De Broglie wavelength of a non-local four-photon state

Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments1,2,3,4. Quantum entanglement5, the coherent superposition of states in multi-particle systems, yields more complex phenomena6,7. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging8; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit9,10,11,12, or quantum lithography beyond the classical diffraction limit13. It has been generally understood14 that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons15,16,17,18. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.