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Journal of the Optical Society of America B

Mesoscopic quantum correlations of Raman photon pairs from a microparticle

C. H. Raymond Ooi, Chan Hin Kam

Published May 31, 2016• 1 citation
Publisher

Abstract

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.

DOI
10.1364/josab.33.001311

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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.
Quantum Langevin formalism with noise operators is used to provide quantum descriptions of photon pairs (the Stokes and anti-Stokes fields) emitted by a mesoscopic spherical particle composed of quantum particles in a double Raman configuration. The spectra of the fields obtained are sensitive to the dimension of the microsphere and can be controlled by pump and control laser fields. Spectral peaks due to quantum coherence are Stark shifted by the laser fields experiencing autofocusing inside the spherical particle, causing broadening of peaks as the size of the microsphere increases. The antinormal-order spectrum is found to be identical to the normal-order spectrum. The anti-Stokes spectrum is identical to the Stokes spectrum when the linear dispersion is neglected. Frequency-dependent dielectric functions of the Stokes and anti-Stokes spectra corresponding to the linear dispersions of the particle yield narrow morphology-dependent resonance gain peaks at certain frequencies of the Stokes and anti-Stokes spectra that depend not only on the particle size but also on the angle of observation.
We present a semi-analytical theory to describe the nonlinear scattering of Raman photon pairs from a cylindrical microparticle comprising of quantum particles in double Raman configuration. The normally ordered Stokes and anti-Stokes spectra are computed to gain insights into the quantum optical properties of the system and the variation of the spectra with microparticle’s size, orientation as well as observation angles are also analyzed and compared with the results obtained in our previous work involving mesoscopic spherical particle. Our results show several features in the spectra that are unique to the case of cylindrical microparticle and not found in the spherical particle case, such as the shifting of the side peaks originally formed due to ac Stark shifts towards the center at certain range of particle radius values, occurrence of side peaks with magnitudes comparable to that of the central peak, formation of additional peaks at certain observation angles and strong dependence of the spectra on the microparticle’s cylinder axis orientation. Most of these effects are either caused by the inhomogeneity of the incident pump and control laser fields within the volume of the cylindrical microparticle or simply due to the lack of three-dimensional symmetry of cylindrical geometry.
The effect of a nearby metallic particle on the quantum optical properties of a quantum particle in the four-level double Raman configuration is studied using the quantum Langevin approach. We obtain analytical expressions for the correlated quantum fields of Stokes and anti-Stokes photons emitted from the system and perform analysis on how the interparticle distance, the direction of observation or detection, the strengths of controllable laser fields, the presence of surface plasmon resonance, and the number density of the quantum particle affect the quantum spectra of the Stokes and anti-Stokes fields. We explore the physics behind the quantum-particle--metallic-nanoparticle interaction within the dipole approximation, that is, when the interparticle distance is much larger than the sizes of the particles. Our results show the dependence of the spectra on the interparticle distance in the form of oscillatory behavior with damping as the interparticle distance increases. At weaker laser fields the enhancement of quantum fields which manifests itself in the form of a Fano dip in the central peak of the spectra becomes significant. Also, the quantum-particle--metallic-nanoparticle coupling, which is affected by the size of the metallic nanoparticle and the number density of the quantum particle, changes the angular dependence of the spectra by breaking the angular rotational symmetry. In the presence of surface plasmon resonance the oscillatory dependence of the spectra on the interparticle distance and angles of observation becomes even stronger due to the plasmonic enhancement effect.
We study the quantum correlation of photon pairs from a double Raman particle driven by laser fields in a modified photon density of states such as a cavity or a defect in a photonic crystal. We obtain an exact semianalytical expression for the photon correlation, which is characterized by two complex decay functions associated with the levels splitting (effective Rabi frequencies) that depend on the control laser field. The position and width of the cavity density of state with respect to the anti-Stokes transition determine the features in the two-photon correlation profile.
We present a largely analytical theory for two-photon correlations G(2){G}^{(2)}G(2) between Stokes (s)(s)(s) and anti-Stokes (a)(a)(a) photon pairs from an extended medium (amplifier) composed of double-$\ensuremath{\Lambda}$ atoms in counterpropagating geometry. We generalize the parametric coupled equations with quantum Langevin noise given in a beautiful experimental paper of Balic et al. [Phys. Rev. Lett. 94, 183601 (2005)] beyond adiabatic approximation and valid for arbitrary strength and detuning of laser fields. We derive an analytical formula for cross correlation ${G}_{as}^{(2)}=⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{s}^{\ifmmode\dagger\else\textdagger\fi{}}(L){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{a}^{\ifmmode\dagger\else\textdagger\fi{}}(0,\ensuremath{\tau}){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{a}(0,\ensuremath{\tau}){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{s}(L)⟩$ and use it to obtain results that are in good quantitative agreement with the experimental data. Results for Gas(2){G}_{as}^{(2)}Gas(2)​ obtained using our coupled equations are in good quantitative agreement with the results using the equations of Balic et al., while perfect agreement is obtained for sufficiently large detuning. We also compute the reverse correlation Gsa(2){G}_{sa}^{(2)}Gsa(2)​ which turns out to be negligibly small and remains classical while the cross correlation violates the Cauchy-Schwartz inequality by a factor of more than a hundred.
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.