Three-photon energy–time entanglement

Abstract

Entangled quantum particles have correlations stronger than those allowed by classical physics. These correlations are at the heart of deep foundational questions in quantum mechanics [1][2][3] , and form the basis of many emerging quantum technologies [4][5][6][7][8][9] . Although the discrete variables of up to 14 ions 10 and the continuous variables between three intense optical beams 11,12 have been entangled, it has remained an open challenge to entangle the continuous properties of three or more individual particles. Here we experimentally demonstrate genuine tripartite continuous-variable entanglement between three separated particles. In our set-up the three particles are photons created directly from a single input photon; the creation process leads to quantum correlations between the energies and emission times of the photons. The entanglement between our photons is the three-party generalization of the Einstein-Podolsky-Rosen 1 correlations for continuous variables, and could serve as a valuable resource in a wide variety of quantum information tasks.We directly generate three entangled photons using the nonlinear process of cascaded spontaneous parametric downconversion (C-SPDC; ref. 13). In downconversion, a pump photon, with frequency ω p , inside a nonlinear material will occasionally fission into a pair of daughter photons with frequencies ω 0 and ω 1 . The total energy in the process is conserved 14 withhω p =hω 0 +hω 1 . The daughter photons share strong energy and time correlations that are the hallmark of entanglement 15,16 . The SPDC process is repeated with one of these daughter photons, at ω 0 , now serving as the pump, creating a pair of granddaughter photons simultaneously at ω 2 and ω 3 . Again energy is conserved, and the total energy of the the three photons created in C-SPDC must sum to the energy of the pump:hω p =hω 1 +hω 2 +hω 3 . The simplified representation of our three-photon state in frequency space, assuming a monochromatic pump, has the form( 1) where G 1 (ω 1 , ω p − ω 1 ) and G 2 (ω 2 , ω p − ω 1 − ω 2 ) are the jointspectral functions resulting from the phase-matching conditions of the first and second SPDC crystals respectively 17 . The three photons, consequently, share strong spectral correlations and exhibit genuine tripartite energy-time entanglement.To verify the tripartite entanglement of the photons generated in our C-SPDC process we use continuous-variable entanglement criteria, which we derive based on the work in ref. A narrowband pump laser at 404 nm downconverts into a pair of orthogonally polarized photons at 842 and 776 nm inside a periodically-poled KTP crystal (PPKTP). A filter (FP) removes the remaining pump light. A polarizing beamsplitter (PBS) is used to separate the two photons, and narrowband filters, F0 and F1, are used to block stray light. The photon at 842 nm is coupled into a single-mode fibre (SMF) and sent to the single-photon detector D1. The photon at 776 nm is coupled into single-mode polarization maintaining fibre (PMF) and sent to a PP...

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