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arXiv:0903.2756 · Journal of the Optical Society of America B

Quantum diffraction of biphotons at a blazed grating

Martin R. Ostermeyer, Dirk Puhlmann, D. Korn

Published Nov 18, 2009• 5 citations
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Abstract

Correlations between photons are interesting for a number of applications and concepts in metrology in particular for resolution improvements in different methods of quantum imaging. Since Fock-states of N-photons of wavelength lambda in interference schemes acquire N-times the phase shift of single photons these states can appear as if they had a de Broglie wavelength of lambda/N. A biphoton beam diffracted at a blazed grating shows this reduced de Broglie wavelength. This experiment can be seen as a purification of biphotons of a certain correlation strength on the one hand. On the other hand the evaluation of the one-photon and two-photon rate distributions in the Fraunhofer far field of the grating allows for an analysis of the spatial correlation between the photons. An experimental demonstration of these ideas tested for a biphoton beam generated by parametric down conversion (PDC) is reported. We demonstrate in addition that the existence of higher order spatial modes is important to observe strong spatial correlations and to observe the photonic de Broglie wavelength of lambda/2 for biphotons.

DOI
10.1364/josab.26.002347

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Correlations between photons are interesting for a number of applications and concepts in metrology in particular for resolution improvements in different methods of quantum imaging. Since Fock-states of N-photons of wavelength lambda in interference schemes acquire N-times the phase shift of single photons these states can appear as if they had a de Broglie wavelength of lambda/N. A biphoton beam diffracted at a blazed grating shows this reduced de Broglie wavelength. This experiment can be seen as a purification of biphotons of a certain correlation strength on the one hand. On the other hand the evaluation of the one-photon and two-photon rate distributions in the Fraunhofer far field of the grating allows for an analysis of the spatial correlation between the photons. An experimental demonstration of these ideas tested for a biphoton beam generated by parametric down conversion (PDC) is reported. We demonstrate in addition that the existence of higher order spatial modes is important to observe strong spatial correlations and to observe the photonic de Broglie wavelength of lambda/2 for biphotons.
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.
We demonstrate one- and two-photon diffraction and interference experiments utilizing parametric down-converted photon pairs (biphotons) and a transmission grating. With two-photon detection, the biphoton exhibits a diffraction-interference pattern equivalent to that of an effective single particle that is associated with half the wavelength of the constituent photons. With one-photon detection, however, no diffraction-interference pattern is observed. We show that these phenomena originate from the spatial quantum correlation between the down-converted photons.
Summary form only given. Recently, Jacobson et al. ( see Phys. Rev. Lett., vol.74, p. 4835 (1995)) proposed the concept of "photonic de Broglie wave" in multiphoton states. They argued that the photonic de Broglie wavelength of an ensemble of photons with wavelength /spl lambda//sub 0/ and average number of photons N can be measured using a special interferometer with "effective beam splitters" that do not split the multiphoton states into constituent photons. Fonseca et al. see Phys. Rev. Lett., vol. 82, p. 2868 (1999)) measured the photonic de Broglie wavelength of a two-photon state ("biphoton") using a kind of Young's interferometer. We propose and demonstrate the measurement of photonic de Broglie wavelength of biphotons generated by parametric down-conversion utilizing the usual Mach-Zehnder interferometer.
Summary form only given. J. Jacobson et al. (1995) have shown theoretically that the measured de Broglie wavelength of an object is dependent on its internal structure. A fourth-order Young interference experiment is done to demonstrate a practical way to measure the photonic de Broglie wavelength of a two-photon wavepacket. Light in the two-photon state generated collinearly in the process of spontaneous parametric down-conversion. By modifying the transverse field profile of the pump laser beam that generates the two-photon beam we demonstrate experimentally and theoretically that it is possible to measure the de Broglie wavelength of the constituents parts of the wavepacket, the de Broglie wavelength of the two-photon wavepacket (biphoton) as a whole and an undefined intermediate de Broglie wavelength between the two cases.