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arXiv:2310.07139 · Physical Review Research

Resonant squeezed light from photonic Cooper pairs

Sanker Timsina, Taha Hammadia, Sahar Gholami Milani, Filomeno Soares de Aguiar Júnior, Alexandre G. Brolo, Rogério de Sousa

Published Jul 15, 2024• 4 citations
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Abstract

Raman scattering of photons into phonons gives rise to entangled photon pairs when the phonon emitted in a Stokes process is coherently absorbed in antiStokes scattering, forming the photonic analog of Cooper pairs. We present a nonperturbative theory for the time evolution of photonic Cooper pairs that treats interacting photons and phonons as a hybrid excitation, the Ramaniton. As the Ramaniton propagates in a waveguide it displays quantum oscillations between photon and phonon occupation, leading to resonant squeezed Stokes-antiStokes light when the phonon occupation becomes equal to zero without recurring back to the photon vacuum. This phenomenon is predicted to generate up to 28 dB of squeezed light even in standard silicon on insulator waveguides. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033067

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Raman scattering of photons into phonons gives rise to entangled photon pairs when the phonon emitted in a Stokes process is coherently absorbed in antiStokes scattering, forming the photonic analog of Cooper pairs. We present a nonperturbative theory for the time evolution of photonic Cooper pairs that treats interacting photons and phonons as a hybrid excitation, the Ramaniton. As the Ramaniton propagates in a waveguide it displays quantum oscillations between photon and phonon occupation, leading to resonant squeezed Stokes-antiStokes light when the phonon occupation becomes equal to zero without recurring back to the photon vacuum. This phenomenon is predicted to generate up to 28 dB of squeezed light even in standard silicon on insulator waveguides. Published by the American Physical Society 2024
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.
Controllable generation of photon pairs is essential for the utilization of quantum pair states for quantum applications such as quantum communication, quantum cryptography, teleportation, and linear optics quantum computing. Raman scattering is one of the most fundamental light-matter interactions and can be used to generate photon pairs. Using the spontaneous Stokes Raman interaction, a photon from a strong pump laser pulse is annihilated, and a Stokes photon and Raman-mediated collective excitation are created. This excitation can then be read out deterministically as an anti-Stokes photon with the application of a second laser pulse within the excitation lifetime, creating a photon pair. The heralding capability of the Stokes photon and lifetime of the excitation makes this source quasi-deterministic, where the anti-Stokes photon can be created at a later time than the Stokes. This gives additional advantages and uses over traditional photon-pair sources using nonlinear interactions of light in a transparent medium, which generate the pair of photons simultaneously. In this thesis, we study the correlations of photon pairs generated via spontaneous Raman interactions and demonstrate how these interactions can be used for quantum applications. First, we develop a model to study the spectral correlations between the Raman generated Stokes and anti-Stokes photons. This model is used to calculate the spectral single-photon purity of the photons in a generic material system ignoring the effects of material dispersion. We calculate how various parameters effect the purity including pump spectral bandwidth, excitation linewidth, and time delay between pump pulses. We then introduced an experimental realization of a Raman-mediated photon-pair source in an integrated quantum photonic circuit platform. Interstitial N2 molecules inherently trapped in silicon nitride thin films during the deposition process possess a sharp Raman mission corresponding to the vibrational mode of the molecules, which can be used as a Raman-mediated photon-pair source. We present evidence of N2 defects in silicon nitride thin films and estimate the defect density and excitation lifetime. By patterning the films into waveguide structures, the photon-matter interaction is enhanced. We perform finite-element simulation of light propagation in our fabricated waveguides and use the results to examine effects from the waveguide on ultrafast optical pulses and phase-matching requirements for efficient photon-pair generation. We then present experimental progress towards detecting Stokes and anti-Stokes photon-pair generation from N2 defects in silicon nitride waveguides. We show results from degenerate and non-degenerate wavelength optical pump pulses. We discuss limitations of the experimental methods and study in detail the sources of noise arising from the silicon nitride waveguide, and conclude by discussing future extensions on the results presented here.
The microscopic theory of superconductivity raised the disruptive idea that electrons couple through the elusive exchange of virtual phonons, overcoming the strong Coulomb repulsion to form Cooper pairs. Light is also known to interact with atomic vibrations, as, for example, in the Raman effect. We show that photon pairs exchange virtual vibrations in transparent media, leading to an effective photon-photon interaction identical to that for electrons in the BCS theory of superconductivity, in spite of the fact that photons are bosons. In this scenario, photons may exchange energy without matching a quantum of vibration of the medium. As a result, pair correlations for photons scattered away from the Raman resonances are expected to be enhanced. An experimental demonstration of this effect is provided here by time-correlated Raman measurements in different media. The experimental data confirm our theoretical interpretation of a photonic Cooper pairing, without the need for any fitting parameters.