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Springer eBooks

Parametric Down Conversion

Bernhard W. Adams

Published Jan 1, 2003• 1 citation
Publisher
DOI
10.1007/978-1-4615-0387-3_5

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Parametric Down-Conversion

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Quantum spatial dynamics of high-gain parametric down-conversion accompanied by cascaded up-conversion

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Quantum cascaded up-conversion (CUpC) of parametric down conversion (PDC) in a finite nonlinear ${\ensuremath{\chi}}^{(2)}$ crystal is studied theoretically within parametric approximation. The exact solution for creation and annihilation operators presented in the form of Bogoliubov transformation is valid for the high-gain regime and explicitly includes the nonzero wave-vector mismatch both for PDC and CUpC. Characteristic equation is used to analyze parametric amplification and oscillating regimes for degenerate, three- and four-mode cases. We show that the parametric amplification exists under the fulfillment of the cascaded phase-matching conditions while both the PDC and CUpC processes are separately non-phase-matched. The influence of CUpC on quadrature squeezing of degenerate PDC is estimated.

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Parametric Down Conversion (PDC) is a very important resource for what concern the development of quantum technologies and for experiments about foundation of quantum mechanics. The interest about this phenomenon is due to the fact that photons emitted by PDC are quantum correlated in many parameters and it is possible to use the PDC to produce states of light with strong non-classical behaviour. The aim of this paper is provide an extensive review on the theory of Parametric Down Conversion whit particular emphasis for what concern the case of Spontaneous Parametric Down Conversion (SPDC) in bulk non-linear crystals.

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Quantum cascaded up-conversion (CUpC) of parametric down conversion (PDC) in a finite nonlinear ${\ensuremath{\chi}}^{(2)}$ crystal is studied theoretically within parametric approximation. The exact solution for creation and annihilation operators presented in the form of Bogoliubov transformation is valid for the high-gain regime and explicitly includes the nonzero wave-vector mismatch both for PDC and CUpC. Characteristic equation is used to analyze parametric amplification and oscillating regimes for degenerate, three- and four-mode cases. We show that the parametric amplification exists under the fulfillment of the cascaded phase-matching conditions while both the PDC and CUpC processes are separately non-phase-matched. The influence of CUpC on quadrature squeezing of degenerate PDC is estimated.
Parametric Down Conversion (PDC) is a very important resource for what concern the development of quantum technologies and for experiments about foundation of quantum mechanics. The interest about this phenomenon is due to the fact that photons emitted by PDC are quantum correlated in many parameters and it is possible to use the PDC to produce states of light with strong non-classical behaviour. The aim of this paper is provide an extensive review on the theory of Parametric Down Conversion whit particular emphasis for what concern the case of Spontaneous Parametric Down Conversion (SPDC) in bulk non-linear crystals.