Microscopic origin of polarization-entangled Stokes–anti-Stokes photons in diamond
Tiago A. Freitas, Paula Machado, Lucas Valente, Diego Sier, Raul Corrêa, Riichiro Saito, Christophe Galland, Marcelo França Santos, Carlos Henrique Monken, Ado Jório
This work shows that Stokes and anti-Stokes photons generated in a degenerate four-wave-mixing process in diamond are entangled in polarization. The degree of entanglement generated by process indeterminacy (electronic or phononic) depends on the detuning of the photon pairs from the excitation laser and on the orientation of the polarization of the incident light with respect to the sample.
This work shows that Stokes and anti-Stokes photons generated in a degenerate four-wave-mixing process in diamond are entangled in polarization. The degree of entanglement generated by process indeterminacy (electronic or phononic) depends on the detuning of the photon pairs from the excitation laser and on the orientation of the polarization of the incident light with respect to the sample.
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.
Recently [T. A. Freitas et al., Phys. Rev. A 108, L051501 (2023)], it was shown that, in a centrosymmetric cubic system, two photons from a broadband intense laser field can be converted into a pair of Stokes and anti-Stokes (SaS) entangled photons. While the previous work was based on symmetry arguments, here we present a fully quantum theory for the SaS scattering that properly explains, quantitatively describes, and provides a means to predict its spectral and polarization properties (for diamond). We also explore the possibilities offered by such a system, designing an entanglement map based on changes in the light-matter system. In particular, we show how the broadband polarization entanglement that emerges from the interference between electronic and phononic degrees of freedom in the SaS scattering depends on parameters such as the Stokes--anti-Stokes Raman shift, scattering geometry, and laser bandwidth, opening the avenue of exploration of such phenomenon in information processing.
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.
We investigate the arrival statistics of Stokes (S) and anti-Stokes (aS) Raman photons generated in thin diamond crystals. Strong quantum correlations between the S and aS signals are observed, which implies that the two processes share the same phonon; that is, the phonon excited in the S process is consumed in the aS process. We show that the intensity cross-correlation g(S,aS)(2)(0), which describes the simultaneous detection of Stokes and anti-Stokes photons, increases steadily with decreasing laser power and saturates at very low pump powers, implying that the number of Stokes-induced aS photons is comparable to the number of spontaneously generated aS photons. Furthermore, the coincidence rate shows a quadratic plus cubic power dependence, indicating the generation of multiple S photons per pulse at high powers.
We investigate the arrival statistics of Stokes (S) and anti-Stokes (aS) Raman photons generated in diamond membranes. Strong quantum correlations between the S and aS signals are observed, which implies that the two processes share the same phonon, that is, the phonon excited by the S process is consumed in the aS process. We show that the intensity cross-correlation gS,aS(2)(0), which describes the simultaneous detection of Stokes and anti-Stokes photons, decreases steadily with laser power as 1/PL. Contrary to many other material systems, diamond exhibits a maximum gS,aS(2)(0) at very low pump powers, implying that the Stokes-induced aS photons outnumber the thermally generated aS photons. On the other hand, the coincidence rate shows a quadratic plus cubic power dependence, which indicates a departure from the Stokes-induced anti-Stokes process.
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.