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Journal of Physics B Atomic and Molecular Physics

Quantum statistics of stimulated hyper-Raman scattering in an inhomogeneously broadened system

B. K. Mohanty, Partha Sarathi Gupta

Published Mar 28, 1981• 2 citations
Publisher

Abstract

A fully quantum mechanical density matrix formalism of stimulated hyper-Raman scattering in an inhomogeneously broadened system is presented including the effects of detuning, higher order non-linearities and loss. The equations are solved to fourth-order in the atom-field coupling constant under a situation of low loss, and Stokes-photon statistics are studied in the steady state. The coherence properties of the Stokes beam are found to increase with increasing amplification factor and with decreasing detuning. The occurrence of anti-bunching phenomena is investigated.

DOI
10.1088/0022-3700/14/6/020

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A fully quantum mechanical density matrix formalism of stimulated hyper-Raman scattering in an inhomogeneously broadened system is presented including the effects of detuning, higher order non-linearities and loss. The equations are solved to fourth-order in the atom-field coupling constant under a situation of low loss, and Stokes-photon statistics are studied in the steady state. The coherence properties of the Stokes beam are found to increase with increasing amplification factor and with decreasing detuning. The occurrence of anti-bunching phenomena is investigated.
The optical mixing of sufficiently coherent radiations of frequency (omega) 1 and (omega) 2 inside a suitable molecular medium can result coherent radiation at new frequency (omega) 3 equals [(omega) 1 + ((omega) 1 - (omega) 2)]. If (omega) 1 is kept fixed and (omega) 2 is varied so that a condition (omega) 1 - (omega) 2 equals (omega) is reached where (omega) is a molecular frequency of the medium, then (omega) 3 equals (omega) 1 + (omega) equals 2(omega) 1 - (omega) 2. In this case (omega) 3 coincides with the anti- Stokes Raman frequency associated with the molecular frequency (omega) . This process of coherent anti-Stokes Raman Scattering (CARS) is an important nonlinear optical process which provides intense collimated signal beams and is also an excellent spectroscopic tool. CARS being a four-wave mixing process, it is of interest to study the process in multi-level system to obtain a better insight into the problem. In the current paper we investigate the different quantum statistical properties of CARS in a inhomogeneously broadened three-level system based on density-matrix formalism where both the atomic system and the radiation fields are quantised. The photon-statistics, coherence characteristics and the occurrence of anti-bunching of the CARS field, in the steady state, are investigated.
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.
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.
A quantum mechanical treatment of stimulated Raman effect in a gaseous system is presented. The atomic system is described by a two-level system. The radiation fields also obey the laws of quantum mechanics. The effects of atomic motion and the detuning in one-photon absorption and two-photon emission are incorporated in the analysis. The equation of motion describing the photon-statistics of all the fields are obtained. As a special case, the time evolution of the average photon number, second order coherence and output variance of the Stokes field is studied. The results show a non-linear dependence on the parameters representing atomic motion, detuning and atomic relaxation constants.
Photon statistics of stimulated Raman scattering and degenerate hyper-Raman scattering in the cavity are investigated using the method of small operator corrections to a c-number solution. Weak non-classical effects and super-Poissonian behaviour of all modes are derived in the case of Raman scattering in stationary regime. Higher-order nonlinearity of hyper-Raman scattering leads to more significant non-classical effects—considerable quadrature squeezing and sub-Poissonian behaviour of laser and Stokes modes (Fano factor lower than 0·8) were obtained. A negative quantum noise component is manifested in oscillations of photon-number distribution and in negative values of Wigner distribution of the integrated intensity. The influence of external driving amplitude and thermal bath is examined.
A quantum-statistical analysis of multi-photon lasers including the effect of detuning and atomic motion is presented. The equations are solved to fourth order in the atom-field coupling constant. Systems in detailed balance (with multi-photon loss mechanism) as well as systems without detailed balance (with single-photon loss mechanism) are considered separately. Treatments for the single-mode and multi-mode processes are given. Expressions for threshold conditions, peak photon number and the half width of photon distribution are obtained. The variation of mean output photon number, the effect of detuning, the coherence characteristics, etc. are studied and results are illustrated for two- and three-photon lasers as examples.