric stretch and the overtone of the bending mode at 1275 cm-1. The weak overtones and generally low resonance Raman cross sections suggest unusually small changes in the N−N bond lengths relative to those expected for valence transitions of small molecules, and/or particularly strong coupling of the electronic transitions to solvent degrees of freedom leading to rapid effective electronic dephasing. Ab initio calculations have been performed on complexes of N3- with three and four water molecules at the single CI level using the 6-311++g** basis with additional diffuse functions on the N atoms. These calculations predict ...

Description of the coherent and incoherent processes in two-photon photoemission on Cu(111) surface

Two-photon photoemission spectroscopy is now widely used, to determine the ultrafast dynamics of the electrons pertaining to the surface states. In the particular case of the Cu(111) surface, the energy spectrum exhibits two main resonances termed n=1 and n=0. The dependence of the two-photon photoemission signal as a function of the delay time between the pump and the probe laser pulses is well understood in the case n=1 and can be explained in terms of two consecutive population processes. However, the corresponding dependence for the second resonance n=0, slightly shifted from the first one by an amount corresponding to the frequency difference between the pump field frequency and the image potential to intrinsic state transition frequency, has frequently been interpreted in terms of a non-resonant excitation from the intrinsic surface state. Here, we show that the process underlying this resonance is a purely coherent process resulting from the overlapping of the laser pulses. The influence of the surface state lifetime and its corresponding electronic dephasing constants enable us to recover the purely symmetric shape of the cross-correlation function. From the fit, lifetime and dephasing constants of the image potential state are evaluated.

Chirped pulse excitation in condensed phases involving intramolecular modes studied by double-sided Feynman diagrams for fast optical dephasing

The effect of the quantum intramolecular modes on the chirped pulse excitation in condensed phase has been studied. Nonperturbative equations for the populations of molecular electronic states under the action of intense chirped pulses have been obtained using the double-sided Feynman diagrams. We have shown that the application of this technique to systems with fast electronic dephasing enables us to include strong system–bath interactions (non-Markovian relaxation) and to perform the summation of diagrams. We have studied the influence of the chirp rate on the integral population of the excited state n2 after the completion of pulse action. We have shown that the effect of the quantum intramolecular modes strongly depends on the carrier pulse frequency. Incorporating these modes increases n2 when a molecule is excited near the 0→1 transition with respect to the quantum intramolecular vibration. If the molecule is excited near the 0→0 transition with respect to the intramolecular mode, the effect is opposite.

Molecular π pulses: Population inversion with positively chirped short pulses

Detailed theoretical analysis and numerical simulation indicate that nearly complete electronic population inversion of molecular systems can be achieved with intense positively chirped broadband laser pulses. To provide a simple physical picture, a two-level model is used to examine the condition for the so-called π pulses and a four-level model is designed to demonstrate for molecular systems the correlation between the sign of the chirp and the excited state population. The proposed molecular π pulse is the combined result of vibrational coherence in the femtosecond regime and adiabatic inversion in the picosecond regime. Numerical results for a displaced oscillator, for LiH and for I2, show that the proposed molecular π pulse scheme is robust with respect to changes in field parameters such as the linear positive chirp rate, field intensity, bandwidth, and carrier frequency, and is stable with respect to thermal and condensed phase conditions including molecular rotation, rovibronic coupling, and electronic dephasing.

Diagram Technique for Nonlinear Optical Spectroscopy in the Fast Electronic Dephasing Limit

AbstractWe show that applying the double‐sided Feynman diagrams to systems with fast electronic dephasing opens up new possibilities for using this technique in resonance nonlinear optical spectroscopy. The novel potentials are including non‐perturbative system‐bath interactions (non‐Markovian relaxation) and the summation of diagrams. The last procedure enables us to obtain new equations for a nonperturbative description of the light‐matter interaction.

The effect of inhomogeneous broadening on optical strong field spectroscopy

We show that a recent theory of strong field spectroscopy (SFS) [R. I. Cukier and M. Morillo, Phys. Rev. B 57, 6972 (1998), M. Morillo and R. I. Cukier, J. Chem. Phys. 110, 7966 (1999)] can be used to circumvent the effects of inhomogeneous broadening on this spectroscopy. In SFS, a strong external field is used to connect, with the transition dipole, two electronic states of a solute immersed in a medium. The electronic dephasing due to the medium is characterized via the power absorbed by the solute. The average absorbed power P̄(t) for resonant, strong fields exhibits an oscillatory decay in time, reflecting the finite change in the population difference of the electronic states and the dephasing arising from the coupling to the medium. The decay rate is characterized by d≡Δ2τc, where Δ and τc are, respectively, the strength and time constant of the correlation function characterizing the solute–medium coupling. The decay can be very rapid, on a 10–100 fs time scale, and this necessitates an indirect procedure to experimentally probe P̄(t) that we develop. For strong, off-resonance fields, P̄(t) returns to an exponential decay regime. The contrasting behavior of resonant and nonresonant strong fields can be used to avoid the loss of information about the homogeneous properties due to inhomogeneous broadening of the optical transition, when this broadening arises from inhomogeneity in the optical transition frequency.

