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Physical Review A

Demonstration of the three-photon de Broglie wavelength by projection measurement

Bi‐Heng Liu, Fang‐Wen Sun, Yan-Xiao Gong, Yun‐Feng Huang, Z. Y. Ou, Guang‐Can Guo

Published Feb 12, 2008• 25 citations
Publisher

Abstract

Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on a proposal by [Wang and Kobayashi, Phys. Rev. A 71, 021802(R) (2005)] that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON-state projection measurement to a three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON-state contribution in these schemes of projection measurement. A detailed multimode analysis is made to account for imperfect situations in the experiments.

DOI
10.1103/physreva.77.023815

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Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on a proposal by [Wang and Kobayashi, Phys. Rev. A 71, 021802(R) (2005)] that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON-state projection measurement to a three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON-state contribution in these schemes of projection measurement. A detailed multimode analysis is made to account for imperfect situations in the experiments.
Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on the proposal by Wang and Kobayashi (Phys. Rev. A {\bf 71}, 021802) that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON state projection measurement to three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON state contribution in these schemes of projection measurement.
We construct a projection measurement process for the maximally entangled NNN-photon state [the NOON state $(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)∕\sqrt{2}$] with only linear optical elements and photodetectors. This measurement process will give null result for any NNN-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N=4N=4N=4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern.
A measurement process is constructed to project an arbitrary two-mode NNN-photon state to a maximally entangled NNN-photon state. The result of this projection measurement shows a typical interference fringe with an NNN-photon de Broglie wavelength. For an experimental demonstration, this measurement process is applied to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. Generalization to the projection measurement of an arbitrary NNN-photon state can be easily made and may have wide applications in quantum information. As an example, we formulate it for precision phase measurement.
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.