Ultrafast Nonlinear Spectroscopic Techniques in the Gas Phase and Their Density Matrix Representation

Two-Dimensional Infrared Spectroscopy of Isolated Molecular Ions

Two-dimensional infrared (2D IR) spectroscopy of mass-selected, cryogenically cooled molecular ions is presented. Nonlinear response pathways, encoded in the time-domain photodissociation action response of weakly bound N2 messenger tags, were isolated using pulse shaping techniques following excitation with four collinear ultrafast IR pulses. 2D IR spectra of Re(CO)3(CH3CN)3+ ions capture off-diagonal cross-peak bleach signals between the asymmetric and symmetric carbonyl stretching transitions. These cross peaks display intensity variations as a function of pump-probe delay time due to coherent coupling between the vibrational modes. Well-resolved 2D IR features in the congested fingerprint region of protonated caffeine (C8H10N4O2H+) are also reported. Importantly, intense cross-peak signals were observed at 3 ps waiting time, indicating that tag-loss dynamics are not competing with the measured nonlinear signals. These demonstrations pave the way for more precise studies of molecular interactions and dynamics that are not easily obtainable with current condensed-phase methodologies.

Ultrafast transient vibrational action spectroscopy of cryogenically cooled ions

Ultrafast transient vibrational action spectra of cryogenically cooled Re(CO)3(CH3CN)3+ ions are presented. Nonlinear spectra were collected in the time domain by monitoring the photodissociation of a weakly bound N2 messenger tag as a function of delay times and phases between a set of three infrared pulses. Frequency-resolved spectra in the carbonyl stretch region show relatively strong bleaching signals that oscillate at the difference frequency between the two observed vibrational features as a function of the pump-probe waiting time. This observation is consistent with the presence of nonlinear pathways resulting from underlying cross-peak signals between the coupled symmetric-asymmetric C≡O stretch pair. The successful demonstration of frequency-resolved ultrafast transient vibrational action spectroscopy of dilute molecular ion ensembles provides an exciting, new framework for the study of molecular dynamics in isolated, complex molecular ion systems.

Time-Domain Vibrational Action Spectroscopy of Cryogenically Cooled, Messenger-Tagged Ions Using Ultrafast IR Pulses

Herein, we present the initial steps toward developing a framework that will enable the characterization of photoinitiated dynamics within large molecular ions in the gas phase with temporal and energy resolution. We combine the established techniques of tag-loss action spectroscopy on cryogenically trapped molecular ions with ultrafast vibrational spectroscopy by measuring the linear action spectrum of N₂-tagged protonated diglycine (GlyGlyH⁺·N₂) with an ultrafast infrared (IR) pulse pair. The presented time-domain data demonstrate that the excited-state vibrational populations in the tagged parent ions are modulated by the ultrafast IR pulse pair and encoded through the messenger tag-loss action response. The Fourier transform of the time-domain action interferograms yields the linear frequency-domain vibrational spectrum of the ion ensemble, and we show that this spectrum matches the linear spectrum collected in a traditional manner using a frequency-resolved IR laser. Time- and frequency-domain interpretations of the data are considered and discussed. Finally, we demonstrate the acquisition of nonlinear signals through cross-polarization pump-probe experiments. These results validate the prerequisite first steps of combining tag-loss action spectroscopy with two-dimensional IR spectroscopy for probing dynamics in gas-phase molecular ions.

Linear and Nonlinear Optical Processes Controlling S2 and S1 Dual Fluorescence in Cyanine Dyes

We report on the changes in the dual fluorescence of two cyanine dyes IR144 and IR140 as a function of viscosity and probe their internal conversion dynamics from S₂ to S₁ via their dependence on a femtosecond laser pulse chirp. Steady-state and time-resolved measurements performed in methanol, ethanol, propanol, ethylene glycol, and glycerol solutions are presented. Quantum calculations reveal the presence of three excited states responsible for the experimental observations. Above the first excited state, we find an excited state, which we designate as S₁', that relaxes to the S₁ minimum, and we find that the S₂ state has two stable configurations. Chirp-dependence measurements, aided by numerical simulations, reveal how internal conversion from S₂ to S₁ depends on solvent viscosity and pulse duration. By combining solvent viscosity, transform-limited pulses, and chirped pulses, we obtain an overall change in the S₂/S₁ population ratio of a factor of 86 and 55 for IR144 and IR140, respectively. The increase in the S₂/S₁ ratio is explained by a two-photon transition to a higher excited state. The ability to maximize the population of higher excited states by delaying or bypassing nonradiative relaxation may lead to the increased efficiency of photochemical processes.

