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Physical Review A

Quantum correlations between a pair of Raman photons from a single atom under arbitrary excitation condition

Anil K. Patnaik, G. S. Agarwal, C. H. Raymond Ooi, Marlan O. Scully

Published Oct 17, 2005• 18 citations
Publisher

Abstract

The quantum correlation between a pair of Stokes and anti-Stokes photons, involving a Raman emission process is calculated. All realistic radiative and nonradiative decays are included in the calculation and the photon correlation between the pair for arbitrarily strong excitation fields and detunings are calculated. The correlation function shows photon antibunching, and a damped sinusoidal behavior with respect to the time delay between the measurement of the two photons. The current system can also produce four photon entanglement.

DOI
10.1103/physreva.72.043811

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The quantum correlation between a pair of Stokes and anti-Stokes photons, involving a Raman emission process is calculated. All realistic radiative and nonradiative decays are included in the calculation and the photon correlation between the pair for arbitrarily strong excitation fields and detunings are calculated. The correlation function shows photon antibunching, and a damped sinusoidal behavior with respect to the time delay between the measurement of the two photons. The current system can also produce four photon entanglement.
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){g}^{(2)}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.
Light with high mutual correlations at different frequencies can be used to create heralded single-photon sources, which may serve as the basic elements of existing quantum cryptography and quantum teleportation schemes. One of the important examples in natural systems of light with high mutual correlations is the light produced by spontaneous Raman scattering on an ensemble of molecules. In this paper, we investigate the possibility of using Raman light to create a heralded single-photon source. We show that when using Stokes scattered light for postselection of anti-Stokes scattered light, the latter may possess single-photon properties. We analyze the influence of various negative factors on the characteristics of such a heralded single-photon source, which include a time delay between Stokes and anti-Stokes photons, the finiteness of the correlation radius of an external source, and background radiation. We show that the low value of the second-order autocorrelation function of the single-photon source is preserved even when the flow of uncorrelated photons exceeds the flow of correlated photons in scattered Raman light by an order of magnitude.
The mesoscopic effects on quantum correlations of photon pairs emitted by a microspherical particle composed of many quantum particles in a double Raman scheme are studied. Quantum Langevin formalism with noise operators is used to compute the nonclassical correlations between the Stokes and anti-Stokes photons, particularly the Glauber’s second-order cross- and self-correlation functions. The theory includes realistic situations of inhomogeneous field distributions of the pump and control laser fields as the result of the focusing effect of the microsphere as well as its linear dispersion. The results show that the photon correlations are affected by the size and density of the microsphere, the detection direction, and the detuning and strength of the laser fields. The self-correlation times of the quantum fields are significantly enhanced by the focusing effect of the microsphere with certain sizes.
We study the cooperative effects between Raman and hyper-Raman processes in which two quanta from a pumping field are absorbed and another two entangled photons are generated. The symmetries of the involved operators can be reduced to SU(2)-algebra in which the Casimir vector of quasi-momentum of the two fields is conserved. Quantum correlations between the pump and the generated field states are investigated. Cooperative stabilization of two-mode coherent states between Stokes and anti-Stokes photons is shown using both semiclassical and quantum approaches. We show that the relaxation of the system is described by coherent states of the two-mode field. The possibilities of observing cross-correlations between the pump field and the generated field are analyzed.
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.
The process in which Raman scattering produces correlated Stokes and anti‐Stokes radiation is known as Stokes–anti‐Stokes (SaS) scattering. It has been shown recently that this process can generate entangled photon pairs, making it a promising tool for quantum optical technologies, but a proper quantum theoretical description was lacking. In this article, a fully quantum derivation of the electric polarization in a medium with vibrational Raman response, with quantized electromagnetic fields, is developed. Using quantum perturbation theory for Heisenberg operators, the solution for the material electric polarization is found and it is shown that a four‐wave mixing‐like correlated SaS scattering appears in the first order of perturbation and completely characterizes the nonresonant SaS photon pair production. It is also discussed how to construct the third‐order nonlinear optical susceptibility for the SaS scattering from the quantum formalism and show that it coincides with the one derived for classical fields in stimulated Raman.