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Low Temperature Physics

Time-resolved CARS measurements of the vibrational decoherence of I2 isolated in an Ar matrix

Michael Karavitis, D. Segale, Z. Bihary, Mika Pettersson, Vartkess Ara Apkarian

Published Sep 1, 2003• 23 citations
Publisher

Abstract

Time-resolved coherent anti-Stokes Raman scattering is applied to prepare and interrogate vibrational coherences on the ground electronic surface of molecular iodine isolated in Ar matrices. The coherence decay time shows a linear dependence on vibrational quantum numbers for v=3–15. The temperature dependence of decoherence rates is negligible for v<7 in the experimental range T=18–32 K. For a v=13, 14 superposition, the temperature dependence indicates dephasing by a 66 cm−1 pseudo-local phonon, just outside the Debye edge of the solid. The accuracy of the data is limited due to two-photon induced dissociation of the molecule, a process which is characterized using polarized fields. The T→0 limit of dephasing is discussed.

DOI
10.1063/1.1614200

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Physical Review A•Mar 1, 1991•15 citations
Time-resolved coherent anti-Stokes Raman scattering is applied to prepare and interrogate vibrational coherences on the ground electronic surface of molecular iodine isolated in Ar matrices. The coherence decay time shows a linear dependence on vibrational quantum numbers for v=3–15. The temperature dependence of decoherence rates is negligible for v<7 in the experimental range T=18–32 K. For a v=13, 14 superposition, the temperature dependence indicates dephasing by a 66 cm−1 pseudo-local phonon, just outside the Debye edge of the solid. The accuracy of the data is limited due to two-photon induced dissociation of the molecule, a process which is characterized using polarized fields. The T→0 limit of dephasing is discussed.
Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out for iodine (I2) in solid krypton matrices. The dependence of vibrational dephasing time on temperature and vibrational quantum number v is studied. The v dependence is approximately quadratic, while the temperature dependence of both vibrational dephasing and spectral shift, although weak, fits the exponential form characteristic of dephasing by pseudolocal phonons. The analysis of the data indicates that the frequency of the pseudolocal phonons is approximately 30 cm(-1). The longest dephasing times are observed for v = 2 being approximately 300 ps and limited by inhomogeneous broadening. An increase in the dephasing rate of v = 2 as the temperature is lowered to T = 2.6 K is taken as a clear indication of lattice-strain-induced inhomogeneity of the ensemble coherence.
Time-resolved, electronically resonant, coherent anti-Stokes Raman scattering is used to prepare and interrogate vibronic coherences of molecular iodine in matrix Ar. Coherences that involve evolution on the excited B(3Π0u) state, first- and third-order coherences, decay in less than one vibrational period (τ<300 fs). In contrast, as many as 200 vibrational periods of motion can be observed for Raman-prepared wave packets consisting of zero-phonon vibrational superpositions on the ground electronic state (second-order coherence). Packets consisting of v=4, 5 and v=3, 4, 5 on the X(1Σg) state decay with a half-life of 10±1 ps at 31 K, allowing a more accurate measure of vibrational level spacings and decoherence time than has been possible in frequency domain. The harmonic frequency of the molecule is reduced by 1.5 cm−1 (0.7%) in the matrix. The lack of recurrence in the excited electronic state ensures that the resonant anti-Stokes scattering arises only from the negative momentum component of the Raman packet. This momentum filter, which should be ubiquitous in condensed media, leads to a signal with deeper modulation than in the gas phase.
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.
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.
The absorption spectrum of I2 in solid Xe shows resolved zero-phonon lines and phonon side bands near the origin of the B←X transition (550-625 nm). The long-lived |B⟩⟨X| coherence in this energy range (T2 = 600 fs on average) emerges as vibrationally unrelaxed fluorescence in resonance Raman (RR) spectra. Upon excitation in the structureless continuum at 532 nm, the oscillatory RR progression exhibits electronic dephasing time of T2 = 150 fs. Two RR progressions with markedly different vibrational coherence on the X-state are observed. The main progression of sharp overtones (T2 > 21 ps) is assigned to molecules trapped in double-substitution sites. The minor progression, which shows dephasing times T2 = 6-0.6 ps for v = 1-8, is assigned to molecules in triple-substitution sites. The line progressions allow a detailed characterization of the solvated B- and X-state potentials. Time-resolved coherent anti-Stokes Raman scattering is used to probe selected vibrational coherences on the X-state. Assignments are obtained through molecular dynamics simulations, which reproduce the relative dephasing rates between the two sites, clarify the role of rotation-translation dynamics, and enable quantum dynamics simulations of the spectra by the potentials of mean force that accurately describe the molecule-surrounding interactions.
Mechanisms of intermolecular dephasings revealed in the time-resolved coherent anti-Stokes Raman scattering (CARS) spectra of a molecular ensemble are theoretically studied by deriving the microscopical expression for the scattered photon intensity averaged over the heat-bath variables. The intermolecular dephasing means the decay of the intermolecular coherence created by the pumping process, i.e., a linear combination of the vibrational Raman transitions of the molecules at different sites. The intensity of the time-resolved CARS is expressed in terms of time-development matrix elements of the intermolecular coherence. An equation of motion for the intermolecular coherence is derived by using the projection operator method. The structure of the intermolecular-dephasing constant is clarified. The intermolecular-dephasing constant consists of the sum of population decay constants and the intermolecular pure dephasing constant that originates from an elastic interaction between the relevant molecules and a common heat-bath mode. The intermolecular pure dephasing constant is expressed in terms of the intramolecular pure dephasing constants and destructive interference of the intramolecular pure dephasings between the relevant two molecules. The intermolecular-dephasing constant is expressed as the sum of the intramolecular-dephasing constants of the relevant molecules when there is no common heat-bath mode. Inhomogeneous effects on the time-resolved CARS spectra are also investigated. A degree of the structural order is introduced to qualitatively express the inhomogeneity of local structures in the molecular ensemble. The microscopic expression derived in this paper has taken into account both incoherent and coherent optical processes in the thermally distributed molecular ensemble.