Nonlinear light absorption in many-electron systems excited by an instantaneous electric field: a non-perturbative approach

Applications of low-cost non-perturbative approaches in real time, such as time-dependent density functional theory, for the study of nonlinear optical properties of large and complex systems are gaining increasing popularity. However, their assessment still requires the analysis and understanding of elementary dynamical processes in simple model systems. Motivated by the aim of simulating optical nonlinearities in molecules, here exemplified by the case of the quaterthiophene oligomer, we investigate light absorption in many-electron interacting systems beyond the linear regime by using a single broadband impulse of an electric field; i.e. an electrical impulse in the instantaneous limit. We determine non-pertubatively the absorption cross section from the Fourier transform of the time-dependent induced dipole moment, which can be obtained from the time evolution of the wavefunction. We discuss the dependence of the resulting cross section on the magnitude of the impulse and we highlight the advantages of this method in comparison with perturbation theory by working on a one-dimensional model system for which numerically exact solutions are accessible. Thus, we demonstrate that the considered non-pertubative approach provides us with an effective tool for investigating fluence-dependent nonlinear optical excitations.

Delocalized excitons and interaction effects in extremely dilute thermal ensembles

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy. Delocalized excitons are detected in the atomic systems at particle densities where the mean interatomic distance (>10 μm) is much greater than the laser wavelength and multi-particle coherences should destructively interfere over the ensemble average. With a combined experimental and theoretical analysis, we identify an effective interaction mechanism, presumably of dipolar nature, as the origin of the excitonic signals. Our study implies that even in highly-dilute thermal atom ensembles, significant transition dipole-dipole interaction networks may form that require advanced modeling beyond the nearest neighbor approximation to quantitatively capture the details of their many-body properties.

Excited State Vibrational Spectra of All- trans Retinal Derivatives in Solution Revealed By Pump-DFWM Experiments

The ultrafast structural changes during the photoinduced isomerization of the retinal-protonated Schiff base (RPSB) is still a poorly understood aspect in the retinal's photochemistry. In this work, we apply pump-degenerate four-wave mixing (pump-DFWM) to all- trans retinal (ATR) and retinal Schiff bases (RSB) to resolve coherent high- and low-frequency vibrational signatures from excited electronic states. We show that the vibrational spectra of excited singlet states in these samples exhibit pronounced differences compared to the relaxed ground state. Pump-DFWM results indicate three major features for ATR and RSB. (i) Excited state vibrational spectra of ATR and RSB consist predominately of low-frequency modes in the energetic range 100-500 cm^-1. (ii) Excited state vibrational spectra show distinct differences for excitation in specific regions of electronic transitions of excited state absorption and emission. (iii) Low-frequency modes in ATR and RSB are inducible during the entire lifetime of the excited electronic states. This latter effect points to a transient molecular structure that, following initial relaxation between different excited electronic states, does not change anymore over the lifetime of the finally populated excited electronic state.

Ultrafast structural molecular dynamics investigated with 2D infrared spectroscopy methods