Electronic Dephasing in the Quantum Hall Regime

By means of degenerate four-wave mixing (FWM), we investigate the quantum coherence of electron-hole pairs in the presence of a two-dimensional electron gas in modulation-doped GaAs-AlGaAs quantum wells in the quantum Hall effect regime. With increasing magnetic field, we observe a crossover from Markovian to non-Markovian behavior, as well as large jumps in the decay time of the FWM signal at even Landau level filling factors. The main observations can be qualitatively reproduced by a model which takes into account scattering by the collective excitations of the two-dimensional electron gas.

An adiabatic picture for electron transfer in mixed-valence systems

An adiabatic picture is proposed to analyze short-time electronic coherence and dephasing in mixed-valence systems, which cannot be described by the Redfield equation or the golden-rule rate theory. In this picture, electronic coherence arises from Rabi oscillations between two adiabatic surfaces and decays as a result of inhomogeneous distributions and thermal fluctuations of Rabi frequencies. The initial preparation and wavepacket dynamics modulate Rabi oscillations and thus influence electronic coherence. Comparisons between exact numerical results and the prediction from the proposed theory verify the accuracy of the adiabatic approximation in describing the short-time electronic dynamics.

The effect of a strong external field on the electronic dephasing of a solute that is strongly coupled to a solvent

A recent theory of strong field spectroscopy (SFS) [R. I. Cukier and M. Morillo, Phys. Rev. B 57, 6972 (1998), M. Morillo and R. I. Cukier, J. Chem. Phys. (110, 7966 (1999)] is generalized to apply to strong solute–solvent coupling. In SFS, a strong external field is used to connect, with the transition dipole, two electronic states of a solute immersed in a medium. In contrast to weak fields, z̄(t), the average population difference of the solute electronic states is changing significantly. For resonant, strong fields, z̄(t) and the average absorbed power, P̄(t), exhibit oscillatory decays in time that reflect the changing z̄(t) and the dissipation arising from the coupling to the medium. When the solute–solvent coupling is relatively weak, the time evolution of the solvent only depends on the initial solute state (autonomous behavior). In this work, appropriate to strong coupling, we derive an equation of motion for the solvent dynamics that depends on the solute’s instantaneous state (nonautonomous behavior). The consequences to z̄(t) and P̄(t) are explored. We find that instead of equalizing the solute populations at long times, now the population is inverted relative to its initial state. We also find that the degree of long-time population inversion can be controlled by turning off the external field before the system has fully relaxed.

Femtosecond time-resolved photoelectron imaging on ultrafast electronic dephasing in an isolated molecule

Ultrafast dephasing in an intermediate case of molecular radiationless transition has been visualized for the first time by femtosecond time-resolved photoelectron imaging. The decay of photoexcited S1(n,π*) state of pyrazine in 100 ps and the corresponding build-up of triplet states were clearly observed.

Disordered Exciton Model for the Core Light-Harvesting Antenna of Rhodopseudomonas viridis

In this work we explain the spectral heterogeneity of the absorption band (Monshouwer et al., 1995. Biochim. Biophys. Acta. 1229:373–380), as well as the spectral evolution of pump-probe spectra for membranes of Rhodopseudomonas ( Rps.) viridis. We propose an exciton model for the LH1 antenna of Rps. viridis and assume that LH1 consists of 24–32 strongly coupled BChl b molecules that form a ring-like structure with a 12- or 16-fold symmetry. The orientations and pigment-pigment distances of the BChls were taken to be the same as for the LH2 complexes of BChl a–containing bacteria. The model gave an excellent fit to the experimental results. The amount of energetic disorder necessary to explain the results could be precisely estimated and gave a value of 440–545 cm −1 (full width at half-maximum) at low temperature and 550–620 cm −1 at room temperature. Within the context of the model we calculated the coherence length of the steady-state exciton wavepacket to correspond to a delocalization over 5–10 BChl molecules at low temperature and over 4–6 molecules at room temperature. Possible origins of the fast electronic dephasing and the observed long-lived vibrational coherence are discussed.

Wavelength-resolved stimulated photon echoes: Direct observation of ultrafast intramolecular vibrational contributions to electronic dephasing

Novel wavelength-resolved stimulated photon echo measurements on a dye molecule in solution are presented. Data are simulated within the multimode Brownian oscillator model using the spectral density of de Boeij et al. [J. Phys. Chem. 100, 11806 (1996)] for the same solute–solvent system. For photon echo population times <50 fs there are considerable differences between the measured and calculated data. Aided by further simulations, we conclude that these discrepancies result from dephasing dynamics of high frequency intramolecular vibrational modes not included in the previously derived spectral density.

Influence of the pure vibrational dephasing processes on the dip structure in pumped sum-frequency generation spectroscopy

Recent theoretical analysis of infrared-visible pumped sum-frequency spectroscopy on adsorbed molecules exhibits a dip structure on the frequency dependence of the sum-frequency signal intensity. To get more physical insight into this dip, which has not yet been observed experimentally, we present a unified description capable of handling, on the same footing, steady-state and pulsed experiments. Contrary to previous treatments, this description is valid for any duration of the dephasing times. Therefore, it enables a detailed discussion about the origin of the dip, as well as a determination of the conditions of its observability. These conditions are, in fact, very sensitive to the pure vibrational dephasing processes. In the nonresonant conditions, usually adopted in these experiments for the visible probe beam, the pure electronic dephasing does not affect the dip structure and the underlying dynamics. However, if the visible probe beam becomes resonant with the electronic transition, the pure electronic dephasing introduces a strong asymmetry of the dip.