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Quantum Electronics

Quantum interference of biphotons with a Doppler frequency shift

E G Lariontsev

Published Aug 22, 2016• 1 citation
Publisher

Abstract

We report a theoretical study of transformation of a biphoton state of light under Bragg diffraction on a travelling sound wave in an acousto-optic modulator (AOM). It is shown that the diffraction of AOM biphotons emitted during the collinear parametric scattering of light leads to a shift of the carrier frequency of a biphoton wave packet, which exceeds twice the Doppler frequency shift for the classical field. A method is proposed for measuring the Doppler frequency shift of a biphoton, which is based on interference between independent biphotons.

DOI
10.1070/qel16096

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We report a theoretical study of transformation of a biphoton state of light under Bragg diffraction on a travelling sound wave in an acousto-optic modulator (AOM). It is shown that the diffraction of AOM biphotons emitted during the collinear parametric scattering of light leads to a shift of the carrier frequency of a biphoton wave packet, which exceeds twice the Doppler frequency shift for the classical field. A method is proposed for measuring the Doppler frequency shift of a biphoton, which is based on interference between independent biphotons.
Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.
This paper presents the results of theoretical and experimental investigations of a Hong–Ou–Mandel interferometer in which an optical beam splitter is replaced by an ultrasonic wave. The ultrasonic wave acts as an acousto-optical beam splitter for light, which is based on the phenomenon of Bragg diffraction on an ultrasonic wave. The Doppler effect was considered in the theoretical considerations and confirmed experimentally. It has been shown theoretically and experimentally that the Doppler effect changes the frequency of two-photon states at the outputs of an acousto-optical beam splitter. The frequency of the two-photon state in the positive diffraction order is increased by the frequency of the ultrasonic wave, whereas in the negative diffraction order, it is reduced by the frequency of the ultrasonic wave. It should be emphasized that there are no states 1112 in the outputs (diffraction orders), which disappear as a result of Hong–Ou–Mandel interference; consequently, the probability of detecting coincidences of photons between the plus first and minus first diffraction orders is zero, as it occurs in the Hong–Ou–Mandel interferometer. The frequency difference between the two-photon states at the outputs of the acousto-optical beam splitter was confirmed by recording the two-photon beat phenomenon. The obtained results changed the current view that the Doppler effect caused by ultrasonic waves can be neglected in the interaction of correlated pairs of photons with ultrasonic waves.
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
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.