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arXiv:1309.3599

Diffraction of collinear correlated photon pairs by an ultrasonic wave

Piotr Kwiek

Published Sep 13, 2013• 1 citation
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Abstract

The phenomenon of collinear correlated photon pairs diffraction by an ultrasonic wave is investigated for Bragg incidence. A BBO crystal was used for producing collinear correlated photon pairs via type-I spontaneous parametric down-conversion (SPDC I-type). It is shown experimentally that the Bragg angle for photon pairs diffraction is identical to the one corresponding to single photons diffraction. The numbers of single photons and photon pairs counts in discrete diffraction orders were measured as functions of the Raman-Nath parameter. Similarly, the number of coincidence photon counts in separate diffraction orders was also investigated. What is more, simple analytical formulas are derived which perfectly describe experimentally obtained data. OCIS codes: (050.1940) Diffraction; (230.1040) Acousto-optical devices; (230.4110) Modulators; (270.4180) Multiphoton processes.

DOI
10.48550/arxiv.1309.3599

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The phenomenon of collinear correlated photon pairs diffraction by an ultrasonic wave is investigated for Bragg incidence. A BBO crystal was used for producing collinear correlated photon pairs via type-I spontaneous parametric down-conversion (SPDC I-type). It is shown experimentally that the Bragg angle for photon pairs diffraction is identical to the one corresponding to single photons diffraction. The numbers of single photons and photon pairs counts in discrete diffraction orders were measured as functions of the Raman-Nath parameter. Similarly, the number of coincidence photon counts in separate diffraction orders was also investigated. What is more, simple analytical formulas are derived which perfectly describe experimentally obtained data. OCIS codes: (050.1940) Diffraction; (230.1040) Acousto-optical devices; (230.4110) Modulators; (270.4180) Multiphoton processes.
The phenomenon of collinear correlated photon pair diffraction by an ultrasonic wave is investigated for Bragg incidence. A beta-barium borate crystal was used for producing collinear correlated photon pairs via type-I spontaneous parametric down-conversion. It is shown experimentally that the Bragg angle for photon pair diffraction is identical to the one corresponding to single-photon diffraction. The numbers of single photon and photon pair counts in discrete diffraction orders were measured as functions of the Raman-Nath parameter. Similarly, the number of coincidence photon counts in separate diffraction orders was also investigated. What is more, simple analytical formulas are derived which perfectly agree with the experimentally obtained data.
Abstract The paper presents a classical and quantum description of the diffraction of two light beams incident on an ultrasonic wave at a positive and negative Bragg angle. The quantum description of the interaction with the ultrasonic wave was carried out for the two-photon NOON state. Study of diffraction of entangled pair of photon was performed in Mach–Zehnder interferometer wherein an output beam splitter is replaced by ultrasonic wave. It has been shown theoretically and experimentally that when a pair of photons generated from a parametric down-conversion was incident on two input ports of Mach–Zehnder interferometer with an acousto-optical beam splitter, then two-photon beats are observed at the output of the interferometer. The phenomenon of two-photon beats with the double frequency of the ultrasonic wave is the result of the Doppler effect on the ultrasonic wave. Time-correlated single-photon counting method was used to register the phenomenon of two-photon beats. The method of calibrating the interferometer with the use of an additional light source was presented in detail, which guarantees the observation of interaction of two-photon NOON state with ultrasonic wave. Graphical abstract
In this paper, we have presented and established a new theoretical formulation of photon optics based on photon path and Feynman path integral idea. We have used Feynman path integral approach to discuss Fraunhofer, Fresnel diffraction of single photon and entangled photon pairs by ultrasonic wave and obtained the following results: i) quantum state and probability distribution of single photon and entangled photon pairs by Fraunhofer and Fresnel ultrasonic diffraction, ii) oblique incidence Raman-Nath and Bragg diffraction conditions, iii) total correlation state and its probability distribution. Our calculation results are in agreement with the experiment results. Comparing one-photon and two-photon diffraction effects by ultrasonic waves, we have found that two-photon diffraction by ultrasonic waves is also a sub-wavelength diffraction.
Photons incident on a periodic medium at the Bragg angle are dynamically diffracted and exhibit the pendell\"osung phenomenon familiar from x-ray and neutron-diffraction experiments. The entangled two-photon state incident from the positive and negative Bragg angle exhibits a pendell\"osung length that is half that for the single-photon case. In our experiment the photon pairs were produced via parametric down-conversion and the periodic medium was a crystal whose refractive index was periodically altered by an acoustic wave. The predicted Pendell\"osung-length behavior was experimentally confirmed.
Summary form only given. We demonstrate a proof-of-principle experiment of quantum lithography utilizing parametric down-converted photons and a transmission grating, and show that the diffraction of a multiphoton state can be also explained by the concept of the photonic de Broglie wave. Pairs of frequency-degenerate photons were collinearly generated by spontaneous parametric down-conversion (SPDC) in a 5 mm long KNbO/sub 3/ (KN) crystal pumped by the second harmonic light of a single longitudinal mode Ti:sapphire laser operating at 861.5 nm. The photon pairs were diffracted by a transmission grating (slit width: 125 /spl mu/m, period: 250 /spl mu/m), placed just after the KN crystal. In this geometry, each photon pair passes together through one of the grating slits. By rotating a mirror, we recorded spatial diffraction-interference patterns at a two-photon detector consisting of two avalanche photodiodes. For comparison, we also observed diffraction-interference patterns of chaotic light from a tungsten lamp using the same apparatus.
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.