Raman scattering as a candidate for photon-pair generation is explored recently both theoretically and experimentally. Here, we systematically analyze the Stokes–anti-Stokes photon-pair generation in Raman scattering, akin signal–idler photon-pair emission in the spontaneous parametric down conversion, to obtain suitable conditions for photon-pair generation. Non-zero mean phonon number and losses in the phonon mode are observed to be relevant parameters in this context in addition to the Raman active material properties and pump power. Specifically, the Raman active materials with stronger anti-Stokes coupling compared to the Stokes coupling constant are suitable for photon-pair generation. Ideal Stokes–anti-Stokes photon-pair generation is possible even for non-zero thermal phonons provided that the phonon losses are negligible. Here, we characterized the performance of photon-pair generation using noise-reduction parameter in detail. We also discuss the effect of phonon losses on the observed non-classical features.
Raman scattering as a candidate for photon-pair generation is explored recently both theoretically and experimentally. Here, we systematically analyze the Stokes–anti-Stokes photon-pair generation in Raman scattering, akin signal–idler photon-pair emission in the spontaneous parametric down conversion, to obtain suitable conditions for photon-pair generation. Non-zero mean phonon number and losses in the phonon mode are observed to be relevant parameters in this context in addition to the Raman active material properties and pump power. Specifically, the Raman active materials with stronger anti-Stokes coupling compared to the Stokes coupling constant are suitable for photon-pair generation. Ideal Stokes–anti-Stokes photon-pair generation is possible even for non-zero thermal phonons provided that the phonon losses are negligible. Here, we characterized the performance of photon-pair generation using noise-reduction parameter in detail. We also discuss the effect of phonon losses on the observed non-classical features.
A quantum model of the Raman process with the independent Stokes and anti-Stokes nonlinear interactions is developed to study nonclassical correlations between the photons in the Stokes and anti-Stokes fields. The role of the laser pump amplitude, the ratio of the Stokes and anti-Stokes coupling constants, and the population and losses of the vibrational mode in forming the correlations is elucidated. The g(2) intensity cross-correlation function, noise-reduction factor, two-mode principal squeezing variance, logarithmic negativity, nonclassicality depth, steering parameter, and the Bell parameter are analyzed side by side to shed light to the correlations between the Stokes and anti-Stokes fields. Conditions for having the Stokes and anti-Stokes fields composed of only photon pairs, similarly as it occurs in twin beams in parametric down-conversion, are revealed. They allow for nonzero mean thermal phonon numbers.
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 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 the correlated Stokes--anti-Stokes scattering (SAS) an incident photon interacts with a Raman-active material, creating a Stokes photon and exciting a quantum vibrational mode in the medium, which is posteriorly annihilated on contact with a second incident photon, producing in turn an anti-Stokes photon. This can be accomplished by real and virtual processes. In the real process the quantum mode shared between the Stokes and anti-Stokes events is a real particle, whereas in virtual processes the pair formation is mediated by the exchange of virtual particles. Here, we introduce a Hamiltonian to describe the pair production in SAS scattering, for both types of process, when stimulated by two orthogonally polarized laser pulses in a pump-and-probe configuration. We also model the effect of the natural decay of the vibration created in the Stokes event and compute the probability of producing SAS pairs. Additionally, we follow the dynamics of the vibration by considering the Stokes and anti-Stokes fields as external reservoirs, obtaining thus a master equation for the reduced density matrix for the vibrational population. Finally, we compare our theoretical results to recently published experimental data.
The photon wave function formalism provides an alternative description of some quantum optical phenomena in a more intuitive way. We use this formalism to describe the Stokesanti-Stokes (SaS) correlated scattering process present in Raman scattering. In this process, two photons from a laser beam are inelastically scattered by a phonon created by the first photon (Stokes processes) and annihilated by the second photon (anti-Stokes process), producing a pair of Stokes–anti-Sokes (SaS) photons. . We arrive at an expression for the two-photon wavefunction, in the time and frequency domains, of the scattered SaS photon pair, which is in agreement with a number of experimental results. It was shown, from the phase matching analysis, that the scattering pattern is compatible with the experiments. It was seen that, in the application for Pump-and-probe experiments, it was possible to generate the correct curves for the decay of the population of phonons in the sample. Finally, it was verified that, through the analysis of the joint spectrum of the pairs, information was obtained about the entanglement in frequency of the scattered photons. Thus, it is concluded that, from the results, the photon wave function formalism provides an intuitive and robust way to calculate the SaS scattering properties.
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.