Ultrafast, multi-dimensional infrared (IR) spectroscopy has been advanced in recent years to a versatile analytical tool with a broad range of applications to elucidate molecular structure on ultrafast timescales, and it can be used for samples in a many different environments. Following a short and general introduction on the benefits of 2D IR spectroscopy, the first part of this chapter contains a brief discussion on basic descriptions and conceptual considerations of 2D IR spectroscopy. Outstanding classical applications of 2D IR are used afterwards to highlight the strengths and basic applicability of the method. This includes the identification of vibrational coupling in molecules, characterization of spectral diffusion dynamics, chemical exchange of chemical bond formation and breaking, as well as dynamics of intra- and intermolecular energy transfer for molecules in bulk solution and thin films. In the second part, several important, recently developed variants and new applications of 2D IR spectroscopy are introduced. These methods focus on (i) applications to molecules under two- and three-dimensional confinement, (ii) the combination of 2D IR with electrochemistry, (iii) ultrafast 2D IR in conjunction with diffraction-limited microscopy, (iv) several variants of non-equilibrium 2D IR spectroscopy such as transient 2D IR and 3D IR, and (v) extensions of the pump and probe spectral regions for multi-dimensional vibrational spectroscopy towards mixed vibrational-electronic spectroscopies. In light of these examples, the important open scientific and conceptual questions with regard to intra- and intermolecular dynamics are highlighted. Such questions can be tackled with the existing arsenal of experimental variants of 2D IR spectroscopy to promote the understanding of fundamentally new aspects in chemistry, biology and materials science. The final part of the chapter introduces several concepts of currently performed technical developments, which aim at exploiting 2D IR spectroscopy as an analytical tool. Such developments embrace the combination of 2D IR spectroscopy and plasmonic spectroscopy for ultrasensitive analytics, merging 2D IR spectroscopy with ultra-high-resolution microscopy (nanoscopy), future variants of transient 2D IR methods, or 2D IR in conjunction with microfluidics. It is expected that these techniques will allow for groundbreaking research in many new areas of natural sciences.

Accurate gas-phase structure of para-dioxane by fs Raman rotational coherence spectroscopy and ab initio calculations

p-Dioxane is non-polar, hence its rotational constants cannot be determined by microwave rotational coherence spectroscopy (RCS). We perform high-resolution gas-phase rotational spectroscopy of para-dioxane-h₈ and -d₈ using femtosecond time-resolved Raman RCS in a gas cell at T = 293 K and in a pulsed supersonic jet at T∼130 K. The inertial tensor of p-dioxane-h₈ is strongly asymmetric, leading to a large number of asymmetry transients in its RCS spectrum. In contrast, the d₈-isotopomer is a near-oblate symmetric top that exhibits a much more regular RCS spectrum with few asymmetry transients. Fitting the fs Raman RCS transients of p-dioxane-h₈ to an asymmetric-top model yields the ground-state rotational constants A₀ = 5084.4(5) MHz, B₀ = 4684(1) MHz, C₀ = 2744.7(8) MHz, and (A₀ + B₀)/2 = 4884.5(7) MHz (±1σ). The analogous values for p-dioxane-d₈ are A₀ = 4083(2) MHz, B₀ = 3925(4) MHz, C₀ = 2347.1(6) MHz, and (A₀ + B₀)/2 = 4002.4(6) MHz. We determine the molecular structure with a semi-experimental approach involving the highly correlated coupled-cluster singles, doubles and iterated triples method and the cc-pCVXZ basis set series from double- to quadruple-zeta (X = D, T, Q). Combining the calculated vibrationally averaged rotational constants A₀^calc(X),B₀^calc(X),C₀^calc(X) for increasing basis-set size X with non-linear extrapolation to the experimental constants A₀^exp,B₀^exp,C₀^exp allows to determine the equilibrium ground state structure of p-dioxane. For instance, the equilibrium C-C and C-O bond lengths are r_e(CC) = 1.5135(3) Å and r_e(CO) = 1.4168(4) Å, and the four axial C-H bond lengths are 0.008 Å longer than the four equatorial ones. The latter is ascribed to the trans-effect (anomeric effect), i.e., the partial delocalization of the electron lone-pairs on the O atoms that are oriented trans, relative to the axial CH bonds.

