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Bulletin of the Russian Academy of Sciences Physics

Statistical Characteristics of Quantum Polarization States Formed in Periodically Poled Nonlinear Crystals: Mathematical Modeling

Aleksandr V. Belinsky, Ranjit Singh

Published Jan 1, 2020• 1 citation
Publisher

Abstract

Abstract A degenerate parametric process and the complete upward generation of ordinary and extraordinary optical waves inside a periodically poled nonlinear crystal (PPNC) with quadratic nonlinearity are considered. A quantum theory is developed for describing statistical characteristics of the polarized states of light in a PPNC. It is found that the degree of polarization can be controlled by creating an imbalance in the intensity of modes at frequencies of ordinary and extraordinary optical waves (i.e., reducing the average number of photons in one and increasing it in the other).

DOI
10.3103/s1062873820010074

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Abstract A degenerate parametric process and the complete upward generation of ordinary and extraordinary optical waves inside a periodically poled nonlinear crystal (PPNC) with quadratic nonlinearity are considered. A quantum theory is developed for describing statistical characteristics of the polarized states of light in a PPNC. It is found that the degree of polarization can be controlled by creating an imbalance in the intensity of modes at frequencies of ordinary and extraordinary optical waves (i.e., reducing the average number of photons in one and increasing it in the other).
Theoretical analysis is presented on quantum state evolution of polarization light waves at frequencies ωoω_{o}ωo​ and ωeω_{e}ωe​ in a periodically poled nonlinear crystal (PPNC). It is shown that the variances of all the four Stokes parameters can be squeezed.
Theoretical calculations on transmission of quantum states such as Schrödinger cat (SC) states are considered in a periodically poled nonlinear crystal (PPNC). Combinations of various initial states (SC, coherent (C),and vacuum (V)) of light waves at frequencies ωeω_{e}ωe​ and 3ωe3ω_{e}3ωe​ at the input of a PPNC are studied. It is shown that the transmission and interference between superposition of macroscopically distinguishable states can be achieved by using a PPNC. Visualization and analyzes of transmission and interference processes are demonstrated with the help of reduced Wigner quasi-probability distribution functions of considered light waves.
Abstract We have investigated the spectral properties and the multimode structure of joint states of photon pair produced by parametric down conversion in periodically poled nonlinear crystals (PPNC) by adding random length to each domain. We have also analysed the effect of additional random length on the output efficiency by considering two different configurations of PPNC and linear crystals, which we call (+, ‐) (PN) and (+, 0,−, 0) (PZNZ) configuration. In this paper we wish to study the effect of length fluctuations of segments which may occur in the preparation of PPNC in the laboratory. We aim at finding out how much error is reasonable in the process. In order to do this, we added random length to each segment and obtained the relevance between the output intensity and length fluctuations of the crystals.
We consider a nondegenerate parametric process ω 3 → ω 1 + ω 2 and simultaneous sum frequency generation ω 1 + ω 3 → ω 4 and ω 2 + ω 3 → ω 5 in periodically poled quadratic crystals. An algorithm is proposed for the numerical description of the system evolution with full allowance for the quantum-mechanical interaction of all five plane monochromatic modes and pump depletion. The behaviour of the average number of photons of interacting modes and their mutual correlations is studied. An effect of inversion of the mutual correlation of the modes of the generated light is found.