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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Enhanced generation rate of the coherent entanglement photon pairs in parametrical down conversion

N. A. Enaki, Viorel Ciornea

Published Sep 25, 2001• 0 citations
Publisher

Abstract

The effect of enhancing nonlinear generation of entangled photons in the process of interaction of the external coherent electromagnetic field with nonlinear dispersive medium is studied in this paper. Taking into account the second and third order of the susceptibility tensor of the crystal, it is demonstrated that in good cavity approximation the bistable behavior of the two photon generation coefficient as a function of intensity of the pump laser field is possible. This effect is stimulated by decreasing the detuning between the frequency of the cavity mode and pump frequency as a function of an harmonicity terms in polarization.

DOI
10.1117/12.441314

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The effect of enhancing nonlinear generation of entangled photons in the process of interaction of the external coherent electromagnetic field with nonlinear dispersive medium is studied in this paper. Taking into account the second and third order of the susceptibility tensor of the crystal, it is demonstrated that in good cavity approximation the bistable behavior of the two photon generation coefficient as a function of intensity of the pump laser field is possible. This effect is stimulated by decreasing the detuning between the frequency of the cavity mode and pump frequency as a function of an harmonicity terms in polarization.
The effect of enhancing nonlinear generation of entangled photons in the process of interaction of the external coherent electromagnetic field with a nonlinear dispersive medium is studied in this paper. Taking into account the second- and third-order susceptibility tensors of the crystal, it is demonstrated that in the good cavity approximation the bistable behaviour of the two-photon generation coefficient as a function of intensity of the pump laser field is possible. This effect is stimulated by decreasing the detuning between the frequency of the cavity mode and pump frequency as a function of anharmonicity terms in polarization.
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A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.
We manipulated the simulation and apparatus to generate the entangled quantum photons by the enhanced higher quality factor in waveguide of whispering gallery mode resonator in silica microsphere. As the several nonlinear optics effects have been validated in micro-disk (lithium niobate materials based), others micro-cavity (microfiber and micro ring on the chip) and second harmonic generation (SHG) on the surface of silica microsphere because of the characterization of enhanced higher quality factor Q and smaller volume mode in these resonator. However until now for the second third nonlinearity of spontaneous parametric down conversion (SPDC), third order nonlinearity of spontaneous parametric down conversion (TOSPDC) and spontaneous four wave mixing (SFWM) in whispering gallery mode (WGM) resonator of silica microsphere rarely have not been fully investigated and verified to generate the triple and pair entangled photons where are widely applied on the applications of biosensor, quantum communications and spectroscopy, respectively. Specially, the features of silica microsphere have attracted many applications due to the simple fabrication, simplified materials melted by silica fiber. The work we demonstrated in this paper based on the breaking of the dispersion rules to make perfect phase matching in normal dispersion in silica microsphere depending on the blue laser spectrum in visible spectrum, then manipulated the modified size of microsphere to detune the pump laser of free spectral range (FSR) and both shift the geometrical dispersion are characterized in the variation of FSR given by (see PDF for equation), where n is refractive index, R is the microspheres radius and m is mode numbers in resonator, to compensate the materials dispersion given by (see PDF for equation), where c is the speed of light and λ is pump laser wavelength to fulfill the perfect phase matching in parametric down conversion regimes and the modeling fabrication coupling results also will be presented.
Quantum computation and quantum communication require sources of entangled photons, especially from low-cost diode lasers. This study considered a polarization entangled photons pulse source produced via a spontaneous parametric down-conversion process in the type-I phase-matching of two nonlinear crystals, incorporating a continuous wave laser diode operating in pulse mode as a pump. The generated photons were measured based on visibility as a function of the pump frequency and collection apertures. A polarization correlation between photon pairs of approximately 93% and a Bell parameter S value of 2.56 ± 0.05 were obtained using the source described here.
A study of the effects of absorption on the nonlinear process of parametric down-conversion is presented. Absorption within the nonlinear medium is accounted for by employing the framework of macroscopic QED and the Green tensor quantization of the electromagnetic field. An effective interaction Hamiltonian, which describes the nonlinear interaction of the electric field and the linear noise polarization field, is used to derive the quantum state of the light leaving a nonlinear crystal. The signal and idler modes of this quantum state are found to be a superposition of the electric and noise polarization fields. Using this state, the expression for the coincident count rates for both type-I and type-II down-conversion are found. The nonlinear interaction with the noise polarization field was shown to cause an increase in the rate on the order of ${10}^{\ensuremath{-}12}$ for absorption of 10% per centimeter. This astonishingly small effect is found to be negligible compared to the decay caused by linear absorption of the propagating modes. From the expressions for the biphoton amplitude, it can be seen that the maximally entangled states can still be produced even in the presence of strong absorption.