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Properties of correlated Stokes-anti-Stokes Raman scattering from diamond

Lucas V. de Carvalho, Tiago A. Freitas, Paula Machado, Raul Correa, Marcelo França Santos, Carlos Henrique Monken, Ado Jório

Published Sep 30, 2022• 0 citations
Publisher

Abstract

The correlated Stokes-anti-Stokes Raman scattering mediated by phonons was introduced in 1977 by Klyshko. In the last two decades, it has been broadly studied experimentally, including results on diamond, graphene and transparent liquid. The theoretical description of non-resonant Stokes-anti-Stokes pair production was shown to be formally similar to the BCS theory of superconductivity, raising attention to the study of pair production as a function of the Raman shift. Intriguingly, the pair production efficiency is not symmetric with respect to the positive versus negative detuning from phonon resonance, a result that was shown for a 180fs pulsed laser, and that remains without a theoretical explanation. Here we show the asymmetry is persistent in diamond measured with lasers of different pulse widths (180 fs and 5 ps) and different wavelengths (633 nm versus 785 nm).

DOI
10.1117/12.2633272

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The correlated Stokes-anti-Stokes Raman scattering mediated by phonons was introduced in 1977 by Klyshko. In the last two decades, it has been broadly studied experimentally, including results on diamond, graphene and transparent liquid. The theoretical description of non-resonant Stokes-anti-Stokes pair production was shown to be formally similar to the BCS theory of superconductivity, raising attention to the study of pair production as a function of the Raman shift. Intriguingly, the pair production efficiency is not symmetric with respect to the positive versus negative detuning from phonon resonance, a result that was shown for a 180fs pulsed laser, and that remains without a theoretical explanation. Here we show the asymmetry is persistent in diamond measured with lasers of different pulse widths (180 fs and 5 ps) and different wavelengths (633 nm versus 785 nm).
In this work, we study the correlated Stokes-anti-Stokes (SaS) Raman scattering in a diamond sample and the influence that the excitation pulse width has in the intensity of generation of the correlated pairs in the process. For this investigation, we used two excitation systems with different temporal pulse width, one with femtosecond temporal width and one with picosecond temporal width. We did two distinct experiments with this excitation systems with difference in the way of filtering the signal: In the first experiment, the signal filtering is made with band-pass filters, this configuration has a greater efficiency that allow us compare better the correlated pair formation efficiency between the different excitation systems. In the second experiment, we used a monochromator to filtering the signal, this configuration allow us to change the wavelength of the detection so we can measure the formation spectrum of the correlated pairs. The results obtained from these experiments show us that the correlated pairs generation efficiency is larger with the use of the system with femtosecond temporal width, what is expected for a non-linear process. In the resonant Raman frequency region, we observed a intensity 1.5 times larger with the use of femtosecond system, and in the out-of-ressonance Raman region, we observed a intensity 5 times larger in the region with lowest Raman shift and 9 times larger in the region with largest Raman shift. We also measure the formation pairs spectrum around the first order Raman peak of the diamond, confirming the existence of a asymmetry in the formation of this pairs with respect to the positive versus negative detuning from phonon resonance. This asymmetry still remains without a satisfactory theoretical explanation.
The correlated Raman scattering, referred to here as the SaS process, occurs with the annihilation, within a material, of two photons of an excitation laser and the creation of a quantum correlated Stokes (S) and anti-Soktes (aS) photon pair where the phonon created in the S process is annihilated in the aS scattering. We found that, in addition to real SaS process where the energy exchange coincides with the energy of a vibrational state of the material, there is also the virtual SaS process, whose the exchange of energy and momentum between the photons of the laser, generating the S-aS photon pair, is mediated by a virtual vibrational excitation, setting up a photon-photon interaction similar to the electron-electron attraction responsible for the creation of Cooper pairs of the BCS theory of superconductivity. We observed the SaS process in transparent media in general, by measuring non-classical values of the normalized second-order cross-correlation function of the Stokes and anti-Stokes fields, 2(0). In diamond, we characterize the intensity of the virtual SaS scattering ( ) as a function of the virtual phonon energy, proving that the SaS process occurs only when the photon-photon interaction is attractive, as in the BCS theory for the Cooper pairs. We show that photons S and aS from the SaS process are scattered predominantly in the same polarization as the excitation laser of the sample and, with this, we implemented the pump-probe technique to study the lifetime of the real phonon (obtained in the diamond order 2.8 ps ) and the lifetime of the virtual excitation, which proved to be inferior to the temporal resolution of the measurement’s, characterizing one of the main differences between the two processes. We also observed that, due to the relations of energy and momentum conservation, have the same spatial intensity profile of the non-interacting laser that crosses the sample, different from the behavior observed for uncorrelated Raman scattering which spreads photons in all directions. We observed that the efficiency of the SaS scattering is proportional to the Raman scattering cross-section when we compare the process in different hydrocarbons and we generalize the observations made in the diamond to the sample of liquid decane. In water, the values of 2(0), predicted by the theoretical description of the process, corroborate the experimental data, validating the BCS theory for virtual SaS scattering, setting the pair of Stokes and anti-Stokes photons as counterparts of the Cooper pairs.
The correlation between the Stokes and anti-Stokes components of Raman scattering has assumed an important role in the field of quantum information. When the Raman shifts match the energy of a phonon in the material, in the real-SaS, one-phonon Fock state are generated. When such resonance is not achieved, the energy exchange is mediated by virtual phonons, generating photonic Cooper pairs (PCPs). In this work, investigations of polarization correlations and scattering time dependences elucidate the fundamental difference between the real and the virtual phenomena.
The present dissertation entails a detailed investigation into the asymmetry in the formation of correlated Stokes and anti-Stokes photon pairs before and after the resonance region in a diamond sample. The analysis undertaken in this study is based on the dependence on polarization and frequency, combined with two distinct crystallographic orientations of the sample, aiming to explore the physical characteristics of this asymmetry. Initially, the physical and structural properties of diamond are presented. Subsequently, the physical phenomenon under study is addressed, starting from uncorrelated Raman scattering to correlated Raman scattering. Following this, the experimental apparatus used to measure the desired physical quantities is described. The results obtained are then discussed. Finally, the conclusion section provides a concise and general analysis of the experimental results, which indicate that correlated Stokes and anti-Stokes Raman scattering constitutes a specific type of four-wave mixing. This four-wave mixing can be divided into a resonant part and a non-resonant part, providing an adequate explanation for the asymmetry issue.
In this study, the correlated Stokes--anti-Stokes Raman scattering, denominated as the SaS process, is investigated in a decane sample, generalizing for a liquid the results observed in crystalline diamond. The production of SaS photon pairs is observed in both real and virtual processes by measuring nonclassical values of the second-order cross-correlation function gSaS2(0){g}_{\text{SaS}}^{2}(0)gSaS2​(0). The correlated Raman spectrum is observed only for Raman shift values below approximately $2900\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is equivalent to the highest vibrational mode of the decane molecule. Furthermore, despite the fact that decane is a liquid, the polarization and spatial profile of the SaS process in decane presents the same properties as those observed in diamond.