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Journal of Optics B Quantum and Semiclassical Optics

Parametric down-conversion and maximal pump depletion

A. Bandilla, G. Drobný, Igor Jex

Published May 24, 2000• 11 citations
Publisher

Abstract

Using the truncated Wigner function approach and the Bloembergen solutions for nondegenerate down-conversion we calculate the conversion efficiency of spontaneous parametric down-conversion. In addition we determine higher moments of the pump and signal photon number. We find the upper bound for the efficiency of energy transfer and give a physically intuitive explanation for its existence. The depletion of the pump mode is immediately characterized by a strong destruction of its coherence.

DOI
10.1088/1464-4266/2/3/308

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Using the truncated Wigner function approach and the Bloembergen solutions for nondegenerate down-conversion we calculate the conversion efficiency of spontaneous parametric down-conversion. In addition we determine higher moments of the pump and signal photon number. We find the upper bound for the efficiency of energy transfer and give a physically intuitive explanation for its existence. The depletion of the pump mode is immediately characterized by a strong destruction of its coherence.
We report the efficient generation of high-gain parametric down-conversion, including pump depletion, with pump powers as low as 100 µW (energies 0.1 µJ/pulse) and conversion efficiencies up to 33%. In our simple configuration, the pump beam is tightly focused into a bulk periodically poled lithium niobate crystal placed in free space. We also observe a change in the photon number statistics for both the pump and down-converted beams as the pump power increases to reach the depleted pump regime. The experimental results are a clear signature of the interplay between the pump and the down-converted beams in highly efficient parametric down-conversion sources.
We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schr"odinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum fluctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.
Abstract We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motion fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum fluctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.
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.
We investigate the methods to obtain maximum correlated photon pairs generated in Type I spontaneous parametric down conversion (SPDC) with focused pump beam. We study the effect of pump focusing on the photon collection efficiency of signal and idler modes. The correlated photon pair collection efficiency decreases asymptotically with input pump beam focusing parameter [1]. The results obtained here are expected to be useful in designing appropriate optical fibers for generating efficient entangled photon sources for quantum information applications.
We show that, with proper modification of the pump field description from plane-wave to spherical-like, which serves to incorporate geometric effects that were discarded in the plane-wave model, the efficiency of the spontaneous parametric down conversion process exhibits dependence on pump intensity, contrary to previous theoretical predictions. Experimental investigations of this behavior are carried out under focused pumping conditions, where pump divergence is kept constant, and pairs of photons are collected behind an aperture that is large compared to the overall down-conversion profile. The resulting photon yield is found to exhibit a strong dependence on pump intensity, and an enhancement of the down-conversion efficiency is observed. The modified pump field description is also modeled numerically and calculations are presented, which are found to display good accordance with experimental observations. The enhanced yield of spontaneous parametrically down-converted photons will prove beneficial for many practical applications of entangled photon pairs where a high flux is desired.