Four Photon Entanglement from Parametric Down Conversion

Abstract

Double-pair emission from type-II parametric down conversion results in a highly entangled 4-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 give a Bell theorem for a 4-photon test of local realistic hidden variable theories. PACS Numbers: 3.65 Bz, 3.67-a, 42.50 Ar Parametric down conversion has proven to be the best source of entangled photon pairs so far in an ever increasing number of experiments on the foundations of quantum mechanics [1] and in the new field of quantum communication. Experimental realizations of concepts like entanglement based quantum cryptography [2], quantum teleportation [3] and its variations [4] demonstrated the usability of this source. New proposals for quantum communication schemes [5] and, of course, for improved tests of local hidden variable theories initiated the quest for entangled multi-photon states. Interference of photons generated by independent down conversion processes enabled the first demonstration of a three-photon Greenberger-Horne-Zeilinger (GHZ)-argument [6] and, quite recently, even the observation of a four-photon GHZ-state [7]. In this report we show that four photon entanglement can be obtained directly from type-II parametric down conversion. Instead of sophisticated but fragile interferometric setups , we utilize bosonic interference in a double-pair emission process. This effect causes strong correlations between measurement results of the 4 photons and renders type-II down conversion a valuable tool for new multi party quantum communication schemes. The analysis of the entanglement inherent in the four photon emission leads us to a new form of inequality distinguishing local hidden variable theories from quantum mechanics, and demonstrates its potentiality for experiments on the foundations of quantum mechanics. In type-II parametric down conversion [8] multiple emission events during a single pump pulse lead to the following state Z exp (−iα(a * V b * H + a * H b * V)) | 0 , (1) where Z is a normalization constant, α is proportional to the pulse amplitude, and where a * V is the creation operator of a photon with vertical polarization in mode a, etc. (Fig. 1). We are interested only in 4 photon effects, i.e. the emission of two pairs. Then only the term in (1) proportional to (a * H b * V + a * V b * H) 2 | 0 , (2) is relevant. The particle interpretation of this term can be obtained by its expansion H) | 0 , (3) and is given by the following superposition of photon number states | 2H a , 2V b + | 2V a , 2H b + | 1H a , 1V a , 1H b , 1V b , (4) where e.g. 2H a means 2 H polarized photons in the beam a. One should stress here that this type of description is valid only for down conversion emissions, which is detected behind filters endowed with a frequency band, which is narrower than that of the pumping fields [9]. If a wide band down-conversion is accepted then such a state is effective only if counts at the detectors are treated as coincidences, when they occur within time windows narrower than the inverse of the bandwidth of the radiation [10]. If such conditions are not met, then the four photon events are essentially emissions of two independent, entangled pairs, with the entanglement existing only within each pair. Let us pass the four photon state via two polarization independent 50 − 50 beam splitters. For simplicity we assume that at the beam splitters a is transformed into 1 √ 2 (a + a ′) and b into 1 √ 2 (b + b ′), with prime denoting the reflected 1