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physica status solidi (b)

Characterization of the Polarization State of Correlated Stokes–Anti‐Stokes Raman Scattering in Diamond

Tiago A. Freitas, Paula Machado, Marcelo França Santos, Carlos Henrique Monken, Ado Jório

Published Jan 8, 2025• 1 citation
Publisher

Abstract

Quantum information research has been through numerous evolutionary stages, and photonic transport is one of the most promising methods for information processing. Within the context of the use of photons for information transportation, Raman spectroscopy, which consists of an optical spectroscopy technique based on the inelastic scatter of light, where the scattered photons carry information from the vibration structure of the medium, is presented as an exciting way for coding and transportation of quantum information. Herein, the phenomenon of correlated Stokes‐anti‐Stokes (SaS) Raman scattering is explored, analyzing the quantum character of the phenomenon. A state tomography is performed to fully characterize the SaS pair's polarization state. During this study, it is possible to observe the influence of the crystallographic orientation of the diamond on the SaS polarization state, which directly influences the entanglement generation. A Clauser, Horne, Shimony, and Holt‐type Bell's inequality measurement is conducted to confirm the entanglement in the polarization of the SaS state.

DOI
10.1002/pssb.202400275

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State tomography of pairs of photons Stokes and anti-Stokes from the inelastic scattering of light in the diamond and violation of Bell inequality

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The last decades have been marked by intense research on the evolution of computer and communication systems. Within this context, quantum computing has been one of the areas that generated large interest and effort from researchers due, to the immense potential offered. Quantum information research has been through numerous evolutionary stages, and photonic transport is one of the most promising methods for information processing. Within the context of the use of photons for information transportation, Raman spectroscopy, which consists of an optical spectroscopy technique based on the inelastic scatter of light, where the scattered photons carry information from the vibration structure of the medium, is presented as an exciting way for coding and transportation of quantum information. In this work, we explore the phenomenon of correlated Stokes- anti-Stokes (SaS) Raman scattering, analyzing the quantum character of the phenomenon. The implementation of the experimental apparatus was performed for the measurement of the correlation of the photons generated in this phenomenon in diamond, confirming its quantum character and optimizing the phenomenon for a complete analysis of the process in order to confirm that besides being correlated, the pair of SaS photons would also be entanglement. Initially, we studied the dependence on phenomenon efficiency with different lasers (continuous, ps, and fs pulsed, and different wavelengths) and the dependence on the correlation function with the Raman shift. These studies have shown that the best configuration for the study regarding the possible entanglement of the process would be using the fs laser in 785nm. In the following steps, state tomography measurements were performed to completely characterize the polarization state of the SaS pair. During this study, it was possible to observe the influence of the crystallographic orientation of the diamond on the SAS polarization state, which directly influences the generation of entanglement. Finally, Bell’s inequality measurements of the CHSH type were performed to confirm the entanglement in polarization of the SaS state.

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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 ${g}_{\text{SaS}}^{2}(0)$. 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.

Physical review. B./Physical review. B•Jan 9, 2024•0 citations
Quantum information research has been through numerous evolutionary stages, and photonic transport is one of the most promising methods for information processing. Within the context of the use of photons for information transportation, Raman spectroscopy, which consists of an optical spectroscopy technique based on the inelastic scatter of light, where the scattered photons carry information from the vibration structure of the medium, is presented as an exciting way for coding and transportation of quantum information. Herein, the phenomenon of correlated Stokes‐anti‐Stokes (SaS) Raman scattering is explored, analyzing the quantum character of the phenomenon. A state tomography is performed to fully characterize the SaS pair's polarization state. During this study, it is possible to observe the influence of the crystallographic orientation of the diamond on the SaS polarization state, which directly influences the entanglement generation. A Clauser, Horne, Shimony, and Holt‐type Bell's inequality measurement is conducted to confirm the entanglement in the polarization of the SaS state.
The last decades have been marked by intense research on the evolution of computer and communication systems. Within this context, quantum computing has been one of the areas that generated large interest and effort from researchers due, to the immense potential offered. Quantum information research has been through numerous evolutionary stages, and photonic transport is one of the most promising methods for information processing. Within the context of the use of photons for information transportation, Raman spectroscopy, which consists of an optical spectroscopy technique based on the inelastic scatter of light, where the scattered photons carry information from the vibration structure of the medium, is presented as an exciting way for coding and transportation of quantum information. In this work, we explore the phenomenon of correlated Stokes- anti-Stokes (SaS) Raman scattering, analyzing the quantum character of the phenomenon. The implementation of the experimental apparatus was performed for the measurement of the correlation of the photons generated in this phenomenon in diamond, confirming its quantum character and optimizing the phenomenon for a complete analysis of the process in order to confirm that besides being correlated, the pair of SaS photons would also be entanglement. Initially, we studied the dependence on phenomenon efficiency with different lasers (continuous, ps, and fs pulsed, and different wavelengths) and the dependence on the correlation function with the Raman shift. These studies have shown that the best configuration for the study regarding the possible entanglement of the process would be using the fs laser in 785nm. In the following steps, state tomography measurements were performed to completely characterize the polarization state of the SaS pair. During this study, it was possible to observe the influence of the crystallographic orientation of the diamond on the SAS polarization state, which directly influences the generation of entanglement. Finally, Bell’s inequality measurements of the CHSH type were performed to confirm the entanglement in polarization of the SaS state.
Degenerate four-wave mixing in diamond generates a quantum state ${\ensuremath{\rho}}_{\mathrm{SaS}}$ composed of Stokes (S) and anti-Stokes (aS) time-correlated photon pairs (SaS). Here, polarization state tomography of ${\ensuremath{\rho}}_{\mathrm{SaS}}$ is performed in four pertinent scattering configurations: Raman shift in resonance and out of resonance with the phonon energy, and incident light polarized in the direction parallel to or $\ensuremath{\pi}/4$ rotated from a diamond crystallographic axis. We reconstruct the density matrix, calculate concurrence and purity for the four configurations, and directly measure and analyze the diagonal terms of ${\ensuremath{\rho}}_{\mathrm{SaS}}$ in different bases. We establish ${\ensuremath{\rho}}_{\mathrm{SaS}}$ as an entangled linear combination of electronic four-wave mixing and SaS Raman process, mixed with uncorrelated S and aS photons, with the weight constants depending on the scattering conditions, which can be engineered for future applications.
The process in which Raman scattering produces correlated Stokes and anti‐Stokes radiation is known as Stokes–anti‐Stokes (SaS) scattering. It has been shown recently that this process can generate entangled photon pairs, making it a promising tool for quantum optical technologies, but a proper quantum theoretical description was lacking. In this article, a fully quantum derivation of the electric polarization in a medium with vibrational Raman response, with quantized electromagnetic fields, is developed. Using quantum perturbation theory for Heisenberg operators, the solution for the material electric polarization is found and it is shown that a four‐wave mixing‐like correlated SaS scattering appears in the first order of perturbation and completely characterizes the nonresonant SaS photon pair production. It is also discussed how to construct the third‐order nonlinear optical susceptibility for the SaS scattering from the quantum formalism and show that it coincides with the one derived for classical fields in stimulated Raman.
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.
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.