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Collective Vibrational Quantum Coherence in a Molecular Liquid under Spontaneous Raman Scattering

Santiago Tarrago Velez, A. Pogrebna, Christophe Galland

Published May 1, 2021• 1 citation
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Abstract

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.

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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 demonstrate coherence measurements of single-photon-level collective excitations of vibrational states using transient coherent spontaneous Raman scattering in liquid methanol. We observe the decay of the 1033 cm−1 mode and coherence oscillations due to simultaneous excitation of the 2834 and 2944 cm−1 modes. The coherence life-times and oscillation frequencies agree with frequency-domain line-shape measurements and femtosecond coherent anti-Stokes Raman scattering measurements. The demonstrated technique is complementary to and, in some cases, simpler than traditional stimulated spectroscopy techniques in that it does not require more than one laser and is free of nonresonant background.
We have detected molecular coherence lasting nearly nine times the collisional dephasing time in a Raman generator. Two laser pulses, separated in time, pumped a common set of hydrogen molecules, producing two Stokes pulses whose relative phase was measured interferometrically. By making repeated measurements, the probability distribution of the relative phase was obtained. The variance of this phase distribution is a direct measure of the memory of the molecular coherence induced by the first scattering process. A one-dimensional theoretical model is developed which implies that the technique is capable of measuring a level of molecular coherence equivalent to between 15 and 50 phonons (delocalized vibrational quanta) in the most strongly excited mode.
Time-resolved Raman spectroscopy techniques offer various ways to study the dynamics of molecular vibrations in liquids or gases and optical phonons in crystals. While these techniques give access to the coherence time of the vibrational modes, they are not able to reveal the fragile quantum correlations that are spontaneously created between light and vibration during the Raman interaction. Here, we present a scheme leveraging universal properties of spontaneous Raman scattering to demonstrate Bell correlations between light and a collective molecular vibration. We measure the decay of these hybrid photon-phonon Bell correlations with sub-picosecond time resolution and find that they survive over several hundred oscillations at ambient conditions. Our method offers a universal approach to generate entanglement between light and molecular vibrations. Moreover, our results pave the way for the study of quantum correlations in more complex solid-state and molecular systems in their natural state.
We present a comparative analysis of spontaneous and coherent Raman scattering on pyridine. The instantaneous excitation of the molecular coherence is done by a pair of ultrashort preparation pulses. Then, a long narrowband probe pulse is scattered off the molecular vibrations. The described hybrid technique allows for the single-shot acquisition of a background-free coherent Raman spectrum within the excitation band and its straightforward comparison with the spontaneous Raman measurements, performed in the same setup. We report a 10(5)-fold increase in the efficiency of the Raman scattering process due to the broadband pump-Stokes preparation. The coherence magnitude (approximately 0.5x10(-3)) is inferred experimentally, without a priori knowledge about the molecular structure.