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arXiv:1202.4046 · Physical Review A

Coherent rovibrational revivals in a thermal molecular ensemble

M. Bitter, E. A. Shapiro, Valery Milner

Published Apr 13, 2012• 7 citations
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Abstract

We report an experimental and theoretical study of the evolution of vibrational coherence in a thermal ensemble of nitrogen molecules. Rotational dephasing and rephasing of the vibrational coherence is detected by coherent anti-Stokes Raman scattering. The existence of rovibrational coupling and the discrete energy spectrum of the rotational bath lead to a whole new class of full and fractional rovibrational revivals. Following the rich rovibrational dynamics on a nanosecond time scale with subpicosecond time resolution enables us to determine the second-order rovibrational constant ${\ensuremath{\gamma}}_{e}$ and assess new possibilities of controlling decoherence.

DOI
10.1103/physreva.85.043410

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We report an experimental and theoretical study of the evolution of vibrational coherence in a thermal ensemble of nitrogen molecules. Rotational dephasing and rephasing of the vibrational coherence is detected by coherent anti-Stokes Raman scattering. The existence of rovibrational coupling and the discrete energy spectrum of the rotational bath lead to a whole new class of full and fractional rovibrational revivals. Following the rich rovibrational dynamics on a nanosecond time scale with subpicosecond time resolution enables us to determine the second-order rovibrational constant \ensuremathγe{\ensuremath{\gamma}}_{e}\ensuremathγe​ and assess new possibilities of controlling decoherence.
Saturation of vibrational Raman coherence and coherent anti-Stokes Raman scattering (CARS) using femtosecond (fs) excitation pulses is investigated theoretically. The pump in a typical fs-CARS configuration has a bandwidth of a few hundred cm${}^{\ensuremath{-}1}$ that can couple tens of rotational states of room-air nitrogen molecules simultaneously, unlike in CARS with longer pulse durations. It is demonstrated that the vibrational coherence and also the vibrational CARS with fs excitation display saturationlike behavior once the rotational coherence is saturated. The Raman saturation threshold for the fs pump is numerically estimated to be at a peak intensity of $\ensuremath{\sim}$1022{10}^{22}1022 W/m2{}^{2}2, which is six to seven orders of magnitude higher than that in the nanosecond regime. The results are compared with the known saturation thresholds in different pulse-duration regimes and placed in perspective with other nonlinear thresholds reported in fs excitation regimes.
Stimulated Raman scattering is conventionally employed to probe vibrational dynamics by inducing a coherent oscillation within a molecular ensemble. In contrast, spontaneous Raman scattering is considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming laser pulse. It raises questions about the nature of the quantum state of a molecular ensemble following spontaneous Stokes scattering: should it be described as a statistical mixture of vibrationally excited molecules, where collective coherence is absent? Here, we measure time-resolved Stokes--anti-Stokes two-photon coincidences on a molecular liquid and find that a coherent superposition of two collective vibrational modes from two isotopic sub-ensembles is generated under spontaneous Raman scattering. Our results confirm that a spatially extended vibrational coherence emerges when a single collective excitation is spontaneously scattered and detected in a single spatiotemporal mode.
Spontaneous vibrational Raman scattering is a ubiquitous form of light-matter interaction whose description necessitates quantization of the electromagnetic field. It is usually considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming field. When probing an ensemble of molecules, the question therefore arises: What quantum state should be used to describe the molecular ensemble following spontaneous Stokes scattering? We experimentally address this question by measuring time-resolved Stokes-anti-Stokes two-photon coincidences on a molecular liquid consisting of several sub-ensembles with slightly different vibrational frequencies. When spontaneously scattered Stokes photons and subsequent anti-Stokes photons are detected into a single spatiotemporal mode, the observed dynamics is inconsistent with a statistical mixture of individually excited molecules. Instead, we show that the data are reproduced if Stokes-anti-Stokes correlations are mediated by a collective vibrational quantum, i.e. a coherent superposition of all molecules interacting with light. Our results demonstrate that the degree of coherence in the vibrational state of the liquid is not an intrinsic property of the material system, but rather depends on the optical excitation and detection geometry.
We present an analytical calculation that predicts the collapse of vibrational wavepackets in molecules due to the coupling of the rotational and vibrational degrees of freedom. At longer times a new class of revivals is predicted in the vibrational degree of freedom, due to the finite size and discrete nature of the rotational reservoir. The interplay of these competing behaviours is studied in the context of current experiments, and conditions for observing the revivals are described. Furthermore, the conditions for which the molecular vibration and rotation can be regarded as a system and its reservoir-like environment are described, in which case the ro-vibrational coupling can be considered effectively as a mechanism for decoherence of the vibrational motion. Comparison of the dephasing time predicted by this model with that observed in recent experiments is made.
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.
The formation of diatomic molecules with rotational and vibrational coherence is demonstrated experimentally in free-to-bound two-photon femtosecond photoassociation of hot atoms. In a thermal gas at a temperature of 1000 K, pairs of magnesium atoms, colliding in their electronic ground state, are excited into coherent superpositions of bound rovibrational levels in an electronically excited state. The rovibrational coherence is probed by a time-delayed third photon, resulting in quantum beats in the UV fluorescence. A comprehensive theoretical model based on ab initio calculations rationalizes the generation of coherence by Franck-Condon filtering of collision energies and partial waves, quantifying it in terms of an increase in quantum purity of the thermal ensemble. Our results open the way to coherent control of a binary reaction.