Two-color vibrational, femtosecond, fully resonant electronically enhanced CARS (FREE-CARS) of gas-phase nitric oxide

A resonantly enhanced, two-color, femtosecond time-resolved coherent anti-Stokes Raman scattering (CARS) approach is demonstrated and used to explore the nature of the frequency- and time-dependent signals produced by gas-phase nitric oxide (NO). Through careful selection of the input pulse wavelengths, this fully resonant electronically enhanced CARS (FREE-CARS) scheme allows rovibronic-state-resolved observation of time-dependent rovibrational wavepackets propagating on the vibrationally excited ground-state potential energy surface of this diatomic species. Despite the use of broadband, ultrafast time-resolved input pulses, high spectral resolution of gas-phase rovibronic transitions is observed in the FREE-CARS signal, dictated by the electronic dephasing timescales of these states. Analysis and computational simulation of the time-dependent spectra observed as a function of pump-Stokes and Stokes-probe delays provide insight into the rotationally resolved wavepacket motion observed on the excited-state and vibrationally excited ground-state potential energy surfaces of NO, respectively.

Rotational constants and structure of para-difluorobenzene determined by femtosecond Raman coherence spectroscopy: A new transient type

Femtosecond Raman rotational coherence spectroscopy (RCS) detected by degenerate four-wave mixing is a background-free method that allows to determine accurate gas-phase rotational constants of non-polar molecules. Raman RCS has so far mostly been applied to the regular coherence patterns of symmetric-top molecules, while its application to nonpolar asymmetric tops has been hampered by the large number of RCS transient types, the resulting variability of the RCS patterns, and the 10(3)-10(4) times larger computational effort to simulate and fit rotational Raman RCS transients. We present the rotational Raman RCS spectra of the nonpolar asymmetric top 1,4-difluorobenzene (para-difluorobenzene, p-DFB) measured in a pulsed Ar supersonic jet and in a gas cell over delay times up to ∼2.5 ns. p-DFB exhibits rotational Raman transitions with ΔJ = 0, 1, 2 and ΔK = 0, 2, leading to the observation of J -, K -, A -, and C-type transients, as well as a novel transient (S-type) that has not been characterized so far. The jet and gas cell RCS measurements were fully analyzed and yield the ground-state (v = 0) rotational constants A0 = 5637.68(20) MHz, B0 = 1428.23(37) MHz, and C0 = 1138.90(48) MHz (1σ uncertainties). Combining the A0, B0, and C0 constants with coupled-cluster with single-, double- and perturbatively corrected triple-excitation calculations using large basis sets allows to determine the semi-experimental equilibrium bond lengths re(C1-C2) = 1.3849(4) Å, re(C2-C3) = 1.3917(4) Å, re(C-F) = 1.3422(3) Å, and re(C2-H2) = 1.0791(5) Å.

Single-shot thermometry and OH detection via femtosecond fully resonant electronically enhanced CARS (FREE-CARS)

Femtosecond time-resolved, fully resonant electronically enhanced coherent anti-Stokes Raman scattering (FREE-CARS) spectroscopy, incorporating a two-color excitation scheme, is used to demonstrate selective and sensitive gas-phase detection of the hydroxyl (OH) radical in a reacting flow. Spectral resolution of the emitted FREE-CARS signal allows simultaneous detection of temperature and relative OH mole fraction under single-laser-shot conditions in a laminar ethylene-air flame. By comparison to previously reported OH concentration and temperature measurements, we demonstrate excellent single-shot temperature accuracies (∼2% deviation from adiabatic flame temperature) and precisions (∼2% standard deviation), with simultaneous relative OH concentration measurements that demonstrate high detection sensitivity (100-300 ppm).

Ultrafast time-resolved vibrational spectroscopies of carotenoids in photosynthesis

This review discusses the application of time-resolved vibrational spectroscopies to the studies of carotenoids in photosynthesis. The focus is on the ultrafast time regime and the study of photophysics and photochemistry of carotenoids by femtosecond time-resolved stimulated Raman and four-wave mixing spectroscopies. This article is part of a Special Issue entitled: Vibrational spectroscopies and bioenergetic systems.

Cascading and local-field effects in non-linear optics revisited: a quantum-field picture based on exchange of photons

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).

