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Journal of Experimental and Theoretical Physics

Generation of phase-correlated light pulses in a hyper-Raman active medium

Yu. P. Malakyan, A. R. Mkhitaryan

Published Jun 1, 1997• 0 citations
Publisher

Abstract

We analysis within the quantum setting the effect of correlation of monochromatic fields of the Stokes and parametric radiation generated in a two-photon-absorbing medium by hyper-Raman scattering and four-wave mixing, respectively. Our results show that when there is destructive interference between the two processes, both modes are amplified in the medium in a correlated way, so that beyond a certain characteristic distance they propagate in a stationary manner with the same amplitudes and photon statistics but with opposite phases, while the medium becomes transparent to them. We calculate the intensity of the fields, the emission linewidths, and the diffusion of the total phase, the latter determining the extent of phase noise correlation at the output. We also show that no matter how the phases of the separate modes diffuse, the quantum fluctuations in the total phase may be completely squeezed.

DOI
10.1134/1.558242

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We develop the quantum theory of stimulated hyper-Raman scattering (HRS) and discuss the quantum statistics of pump and Stokes fields. We show that the initially coherent pump field acquires a strong squeezing that exceeds the similar squeezing in other nonlinear processes also involving two-photon absorption. Stokes field statistics are analysed in detail as a function of the initial statistics of both modes. Bunching effects are shown to be amplified in the short-time region, while in asymptotics the antibunching of Stokes photons becomes dominant, which in many cases results in sub-Poissonian statistics of Stokes mode. We also find a number of correlation effects between the photons of the two modes.
We present a comprehensive study of co- and counterpropagating Stokes and anti-Stokes quantum fields in double Raman four-wave mixing parametric oscillators using full quantum Heisenberg-Langevin framework with noise operators. General analytical solutions of the fields operators at any point in the Raman medium are obtained for four cases: two possible copropagating (forward) and two counterpropagating (backward) Stokes and anti-Stokes. We analyze the symmetrical properties of the complex linear and nonlinear susceptibilities spectra of the quantum fields, nonclassicality of two-photon correlation functions, spatial variations of the quantum fields, and the two-mode relative intensity squeezing. We compare the results of forward and backward cases for several limiting double Raman schemes. We find interesting resonant effects of medium length, laser detunings and laser field strengths (Rabi frequencies) for backward-propagating geometries. Analysis of the solutions provide insights on the resonant conditions while computation over multiple variables enables us to identify the values of laser detuning, field strength, and propagation length that give enhanced nonclassical intensity squeezing and persistent correlations. The present work sets the crucial foundations for optimization of the nonclassicality of photons in double Raman systems and would be useful for quantum information storage, quantum nonlinear optics, and quantum spectroscopy.
Using the approximation of small fluctuations around a stationary solution, photon statistics and quadrature variances are derived in stimulated Raman and hyper-Raman scattering including the coupling of pumping, Stokes, anti-Stokes and phonon modes. The depletion of pump light is included. Compared to Raman scattering, additional regimes to generate anti-bunched, sub-Poisson and squeezed light were found caused by self-interaction of the pump mode. It was possible to include effects of nonlinear dynamics, initial squeezing of radiation and phonon system, external noise and losses.
A pencil shaped region of a Raman-active medium forms a source for Stokes-shifted light via stimulated Raman Scattering (SRS) when driven by an intense laser pulse. Stokes photons are scattered spontaneously at first, and then amplified during propagation through the medium. Since the scattering is initiated by quantum noise, the actual number of photons produced in any given pulse will be highly uncertain, even if the pulse energy of the driving laser is constant1. As the Stokes light propagates through such an extended region, it's coherence properties will be changed. The spatial coherence is determined by the size and shape of the region, which may be characterized by its Fresnel number F, defined as F= A/λSL, where A is the cross-sectional area of the interaction region, which has length L, and λS is the Stokes wavelength. The rate at which the microscopic scatterers (atoms or molecules) are dephased by collisions affects the temporal coherence of the Stokes light, characterised by the temporal coherence parameter Γτ /gL, where Γ is the collisional dephasing rate, τ is the laser pulse duration and g is the steady-state Raman gain coefficient.
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.