Projection measurement of the maximally entangled N -photon state for a demonstration of the N -photon de Broglie wavelength
Fang‐Wen Sun, Z. Y. Ou, Guang‐Can Guo · Physical Review A · 2006
We construct a projection measurement process for the maximally entangled $N$-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 $N$-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for $N=4$ 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.