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 experiments(1-4). Quantum entanglement(5), the coherent superposition of states in multi-particle systems, yields more complex phenomena(6,7). 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 imaging(8); these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit(9-12), or quantum lithography beyond the classical diffraction limit(13). It has been generally understood(14) 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 photons(15-18). 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.