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arXiv:1311.3978 · Physical Review A

Emergence of molecular chirality by vibrational Raman scattering

Farhad Taher Ghahramani, Afshin Shafiee

Published Sep 9, 2013• 8 citations
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Abstract

In this study, we apply the monitoring master equation describing decoherence of internal states to an optically active molecule prepared in a coherent superposition of nondegenerate internal states interacting with thermal photons at low temperatures. We use vibrational Raman scattering theory up to the first chiral-sensitive contribution, i.e., the mixed electric-magnetic interaction, to obtain scattering amplitudes in terms of molecular polarizability tensors. The resulting density matrix is used to obtain elastic decoherence rates.

DOI
10.1103/physreva.88.032504

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In this study, we apply the monitoring master equation describing decoherence of internal states to an optically active molecule prepared in a coherent superposition of nondegenerate internal states interacting with thermal photons at low temperatures. We use vibrational Raman scattering theory up to the first chiral-sensitive contribution, i.e., the mixed electric-magnetic interaction, to obtain scattering amplitudes in terms of molecular polarizability tensors. The resulting density matrix is used to obtain elastic decoherence rates.
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The temperature effect on the resonance Raman scattering from molecules is investigated. Considering a total system consisting of a molecular system, a heat bath, and the weak radiation field, a general expression for the relaxation processes is derived utilizing the Liouville operator technique for the time evolution of the density matrix of the total system. By using the perturbation method with respect to the radiation and matter up to second order, rate constants for zero photon (radiationless processes), one-photon and two-photon processes are derived after taking the long time limit in the Markoff approximation. Assuming a weak interaction between the molecular system and heat bath, a temperature-dependent resonance Raman scattering cross section is formulated in the adiabatic basis set for the molecular systems. In the displaced harmonic oscillator model, we obtain an analytical expression for the temperature-dependent Raman scattering cross section for the multimode case, which is suitable for both weak coupling and strong coupling cases. Analytical expressions for the Stokes and anti-Stokes bands of the jth order vibrational transition in the one oscillator model can easily be obtained from the general expression for the resonance Raman scattering cross section derived. An approximate Stokes to anti-Stokes ratio is given up to the second order of the dimensionless displacement Δ. The resonance Raman scattering cross section and the excitation energy profiles are numerically calculated as a function of physical constant such as temperature, molecular vibrational frequency and Δ. It is shown that the excitation profiles of the anti-Stokes band of the jth order vibrational transition have the similar envelope of the corresponding Stokes band shifted by jh/ω. The inverse Raman effect which is closely related to the ordinary Raman effect is also discussed.
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.