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The European Physical Journal D

Interaction of two-photon NOON state with ultrasonic wave

Piotr Kwiek

Published Sep 1, 2022• 3 citations
Publisher

Abstract

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

DOI
10.1140/epjd/s10053-022-00467-7

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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
The accurate theory describing interaction of two coherent light beams with ultrasonic wave where one of the light beam is incident at positive Bragg angle while the other at negative was developed by Leroy and Blomme in 1984 . The assumed geometry in this theory resembles an interferometer wherein ultrasonic beam plays a role of the output beam splitter of the light. The output light intensity is modulated with ultrasonic frequency as a result of interference between the light in diffraction orders in which the frequency is changed due to the Doppler effects with those diffracted with unchanged frequency. Temporal modulation of the light intensities in diffraction orders, that was foreseen by Leroy and Blomme, was confirmed experimentally and the results will be presented. In addition, the Leroy-Blomme theory has been extended to include the effect of the initial phase of the ultrasonic wave on the phase of modulation of light intensity in diffraction orders. According to the best knowledge of the author, Leroy and Blomme theory has not been verified experimentally, although many years have passed. This theory could be applied to the quantum optics phenomenon when pairs of entangled photons are incident on ultrasonic wave instead of two coherent light beams. The geometry of interaction of two coherent light beams with ultrasonic wave in Leroy-Blomme theory is the same as for Hong-Ou-Mandel interferometer wherein a beam splitter is replaced by the ultrasonic wave. Similarities and differences between Leroy-Blomme and Hong-Ou-Mandel interferometers will be presented.
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.
A two-photon interference experiment is presented in which an entangled pair of photons generated from a parametric down-conversion was incident on two input ports of a Mach-Zehnder interferometer. The experiment was carried out using two photon coincidence detection with two detectors at the two output ports of the interferometer. The measured coincidence counts exhibit an interference effect with visibility of 0.75 at simultaneous inputs and 0.38 at inputs with different arrival times according to the degree of photon number entanglement.
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.
In this paper, we theoretically study the concept of the wave–particle duality of two entangled neutral Bragg diffracted atoms. This is an extension of a recent study where the same idea was proposed in the photonic setup [Man et al., Sci. Rep. 7, 42539 (2017)] using two independent Mach–Zehnder interferometers. Now, we propose a similar scheme using the cavity-QED based setup, which comprises two independent atomic de Broglie Mach–Zehnder–Bragg interferometers, a source cavity that generates two external momenta state entangled atoms. Once the atoms pass through the source cavity initially prepared in the superposition of zero and one photon, they emerge out of the cavity in entangled momenta state such that if one atom is transmitted to the upper interferometer, then the second atom must traverse the lower interferometer, and vice versa. The final atomic de Broglie beam splitter at the top interferometer is prepared in the superposition of zero and one photon and facilitates observing the wave or particle aspect in a single setting. This entire setup functions in off-resonant Bragg diffraction and the proposed schematics are shown to be experimentally feasible under contemporary research scenarios.