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Quantum Electronics and Laser Science Conference

Quantum diffraction and interference of biphotons generated by parametric down conversion

Ryōsuke Shimizu, Keiichi Edamatsu, T. Itoh

Published Jun 25, 2003• 0 citations
Publisher

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.

DOI
10.1109/qels.2002.1031045

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CRC Press eBooks•Oct 15, 2025•0 citations
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.
Diffraction-interference patterns of parametric down-converted photons through a transmission grating by both one- and two-photon detection schemes are presented. The measured patterns are explained by the Fourier analysis of the two-photon wave packet, considering the quantum spatial correlation between the constituent photons. Spatial diffraction-interference patterns were recorded by a two-photon detector consisting of two avalanche photodiodes. For comparison, diffraction-interference patterns of Ti:sapphire laser are also observed using the same apparatus (a uncorrelated case).
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.
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. 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. Pairs of entangled photons display a complex quantum state that cannot be represented through a product of single-particle states. The spontaneous parametric down-conversion (SPDC) process, that takes place when a laser pulse pumps a second-order nonlinear crystal has become recently a convenient source of such nonclassical states of light in quantum optics experiments. Nonstationary effects are mainly observed when the pump pulse temporal duration is significantly shorter than the characteristic interaction time in the nonlinear crystal. We introduce a nonstationary theory of SPDC to describe the results of fourth-order quantum-interference experiments when no spectral filtering is applied to the down-converted fields. Experiments involving nonlinear SPDC crystals with three different lengths were performed. The ultraviolet laser pulses were obtained from a Ti:sapphire femtosecond laser with a second-harmonic generator. These pulses were used to pump nonlinear crystals to initiate the process of nonstationary spdc and generate orthogonally-polarized photon pairs. These pairs then went into a polarization interferometer, and the coincidence counts of the detectors at the two output ports of the interferometer were recorded.
Beamlike photon pairs were generated by spontaneous parametric down-conversion using a type-II β-BaB 2 O 4 crystal. A pump laser generated photon pairs when it was transmitted through the crystal and was reflected back into the crystal by a mirror to generate more photon pairs. The photon pairs generated when the pump laser first transmitted through the crystal (first photon pairs) were also reflected back into the crystal to overlap with the light path of the photon pairs generated in the second transmission of the pump laser through the crystal (second photon pairs). We observed interference between the first and second photon pairs modulated with a half period of the wavelength of the photon pairs, which demonstrates two-photon interference using the beamlike photon pairs. The fringe period confirms that the observed interference is not classical interference but quantum two-photon interference. Through rotating the angles of quarter-wave plates in the light paths of the photon pairs, we generated beamlike photon pairs with entangled polarization. The phase between the first and second photon pairs could be tuned by changing the position of mirrors reflecting the pump pulses and photon pairs. The fringes of coincidence counts showed that the beamlike photon pairs have polarization entanglement.