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Physical Review A

Distinguishing four photons in an entangled state from two independent pairs of photons

Z. Y. Ou

Published Nov 21, 2005• 28 citations
Publisher

Abstract

We analyze in a multimode model a recent scheme [Tsujino et al., Phys. Rev. Lett. 92, 153602 (2004)] to distinguish entangled four-photon polarization state from two independent polarization entangled pairs of photons in a single type-II parametric down-conversion process. The fraction of the four-photon entangled state among the two detected photon pairs is found to be related to a quantity that is responsible for the temporal mode match between the photon pairs. A comparison with the single mode models is discussed.

DOI
10.1103/physreva.72.053814

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We analyze in a multimode model a recent scheme [Tsujino et al., Phys. Rev. Lett. 92, 153602 (2004)] to distinguish entangled four-photon polarization state from two independent polarization entangled pairs of photons in a single type-II parametric down-conversion process. The fraction of the four-photon entangled state among the two detected photon pairs is found to be related to a quantity that is responsible for the temporal mode match between the photon pairs. A comparison with the single mode models is discussed.
Double-pair emission from type-II parametric down-conversion results in a highly entangled four-photon state. Due to interference, which is similar to bunching from thermal emission, this state is not simply a product of two pairs. The observation of this state can be achieved by splitting the two emission modes at beam splitters and subsequent detection of a photon in each output. Here we describe the features of this state and construct a Bell-type inequality, which gives a necessary and sufficient condition for a four-photon test of local realistic hidden variable theories.
An experiment is performed to demonstrate the temporal distinguishability of a four-photon state and a six-photon state, both from parametric down-conversion. The experiment is based on a multiphoton interference scheme in a recently discovered projection measurement of a maximally entangled N-photon state. By measuring the visibility of the interference dip, we can distinguish the various scenarios in the temporal distribution of the pairs and, thus, quantitatively determine the degree of temporal distinguishability of a multiphoton state.
We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t ph c is much shorter than the duration of the pump pulse Δt, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter χ, which is a function of t ph c Δt. We present a direct measurement of χ through a simple experimental set-up. The full theoretical analysis is also provided.