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Physical Review A

Evaluation of multiphoton effects in down-conversion

Kazuyoshi Yoshimi, Kazuki Koshino

Published Apr 7, 2010• 0 citations
Publisher

Abstract

Multiphoton effects in down-conversion are investigated based on the full-quantum multimode formalism by considering a three-level system as a prototype nonlinear system. We analytically derive the three-photon output wave function for two input photons, where one of the two input photons is down-converted and the other one is not. Using this output wave function, we calculate the down-conversion probability, the purity, and the fidelity to evaluate the entanglement between a down-converted photon pair and a non-down-converted photon. It is shown that the saturation effect occurs by multiphoton input and that it affects both the down-conversion probability and the quantum correlation between the down-converted photon pair and the non-down-converted photon. We also reveal the necessary conditions for multiphoton effects to be strong.

DOI
10.1103/physreva.81.043806

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The up-conversion dynamics of two photons in a three-level system is investigated theoretically. The analysis is based on a rigorous formalism that incorporates the multimode nature of the photon field, enabling quantitative handling of the spatial profiles of the photon pulses. We have derived an analytic formula that connects the wavefunction of two input photons to that of an up-converted output photon. The up-conversion efficiency and the output pulse profile are numerically calculated using this formula.
Nonlinear multiphoton conversion processes are theoretically and experimentally challenging systems in quantum optics and related areas. These phenomena bring remarkable quantum properties and can be of fundamental relevance in quantum information and computation applications. Based on recent experimental advances and the possible uses in generalized three-photon squeezing, we investigate degenerate three-photon parametric down-conversion generated inside a cavity fed by a classical pump. In addition, we consider that the process is stimulated by a coherent driving mode and subjected to dissipation by spontaneous emission of the cavity. A treatment using phase-space methods and stochastic differential equations is applied and the stability conditions of its steady states are found. We find that the system does not exhibit multistability, instead it has a limited parameter region leading to a single stable steady branch, alongside multiple unstable branches. Focusing on the stable steady states and linearizing the dynamics around them, we calculate the spectral densities of the quadrature variables. We identify and characterize the squeezing of three-photon down-conversion. Moreover, since the quasi-probability differential equations of the higher-order multiphoton processes have higher-order derivatives, hindering their mapping into stochastic differential equations, we make use of a positive Wigner function approach to calculate two-dimensional spectral densities associated with three-time correlation functions, with the goal of studying non-Gaussian properties of the system.
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