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 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 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, we study the correlated Stokes-anti-Stokes (SaS) Raman scattering in a diamond sample and the influence that the excitation pulse width has in the intensity of generation of the correlated pairs in the process. For this investigation, we used two excitation systems with different temporal pulse width, one with femtosecond temporal width and one with picosecond temporal width. We did two distinct experiments with this excitation systems with difference in the way of filtering the signal: In the first experiment, the signal filtering is made with band-pass filters, this configuration has a greater efficiency that allow us compare better the correlated pair formation efficiency between the different excitation systems. In the second experiment, we used a monochromator to filtering the signal, this configuration allow us to change the wavelength of the detection so we can measure the formation spectrum of the correlated pairs. The results obtained from these experiments show us that the correlated pairs generation efficiency is larger with the use of the system with femtosecond temporal width, what is expected for a non-linear process. In the resonant Raman frequency region, we observed a intensity 1.5 times larger with the use of femtosecond system, and in the out-of-ressonance Raman region, we observed a intensity 5 times larger in the region with lowest Raman shift and 9 times larger in the region with largest Raman shift. We also measure the formation pairs spectrum around the first order Raman peak of the diamond, confirming the existence of a asymmetry in the formation of this pairs with respect to the positive versus negative detuning from phonon resonance. This asymmetry still remains without a satisfactory theoretical explanation.
In this work we study the correlated Stokes and anti-Stokes Raman scattering, called here SaS. The SaS is an event where the same phonon participates in the of Stokes and anti-Stokes scattering processes. This process is not considered in current treatments of Raman scattering and can bring changes in the use of Raman spectroscopy for localtemperature measurements. Furthermore, these photons emerge as an important source of correlated photons pairs, widely used in quantum information, for example in implementing a quantum memory. We checked, by measurements of coincidence counting, that the Stokes and anti-Stokes photons generated in the Raman scattering from water, morespecifically the bands at }1644 1 concerning the angle variation mode between the H atoms, are quantum correlated. We get a value of 2(0) 517, much higher than what has been measured in others materials, as reported in the literature. We found that theintensity of the anti-Stokes signal has a quadratic dependence on the laser power, being another indication of the SaS occurrence. The value of 2(0) decays to high power values, in agreement with theoretical predictions. We have also obtained evidences that the SaScorrelation exhibits a dependence on the S and aS photon polarizations and can thus be exploited in future entanglement experiments.
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.
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.