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Physical Review A

Angular and temperature dependence of photon pair rates in spontaneous parametric down-conversion from a periodically poled crystal

G. Daniel Jimenez, Veneranda G. Garces, Kevin A. O’Donnell

Published Aug 11, 2017• 4 citations
Publisher

Abstract

We present a theoretical and experimental study of the angular and temperature dependence of the photon pairs produced by spontaneous parametric down-conversion in a periodically poled KTP crystal. In the experiment, two detectors are placed at different angles in the emitted light, and the detected photon pair rate is measured as a function of one angle or of crystal temperature. In the theoretical work, exact results for the pair rates are obtained through importance-sampled numerical integration of the fourth-order coherence function over regions representing the experimental integration parameters. Conditions studied range from well-resolved results in which detector angular and filter bandwidth integration effects are negligible, to other cases in which such effects are large and pair rates exceed ${10}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Throughout these cases, good agreement is often seen between experimental and theoretical results, while some differences that are noted provide insight into the actual crystal quasi-phase-matching function.

DOI
10.1103/physreva.96.023828

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We present a theoretical and experimental study of the angular and temperature dependence of the photon pairs produced by spontaneous parametric down-conversion in a periodically poled KTP crystal. In the experiment, two detectors are placed at different angles in the emitted light, and the detected photon pair rate is measured as a function of one angle or of crystal temperature. In the theoretical work, exact results for the pair rates are obtained through importance-sampled numerical integration of the fourth-order coherence function over regions representing the experimental integration parameters. Conditions studied range from well-resolved results in which detector angular and filter bandwidth integration effects are negligible, to other cases in which such effects are large and pair rates exceed 105s\ensuremath−1{10}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}105s\ensuremath−1. Throughout these cases, good agreement is often seen between experimental and theoretical results, while some differences that are noted provide insight into the actual crystal quasi-phase-matching function.
The process of spontaneous parametric down-conversion (SPDC) in nonlinear crystals makes it fairly easy to generate entangled photon states. It has been known for some time that the conversion efficiency can be improved by employing quasi-phase-matching in periodically poled crystals. Using two single-photon detectors, we have analyzed the photon pairs generated by SPDC in a periodically poled lithium niobate crystal pumped by a femtosecond laser. Several parameters could be varied in our setup, allowing us to obtain data in close agreement with both thermal and Poissonian photon-pair distributions.
Efficient entangled photon pair sources are the main component for several applications based on quantum imaging. Specifically for ghost imaging, different wavelengths of signal (imaging photons) and idler (interaction with the object) photons are desired. An efficient and narrowband generation of entangled photons exploiting spontaneous parametric down-conversion using periodically poled (pp) nonlinear crystals is therefore a fundamental preliminary requirement to achieve (the process of) ghost imaging. This work presents the design and implementation of a precise and efficient crystalheater as a variable photon pair source and compares the achieved experimental values of the SPDC-wavelengths with theoretical calculations. A periodically poled nonlinear crystal from potassium titanyl phosphate (ppKTP) can generate various non-degenerate wavelengths from a pump radiation of 405 nm by temperature changes and satisfaction of energy conservation and quasi-phase-matching conditions. For this purpose, the crystal is securely housed in a custom-built mechanical mount. A computation and adjustment of various control parameters, as well as a precise determination of the current temperature via two temperature sensors allow the heater to set the target temperature with an accuracy of 0.1 °C±0.015 °C. A method for the theoretical determination of the temperature-dependent shift of the nondegenerate wavelengths, provides a foundation from which experimental verification of achievable wavelengths and intensities can be compared. By experimental verification, the efficiency and functionality of the photon pair source and SPDC-process is verified. These presented investigations and the design of the crystal-heater provide the basis for a precise and effective photon pair source, for subsequent studies in the field of ghost imaging.
Abstract Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.
We report the generation of frequency-uncorrelated photon pairs from counter-propagating spontaneous parametric down-conversion in a periodically-poled KTP waveguide. The joint spectral intensity of photon pairs is characterized by measuring the corresponding stimulated process, namely, the difference frequency generation process. The experimental result shows a clear uncorrelated joint spectrum, where the backward-propagating photon has a narrow bandwidth of 7.46 GHz and the forward-propagating one has a bandwidth of 0.23 THz like the pump light. The heralded single-photon purity estimated through Schmidt decomposition is as high as 0.996, showing a perspective for ultra-purity and narrow-band single-photon generation. Such unique feature results from the backward-wave quasi-phase-matching condition and does not has a strict limitation on the material and working wavelength, thus fascinating its application in photonic quantum technologies.
We present a theoretical and experimental analysis of the joint effects of the transverse electric field distribution and of the nonlinear crystal characteristics on the properties of photon pairs generated by spontaneous parametric downconversion (SPDC). While it is known that for a sufficiently short crystal the pump electric field distribution fully determines the joint signal–idler properties, for longer crystals the nonlinear crystal properties also play an important role. In this paper we present experimental measurements of the angular spectrum (AS) and of the conditional angular spectrum (CAS) of photon pairs produced by SPDC, carried out through spatially resolved photon counting. In our experiment we control whether or not the source operates in the short-crystal regime through the degree of pump focusing, and explicitly show how the AS and CAS measurements differ in these two regimes. Our theory provides an understanding of the boundary between these two regimes and also predicts the corresponding differing behaviors.