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arXiv:1810.12461 · Physical review. B./Physical review. B

Stokes–anti-Stokes correlated photon properties akin to photonic Cooper pairs

Filomeno Soares de Aguiar Júnior, André Saraiva, Marcelo França Santos, Belita Koiller, Reinaldo de Melo e Souza, Arthur Patrocínio Pena, Raigna A. Silva, Carlos Henrique Monken, Ado Jório

Published Mar 13, 2019• 13 citations
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Abstract

Photons interact in condensed matter through the same mechanism that forms Cooper pairs in superconductors. The production rate depends on the energy shifts, which in the BCS theory determines whether interaction is attractive or repulsive. Only correlated photons in the case of attractive interactions are observed. While traditional photon-phonon collisions scatter light in all directions, the correlated photons follow the same path as the noninteracting laser. The observed phenomenon is rare, but the authors indicate paths to achieve higher interaction energies.

DOI
10.1103/physrevb.99.100503

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Photons interact in condensed matter through the same mechanism that forms Cooper pairs in superconductors. The production rate depends on the energy shifts, which in the BCS theory determines whether interaction is attractive or repulsive. Only correlated photons in the case of attractive interactions are observed. While traditional photon-phonon collisions scatter light in all directions, the correlated photons follow the same path as the noninteracting laser. The observed phenomenon is rare, but the authors indicate paths to achieve higher interaction energies.
Photons interact with each other in condensed matter through the same mechanism that forms Cooper pairs in superconductors, the exchange of virtual vibrational quanta [PRL 119, 193603 (2017)]. It is however unclear which consequences of this pairing will be observable and potentially lead to further analogy with superconductivity. We investigate the energy, momentum and production rate of such a photon-photon collision in diamond and other transparent media, experiencing properties akin to those of traditional electronic Cooper pairs. The rate of pair production depends on the energy shifts of the pair, which in theory determines whether there should be an attractive or repulsive interaction between these massless and chargeless particles. We only observe pair formation in the case of attractive interactions. In contrast with traditional photon-phonon collisions, which scatter light in all directions, the photonic Cooper pairs follow the same path as the noninteracting laser. Due to the low interaction energy between photons, the observed light-by-light collision is extremely rare, approximately one event for every 10^15 incident photons. However, our model indicates paths to achieve the higher interaction energies needed to make the effect instrumental for applications.
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 work, the Stokes-anti-Stokes¿ time-correlation phenomena was studied. The timecorrelated scattering process occurs when the same vibrational quantum from a material participates in the Stokes and anti-Stokes photon generation process in the inelastic scattering of light. We demonstrate that the SaS phenomenon occurs in different bands of the Raman spectra, from different transparent liquid materials. The observation of time-correlated SaS pairs in energy bands out of the resonance region indicates the possibility of energy exchange between photons via virtual phonons, which allows drawing a parallel with the Cooper pair formation phenomenon for electrons, from the BCS superconductivity theory. In this dissertation, we discuss the fundamentals of the theory and the instrumentation related to the concepts about the discussed phenomena, as well as demonstrate that the rate of SaS pair formation exhibits a linear relation with the supertransparency gap, concept brought from the BCS superconductivity theory.
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).