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arXiv:quant-ph/0103049 · Physical Review A

Four-photon entanglement from down-conversion

Harald Weinfurter, Marek Żukowski

Published Jun 7, 2001• 183 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.64.010102

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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.
Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-II spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in simple beam-splitter (Hanburry Brown-Twiss) anticorrelation and quantum beating experiments. The cancellation of two-photon probability amplitudes as a result of this double entanglement allow us to demonstrate two different types of Bell's inequality violations in one experimental setup.
Simultaneous entanglement in spin and space-time of a two-photon quantum state generated in type-2 spontaneous parametric down-conversion is demonstrated by the observation of quantum interference with 98% visibility in a simple beam-splitter (Hanburry Brown-Twiss) anticorrelation experiment. The nonlocal cancellation of two-photon probability amplitudes as a result of this double entanglement allows us to demonstrate two different types of Bell's inequality violations in one experimental setup.
In the last few years the parametric down-conversion of light has attracted the attention of the researchers in foundations of quantum physics. The photons that come out from the non-linear crystal are highly correlated in many variables. One of the most important consequences of entanglement is the possibility of violating the so called Einstein locality expressed in Bell's inequality. In general factorizable state vectors do not violate Bell's inequality, but we will show that the factorizable state vector produced with a beam-splitter set on the paths of parametric down-conversion photons violates a new inequality that can be deduced from local realism. This inequality is more stringent than those used up to now to test the locality.
Nowadays,the generation of multiphoton entangled states is almost realized by combining the coupled entangled photons emitted from spontaneous parametric down-conversion (SPDC) with the first-order term.In this case,one may focus mainly on the first-order term,and then avoid multipair emission events by restricting experimental parameters.On the other hand,for the higher-order terms in SPDC source,these emitted entangled photons have interesting features.For example,they are entangled maximally not only in photon number for the spatial modes,but also in polarization degree of freedom.In general,two photons,which are entangled in two or more degrees of freedom,are called hyperentangled pair of photons or hyperentangled state.We present a scheme to generate the four-photon hyperentangled state based on four indistinguishable photons emitted from SPDC source with the second-order term.Consider two SPDC sources with equal probability of emission of photons in respective spatial modes.With the passive linear optical devices,i.e., beam splitters,half wave plates,polarizing beam splitters,etc.,under the condition of registering a specified four-photon coincidence,we can obtain the four-photon hyperentangled state in which the photons are entangled in both polarization and spatial-mode degrees of freedom.Here,of course,for an arbitrary fourfold coincidence detection,one obtains a canonical four-photon Greenberger-Horne-Zeilinger (GHZ) state.Then we show the results of fourfold coincidence detections and the corresponding probabilities for the four-photon GHZ states,where the generation of the four-photon hyperentangled state is included as long as we are not to distinguish the two detectors located at the same locations. As a result,our scheme has two notable features.When we only consider the second-order emission,since it is not needed for us to distinguish between the two SPDC sources,the present scheme is simple and feasible.Also,based on the postselection with fourfold coincidence detection,our scheme is suitable for the normal first-order emission where we restrict the four photons emitted from the same source.In this sense,our scheme is efficient.In a word,we describe a method to generate the four-photon hyperentangled state with the second-order emission in SPDC source,which may contribute to the exploration of multipair entanglement with higher-order emissions from the SPDC source.
Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographic protocols, and fundamental tests of quantum theory. Spontaneous parametric down-conversion is the most effective source for polarization entangled photon pairs. Here we show, that a entangled 4-photon state can be directly created by parametric down-conversion. This state exhibit perfect quantum correlations and a high robustness of entanglement against photon loss. We have used this state for four-particle test of local realistic theories. Therefore this state can be used for new types of quantum communication. We also report on possibilities for the experimentally realization of a 3-photon entangled state, the so called W-state, and discuss some of its properties.
When four photons arrive at a beam splitter, two from each side, a four-photon, six-path interference effect occurs to yield a sixfold enhancement of the probability for all four photons to exit together from the beam splitter. We produce the four-photon state by using the stimulated emission process in a pulsed parametric down-conversion and measure the probability for all four photons to exit from one side of the beam splitter. The observed enhancement factor is in good agreement with a multimode treatment of pulsed down-conversion.