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Journal of the Optical Society of America B

Nonlinear version of Einstein coefficients in parametric conversions

Shin Arahira, Hitoshi Murai, Hironori Sasaki

Published Feb 1, 2017• 2 citations
Publisher

Abstract

In this paper, we report an experimental investigation on the relation between efficiencies of stimulated and spontaneous parametric conversion processes in nonlinear optical devices. We have found that the generation rate of photon pairs in the spontaneous process, μ, and the conversion efficiency in the stimulated process, η, had a simple linear relationship of μ=Kη. The factor of proportionality, K, was found to be 1 pair/Hz/s, regardless of the types of the devices and the parametric processes. This new finding implies that there is a simple relationship, like the Einstein coefficients, between the spontaneous and the stimulated processes of optical nonlinearities.

DOI
10.1364/josab.34.000527

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In this paper, we report an experimental investigation on the relation between efficiencies of stimulated and spontaneous parametric conversion processes in nonlinear optical devices. We have found that the generation rate of photon pairs in the spontaneous process, μ, and the conversion efficiency in the stimulated process, η, had a simple linear relationship of μ=Kη. The factor of proportionality, K, was found to be 1 pair/Hz/s, regardless of the types of the devices and the parametric processes. This new finding implies that there is a simple relationship, like the Einstein coefficients, between the spontaneous and the stimulated processes of optical nonlinearities.
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The importance of photon pair generation can never be overemphasized. It has formed the basis of most fundamental quantum optical experiments like Bell-experiments, quantum teleportation and entanglement swapping. However for considerable number of years Quantum Mechanics in general has remained largely theoretical and within the four corners of laboratories. Quantum Key Distribution is one of the first quantum applications to break this barrier. It provides us with unconditionally secured communication by providing us with efficient alternative to classical cryptography. This study forms part of the effort in realizing efficient way of generating photon pairs through the Spontaneous Parametric Down-Conversion process using a nonlinear crystal cut for type-I phase matching. After generating the photon pairs, the paper examined how they can be detected efficiently. We measured the rate of single photon generation (up to 200 kHz) as well as the rate at which they are detected in coincidence (150 coincidences per second). We further investigated a quantum interference effect (the Hong-Ou-Mandel effect) which classical wave theory has failed to describe. This effect has numerous applications in scalable quantum networks and in linear quantum computing. Finally, a remarkable conversion efficiency of 2.2
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Using the approach of coupled wave equations, we consider spontaneous parametric down conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation. We find simple expressions in terms of mode-overlap integrals for the absolute pair-production rate into single-spatial modes and simple relationships between the efficiencies of the classical and quantum processes. The results, obtained with Green function techniques, are not specific to any geometry or nonlinear crystal. The theory is applied to both degenerate and nondegenerate SPDC. We also find a time-domain expression for the correlation function between filtered signal and idler fields.
A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality.