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Molecular Physics

Probing intermolecular communication via lattice phonons with time-resolved coherent anti-Stokes Raman scattering†

Mary A. Rohrdanz, Jeffrey A. Cina

Published Mar 31, 2006• 12 citations
Publisher

Abstract

Calculations are presented demonstrating controlled intermolecular communication between dopant molecules via lattice phonons in a cryogenic matrix. By simulating a time-resolved coherent anti-Stokes Raman scattering (tr-CARS) experiment on an I2-molecule ‘receiver,’ its reception from a Ca-atom ‘transmitter’ of coherent lattice waves in a compressed linear chain of Ar atoms is monitored. A short pulse resonant with an atomic transition in Ca arrives at the sample before the tr-CARS pulses, and the coherent response of the host medium to the electronic excitation sends a rarefaction wave through the lattice. The arrival of this propagating distortion at the I2 molecule is detected through the tr-CARS difference signal, the difference between tr-CARS signals with and without the Ca pulse. A normal-mode analysis of the equilibrium configuration is used to construct an initial Gaussian wave packet, which is propagated by locally quadratic approximations to the relevant many-body nuclear Hamiltonians. Results are presented for both resonant and sub-resonant excitation of the Ca atom. Calculations show a difference signal that turns on abruptly as the lattice wave generated by resonant Ca excitation reaches the I2 chromophore.

DOI
10.1080/00268970500525515

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Physical Review A•Oct 5, 2021•7 citations
Calculations are presented demonstrating controlled intermolecular communication between dopant molecules via lattice phonons in a cryogenic matrix. By simulating a time-resolved coherent anti-Stokes Raman scattering (tr-CARS) experiment on an I2-molecule ‘receiver,’ its reception from a Ca-atom ‘transmitter’ of coherent lattice waves in a compressed linear chain of Ar atoms is monitored. A short pulse resonant with an atomic transition in Ca arrives at the sample before the tr-CARS pulses, and the coherent response of the host medium to the electronic excitation sends a rarefaction wave through the lattice. The arrival of this propagating distortion at the I2 molecule is detected through the tr-CARS difference signal, the difference between tr-CARS signals with and without the Ca pulse. A normal-mode analysis of the equilibrium configuration is used to construct an initial Gaussian wave packet, which is propagated by locally quadratic approximations to the relevant many-body nuclear Hamiltonians. Results are presented for both resonant and sub-resonant excitation of the Ca atom. Calculations show a difference signal that turns on abruptly as the lattice wave generated by resonant Ca excitation reaches the I2 chromophore.
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.
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.
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 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.
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.
A semiclassical theory that describes the generation of a coherent anti-Stokes Raman scattering (CARS) signal is presented that maximizes vibrational coherence in a mode predetermined by the pump, the Stokes, and the probe chirped pulse trains and takes into account the field propagation effects in a cloud of molecules. The buildup of the anti-Stokes signal, which may be used as a molecular signature in the backward CARS signal, is demonstrated numerically. The theory is based on the solution of the coupled Maxwell's and Liouville--von Neumann equations and focuses on the quantum effects induced in the target molecules by the control pulse trains. A deep convolutional neural network technique is implemented to evaluate time-dependent phase characteristics of the control fields. The effect of decoherence induced by spontaneous decay and collisional dephasing is examined.