Laser-induced alignment and anti-alignment of rotationally excited molecules

We numerically investigate the post-pulse alignment of rotationally excited diatomic molecules upon nonresonant interaction with a linearly polarized laser pulse. In addition to the simulations, we develop a simple model which qualitatively describes the shape and amplitude of post-pulse alignment induced by a laser pulse of moderate power density. In our treatment we take into account that molecules in rotationally excited states can interact with a laser pulse not only by absorbing energy but also by stimulated emission. The extent to which these processes are present in the interaction depends, on the one hand, on the directionality of the molecular angular momentum (given by the M quantum number), and on the other hand on the ratio of transition frequencies and pulse duration (determined by the J number). A rotational wave packet created by a strong pulse from an initially pure state contains a broad range of rotational levels, over which the character of the interaction can change from non-adiabatic to adiabatic. Depending on the laser pulse duration and amplitude, the transition from the non-adiabatic to the adiabatic limit proceeds through a region with dominant rotational heating, or alignment, for short pulses and a large region with rotational cooling, and correspondingly preferred anti-alignment, for longer pulses.

Accurate determination of the structure of cyclohexane by femtosecond rotational coherence spectroscopy and ab initio calculations

We combine femtosecond time-resolved rotational coherence spectroscopy with high-level ab initio theory to obtain accurate structural information for the nonpolar molecules cyclohexane (C(6)H(12)) and cyclohexane-d(12) (C(6)D(12)). We measured the rotational B(0) and centrifugal distortion constants D(J), D(JK) of the v = 0 states of C(6)H(12) and C(6)D(12) to high accuracy, for example, B(0)(C(6)H(12)) = 4306.08(5) MHz, as well as B(v) for the vibrationally excited states ν(32), ν(6), ν(16) and ν(24) of C(6)H(12) and additionally ν(15) for C(6)D(12). To successfully reproduce the experimental RCS transient, the overtone and combination levels 2ν(32), 3ν(32), ν(32) + ν(6), and ν(32) + ν(16) had to be included in the RCS model calculations. The experimental rotational constants are compared to those obtained at the second-order Møller-Plesset (MP2) level. Combining the experimental and calculated rotational constants with the calculated equilibrium bond lengths and angles allows determination of accurate semiexperimental equilibrium structure parameters, for example, r(e)(C-C) = 1.526 ± 0.001 Å, r(e)(C-H(axial)) = 1.098 ± 0.001 Å, and r(e)(C-H(equatorial)) = 1.093 ± 0.001 Å. The equilibrium C-C bond length of C(6)H(12) is only 0.004 Å longer than that of ethane. The effect of ring strain due to the unfavorable gauche interactions is mainly manifested as small deviations from the C-C-C, C-C-H(axial), and C-C-H(equatorial) angles from the tetrahedral value.

Enhancement of vibrational coherence by femtosecond degenerate four-wave-mixing for a chromophore in 1-propanol glass

The enhancement effect of vibrational coherence by femtosecond degenerate four-wave-mixing (DFWM) technique was investigated with a dye, NK-2990, doped in low temperature 1-propanol glass. The strongest enhancement was observed with the delay between the first and the second pulses, t(13), set at about quarter of the oscillation period, which does not coincide with the theoretical prediction of half the period. One of the enhanced vibrational modes at ca. 90 cm(-1) became significantly broader below the glass transition temperature, indicating its sensitivity towards microscopic viscosity of the environment.

Linear and nonlinear optical responses in bacteriochlorophyll a

Nonlinear optical responses of bacteriochlorophyll a (BChl a) were investigated by means of the three-pulse four-wave mixing (FWM) technique under the resonant excitation into the Q ( y ) band. The experimental results are explained by a theoretical model calculation including the Brownian oscillation mode of the solvent. We have determined the spectral density, which is the most important function with which to calculate optical signals. The linear absorption spectrum can be reproduced fairly well when the vibronic oscillation modes of the solvent together with those of BChl a are properly taken into consideration. The FWM signal was also calculated using the spectral density. It was found that a simple two-level model could not explain the experimental result. The effect of the higher-order interactions is discussed.

