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Journal of Modern Optics

Non-classical Properties of Stimulated Raman and Hyper-Raman Scattering in Stationary Regime

Marek Olivík, Jan Peřina

Published Jan 1, 1995• 5 citations
Publisher

Abstract

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.

DOI
10.1080/09500349514550161

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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.
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.
Photon statistics of stimulated Raman scattering of squeezed light are considered including additive noise. The phonon system is assumed to be in chaotic or squeezed chaotic states. The influence of nonlinear dynamics is established on the initial non-classical features of light adopting quasi-distribution related to anti-normal ordering, photocount distribution, its factorial moments and principal squeezing parameter. It is shown that the initial non-classical effects are increased by the nonlinear dynamics provided that the Stokes mode is less amplified than the anti-Stokes mode is damped, whereas in the opposite case the non-classical effects are swiftly smoothed out. The frequency detuning can be optimized to have maximum non-classical effects, which can periodically return. However, above a certain bound the non-classical effects are missing with frequency detuning, and also with increasing phonon number, even if the phonon system is squeezed. Small initial squeezing can be increased by the nonlinear dynamics, whereas strong squeezing can only be diminished.
Quantum statistical properties are derived for stimulated Raman scattering by squeezed phonons including squeezing of vacuum fluctuations in radiation modes and sub-Poisson photon behaviour.Initial radiation can be in squeezed thermalized and/or sub-Poisson states, phonon system can also be squeezed.In particular, effects of initial phase conditions, losses, initial nonclassical behaviour and phonon squeezing are demonstrated in terms of reduced factorial moments up to the fifth order in combined photon-photon and photon-phonon modes.Also photon number distribution, quadrature variances and principał squeeze parameters are shown.
A perturbative analytic operator solution of a completely quantum mechanical Hamiltonian of multi-photon pump non-degenerate hyper-Raman process is obtained. It is shown that the obtained solution is general in nature as the solutions of non-degenerate hyper-Raman and stimulated Raman processes can be obtained as special cases of the present solution. The analytic solutions obtained here are used to investigate the nonclassical properties of the different modes in the stimulated, spontaneous and partially spontaneous multi-photon pump non-degenerate hyper-Raman processes. The nonclassical nature of these processes is witnessed by means of single mode and intermodal quadrature squeezing, intermodal entanglement of different orders, lower order and higher order photon antibunching. Interestingly, manifesting the multiphoton nature of the pump modes, a bunch of nonclassicality involving them are observed due to self-interaction of various pump modes.
The process of stimulated Raman scattering is described by the model of 2D oscillator. The photons of Stokes mode are described by one mode of the oscillator and phonons of the medium are described by the other mode of oscillator. The interaction of photons and phonons is taken to be quadratic in the creation and annihilation operators of the photons and phonons. New time-dependent integrals of motion are found for stimulated Raman scattering within the framework of this model. The photon-phonon probability-distribution function is found in terms of Hermite polynomials of four variables. It is shown that the squeezing phenomenon can be transferred from one mode to the other due to interaction. The statistical dependence appears due to interaction as well. An explicit formula of the photon-number probability distribution as a function of the laser-field intensity and the medium parameters is obtained both in terms of Hermite polynomials of two variables and in terms of Legendre polynomials after the averaging of the photon-phonon probability-distribution function over the phonon mode. The mean photon number and its dispersion in the Stokes mode are expressed as functions of the medium parameters and a parameter of the interaction. It is shown that if the medium is initially prepared, then after the interaction with laser field the photons are created in squeezed state. The classical propagator for stimulated Raman scattering is found within the framework of the symplectic tomography scheme.