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Physical Review A

Enhancement of Stokes–anti-Stokes correlations by the classical incoherent incident light

Vladislav Yu. Shishkov, E. S. Andrianov, Alexander Pukhov, Alexey P. Vinogradov

Published Jan 14, 2021• 3 citations
Publisher

Abstract

It is known that spontaneous Raman scattering is accompanied by the appearance of nonclassical cross correlations of photons at Stokes and anti-Stokes frequencies. Such correlations occur due to the internal nonlinear interaction between electronic and nuclear vibration degrees of freedom. Since the properties of a given media are unchangeable, the possibilities for controlling the cross correlations are limited. This, in turn, restricts the possible applications of the correlated light obtained during the spontaneous Raman scattering. In this work, we investigate the influence of statistical properties of an incident light on the cross correlations of Stokes and anti-Stokes light. We show that the incoherence of the incident light results not only in the incoherence of the scattered light but also in the enhancement of the interbeam coherence at different frequencies. We demonstrate that the cross correlations of Stokes and anti-Stokes light intensities are enhanced when the incident light with high second-order autocorrelation function is applied. Our results pave the way to control correlated light obtained in the process of spontaneous Raman scattering.

DOI
10.1103/physreva.103.013514

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As is well known, light arising from Raman scattering on molecules shows nonclassical mutual correlations between the Stokes and anti-Stokes components. However, the practical use of nonclassical Raman light is limited, due to its low intensity. The Raman signal can be enhanced in surface-enhanced Raman scattering (SERS) experiments by placing Raman active molecules near a plasmonic nanoantenna, due to the Purcell effect. Since the main contribution to emission in SERS experiments is re-emitted light from the plasmonic nanoantenna with no nonclassical correlations, the question arises as to whether it is possible to simultaneously amplify the Raman signal and preserve the nonclassical correlations. In this work, we give a positive answer to this question. We show that plasmonic nanoantennas can be used to enhance the nonclassical light intensity. We demonstrate that the main factor causing deterioration of the cross correlations of SERS light is the fluorescent background of the plasmonic nanoantenna. We analyze the way in which the geometry of a plasmonic nanoantenna affects the nonclassical cross correlations of the Raman light, and show that there is an optimal size of plasmonic nanoantenna that both increases the Raman signal and preserves the nonclassical correlations of the light at the level of a single molecule. The obtained results pave the way for the creation of sources with controlled intensity and a degree of nonclassicality.