Bichromatic, phase compensating interferometer based on prism pair compressors

We present a bichromatic prism pair interferometer (BPPI) for controlling the delay between laser pulses of two different frequencies propagating collinearly in a single beam. The BPPI is especially useful when working with ultrafast laser pulses because it intrinsically allows for independent control over the second-order dispersion experienced by the differently colored pulses. We use this control to demonstrate successful precompensation for blue (lambda approximately 390 nm) and UV (lambda approximately 260 nm) pulses that pass through 2.2 cm of dispersive material after the interferometer. The BPPI is extremely flexible and works with all frequencies from the UV to the near-infrared. We demonstrate this by describing measurements made with BPPIs configured for three different combinations of central frequencies.

Femtosecond degenerate four-wave mixing of carbon disulfide: High-accuracy rotational constants

Femtosecond degenerate four-wave mixing (fs-DFWM) rotational coherence spectroscopy (RCS) has been used to determine the rotational and centrifugal distortion constants of the 00 (0)0 ground and 01 (1)0 vibrationally excited states of gas-phase CS(2). RCS transients were recorded over the 0-3300 ps optical delay range, allowing the observation of 87 recurrences. The fits yield rotational constants B(00 (0)0)=3.271 549 2(18) GHz for (12)C(32)S(2) and B(00 (0)0)=3.175 06(21) GHz for the (12)C(32)S(34)S isotopomer. The rotational constants of the degenerate 01 (1)0 bending level of (12)C(32)S(2) are B(01 (1)0)=3.276 72(40) and 3.279 03(40) GHz for the e and f substrates, respectively. These fs-DFWM rotational constants are ten times more accurate than those obtained by CO(2) laser/microwave heterodyne measurements and are comparable to those obtained by high-resolution Fourier transform infrared spectroscopy. Ab initio calculations were performed at two levels, second-order Moller-Plesset theory and coupled-cluster singles, doubles, and iterative triples [CCSD(T)]. The equilibrium and vibrationally averaged C=S distances were calculated using large Dunning basis sets. An extrapolation procedure combining the ab initio rotational constants with the experiment yields an equilibrium C=S bond length of 155.448 pm to an accuracy of +/-20 fm. The theoretical C=S bond length obtained by a complete basis set extrapolation at the CCSD(T) level is r(e)(C=S)=155.579 pm, or 0.13 pm longer than that in the experiment.

Systematic Control of Nonlinear Optical Processes Using Optimally Shaped Femtosecond Pulses

This article reviews experimental efforts to control multiphoton transitions using shaped femtosecond laser pulses, and it lays out the systematic study being followed by us for elucidating the effect of phase on nonlinear optical laser-molecule interactions. Starting with a brief review of nonlinear optics and how nonlinear optical processes depend on the electric field inducing them, a number of conclusions can be drawn directly from analytical solutions of the equations. From a Taylor expansion of the phase in the frequency domain, we learn that nonlinear optical processes are affected only by the second- and higher-order terms. This simple result has significant implications on how pulse-shaping experiments are to be designed. If the phase is allowed to vary arbitrarily as a continuous function, then an infinite redundancy that arises from the addition of a linear phase function across the spectrum with arbitrary offset and slope could prevent us from carrying out a closed-loop optimization experiment. The early results illustrate how the outcome of a nonlinear optical transition depends on the cooperative action of all frequencies in the bandwidth of a laser pulse. Maximum constructive or destructive interference can be achieved by programming the phase using only two phase values, 0 and pi. This assertion has been confirmed experimentally, where binary phase shaping (BPS) was shown to outperform other alternative functions, sometimes by at least on order of magnitude, in controlling multiphoton processes. Here we discuss the solution of a number of nonlinear problems that range from narrowing the second harmonic spectrum of a laser pulse to optimizing the competition between two- and three-photon transitions. This Review explores some present and future applications of pulse shaping and coherent control.

Femtosecond degenerate four-wave mixing of cyclopropane

Femtosecond degenerate four-wave mixing (fs-DFWM) is applied for the measurement of rotational constants of cyclopropane (C3H6). The rotational coherence method yields a very accurate B0 = 20,093.322(12) MHz and centrifugal distortion constants D(J) and D(JK). To exploit the full resolution of the fs-DFWM method, the accuracy of the optical delay measurement was increased by nearly two orders of magnitude, including elimination of effects from the refractive index of air. The fs-DFWM molecular constants are comparable in accuracy to those from high-resolution infrared spectroscopy and are only surpassed by those of dipole distortion microwave spectroscopy. In parallel, the equilibrium structure, vibrationally averaged structure parameters and rotational constants were calculated using high-level ab initio methods and large basis sets. Combining these with the results of previous calculations and the measured rotational constants yields r(e)(C-C) = 1.5034(3) A, r(e)(C-H) = 1.0775(5) A, and alpha(e)(H-C-H) = 115.09(10) degrees.

Enhancement and Suppression of Vibrational Coherence in Degenerate Four-Wave-Mixing Signal Generated from Dye-Doped Polymer Films

Vibrational coherence in the degenerate four-wave-mixing (DFWM) signal generated from polymer films doped with a dye, oxazine 4 (Ox4), at 10 K was investigated. It was found that the amplitudes of some low-frequency oscillations (<400 cm(-1)) were enhanced when the delay between the first and second femtosecond pulses was set out of phase with the oscillation period. Frequency and reorganization energy dependence was investigated by computer simulation based on the response function formalism which considers all the possible Liouville space pathways for the DFWM signal. It was revealed that low-frequency oscillations with weak coupling to the optical transition can be enhanced in the stimulated photon echo signal compared to the transient grating signal.

Onset of decoherence: Six-wave mixing measurements of vibrational decoherence on the excited electronic state of I2 in solid argon

Pump-probe, four-wave, and six-wave mixing measurements of I2 isolated in solid argon are used to provide a clear experimental measure for the onset of vibrational quantum decoherence on the excited electronic state. The electronically resonant, six-wave mixing measurements bypass the rapid electronic dephasing, and measure the quantum cross-correlation between two packets launched on the B-state. The vibrational quantum coherence survives one period of motion, 400 fs, during which approximately 2000 cm(-1) of energy is transferred to the lattice. The decoherence occurs during the second cycle of motion, while classically coherent motion measured via pump-probe spectroscopy using the same electronic resonances continues for approximately 15 periods. This is contrasted with vibrational dephasing on the ground electronic surface, which lasts for 10(2) periods, as measured through time-resolved coherent anti-Stokes Raman scattering. The measurements and observables are discussed through time-circuit diagrams, and a mechanistic description of decoherence is derived through semiclassical analysis and simulations that reproduce the experiments.

Vibrational coherence of I2 in solid Kr

Time-resolved coherent anti-Stokes Raman scattering, with a resolution of 20 fs, is used to prepare a broadband vibrational superposition on the ground electronic state of I2 isolated in solid Kr. The coherent evolution of a packet consisting of nu=1-6 is monitored for as many as 1000 periods, allowing a precise analysis of the material response and radiation coherence. The molecular vibrations are characterized by omega(e)=211.330(2) cm(-1), omega(e)x(e)=0.6523(6) cm(-1), omega(e)y(e)=2.9(1) x 10(-3) cm(-1); the dephasing rates at 32 K range from 110 ps for nu=1 to 34 ps for nu=6, with nu dependence: gamma(nu)=8.5 x 10(-3)+4.9 x 10(-4)nu2+2.1 x 10(-6)nu4 ps(-1). The signal amplitude is also modulated at omega(q)=41.56(3) cm(-1); which can be interpreted as coupling between the molecule and a local mode. The surprising implication is that this resonant local mode is decoupled from the lattice phonons, a finding that cannot be rationalized based on a normal-mode analysis.

High-precision molecular wave-packet interferometry with HgAr dimers

Molecular wave-packet (WP) interferometry has been demonstrated in the A electronic state of the HgAr van der Waals complex with two time-delayed UV fs pulses at 254 nm. The interferograms of three vibrational levels in the WP's display almost 100% fringe contrast as a function of the interpulse delay tau, which is tuned with sub-10 as stability and resolution. It is clearly observed that the three interferograms show their dephasing and rephasing within a single vibrational period, allowing us to prepare arbitrary relative populations of the three levels by adjusting a single parameter tau.