Physical Review A•Jan 26, 2021•3 citations
It is known that spontaneous Raman scattering is accompanied by the appearance of nonclassical cross correlations of photons at Stokes and anti-Stokes frequencies. Such correlations occur due to the internal nonlinear interaction between electronic and nuclear vibration degrees of freedom. Since the properties of a given media are unchangeable, the possibilities for controlling the cross correlations are limited. This, in turn, restricts the possible applications of the correlated light obtained during the spontaneous Raman scattering. In this work, we investigate the influence of statistical properties of an incident light on the cross correlations of Stokes and anti-Stokes light. We show that the incoherence of the incident light results not only in the incoherence of the scattered light but also in the enhancement of the interbeam coherence at different frequencies. We demonstrate that the cross correlations of Stokes and anti-Stokes light intensities are enhanced when the incident light with high second-order autocorrelation function is applied. Our results pave the way to control correlated light obtained in the process of spontaneous Raman scattering.
Statistical properties of light produced in spontaneous Raman scattering on an ensemble of molecules indicate the quantum nature of this phenomenon. The scattered light is non-classical and has high non-classical intensity correlations between Stokes and anti-Stokes components. The temporal coherence of this light is well investigated, while many questions related to spatial coherence remain open. Recent experiments reveal two peculiar features of the spatial coherence of the Stokes and anti-Stokes light. First, the intensity correlations between Stokes and anti-Stokes light remain non-classical even for macroscopic samples containing many molecules. Second, these correlations decrease when signal propagates through a multi-mode optical fiber: the more propagating fiber modes at Stokes and anti-Stokes frequencies the less the correlations. Moreover, the second-order autocorrelation function of Stokes and anti-Stokes light also decreases with the number of propagating modes in multi-mode fiber. In this paper, we build a model of spontaneous Raman scattering correlations of light produced by an ensemble of molecules and propagating through weakly guiding optical fiber that quantitatively explains all these observations. We show that spacial orthogonality of the fiber modes makes the light propagating through these modes uncorrelated in the standard detection scheme. This leads to suppression of non-classical intensity correlations of the total field in the multi-mode fiber. We find the degree of non-classical correlations on fiber parameters. The obtained results pave the way for engineering of non-classical Stokes -- anti-Stokes correlations.
Spontaneous vibrational Raman scattering is a ubiquitous form of light-matter interaction whose description necessitates quantization of the electromagnetic field. It is usually considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming field. When probing an ensemble of molecules, the question therefore arises: What quantum state should be used to describe the molecular ensemble following spontaneous Stokes scattering? We experimentally address this question by measuring time-resolved Stokes-anti-Stokes two-photon coincidences on a molecular liquid consisting of several sub-ensembles with slightly different vibrational frequencies. When spontaneously scattered Stokes photons and subsequent anti-Stokes photons are detected into a single spatiotemporal mode, the observed dynamics is inconsistent with a statistical mixture of individually excited molecules. Instead, we show that the data are reproduced if Stokes-anti-Stokes correlations are mediated by a collective vibrational quantum, i.e. a coherent superposition of all molecules interacting with light. Our results demonstrate that the degree of coherence in the vibrational state of the liquid is not an intrinsic property of the material system, but rather depends on the optical excitation and detection geometry.
The degree of phase cross correlation between a fluctuating pump wave and the Stokes wave, which is generated by stimulated Raman scattering, can be determined by observing the spectrum of anti-Stokes light generated by coherent anti-Stokes Raman scattering (CARS). The spectrum of the anti-Stokes light has two distinct features: one that arises from scattering through an off-resonant virtual level and one that arises from resonant scattering through the real level. This provides a method to measure the phase cross correlation between two optical fields of different color. The intensity of the anti-Stokes signal strongly depends on the degree of cross correlation. Depending on the detuning from Raman resonance in the CARS process, the anti-Stokes intensity can be either enhanced or suppressed with respect to the case of uncorrelated fields.1
It is shown that the Stokes and anti-Stokes components, related by the conditions ω s + ω α = 2 ω L and k s + k α =2 k L , are correlated. When the temperature of the scattering material is high [ kT ≫ h ( ω L – ω s )] and/or stimulated scattering exists, this correlation assumes a classical form and is analogous to the Brown-Twiss intensity correlation. This intensity correlation is readily explained by modulation of the pump wave due to molecular vibrations so that the thermal fluctuations of energy of these vibrations are synchronously transferred into the s and α sidebands. At low temperatures and pump intensities (as well as outside Raman resonances) a photon correlation is found which is explained by the simultaneous production of pairs of s and α photons as a result of the spontaneous decay of two pump photons. The statistics of the scattering field in this case assumes a nonclassical form characterized by a relatively high ( m ≫1) probability of pair production compared with the product of the probabilities for the production of separate s and α photons (with the intensity correlation m≤1). An estimate of the rate of coincidences for the scattering of 1-W focused TEM 00 pump radiation in liquid nitrogen yielded ~6 sec –1 and m~10 3 . Analogs of the Kirchhoff equation were obtained for the inelastic scattering of light. These formulas, derived from the conditions of unitarity of the scattering process and equilibrium of matter, define the statistics of the scattered light in terms of the Raman gain and the parametric conversion coefficient.
As is well known, light arising from Raman scattering on molecules shows nonclassical mutual correlations between the Stokes and anti-Stokes components. However, the practical use of nonclassical Raman light is limited, due to its low intensity. The Raman signal can be enhanced in surface-enhanced Raman scattering (SERS) experiments by placing Raman active molecules near a plasmonic nanoantenna, due to the Purcell effect. Since the main contribution to emission in SERS experiments is re-emitted light from the plasmonic nanoantenna with no nonclassical correlations, the question arises as to whether it is possible to simultaneously amplify the Raman signal and preserve the nonclassical correlations. In this work, we give a positive answer to this question. We show that plasmonic nanoantennas can be used to enhance the nonclassical light intensity. We demonstrate that the main factor causing deterioration of the cross correlations of SERS light is the fluorescent background of the plasmonic nanoantenna. We analyze the way in which the geometry of a plasmonic nanoantenna affects the nonclassical cross correlations of the Raman light, and show that there is an optimal size of plasmonic nanoantenna that both increases the Raman signal and preserves the nonclassical correlations of the light at the level of a single molecule. The obtained results pave the way for the creation of sources with controlled intensity and a degree of nonclassicality.