Artificial coherent states of light by multi-photon interference in a single-photon stream

Coherent optical states consist of a quantum superposition of different photon number (Fock) states, but because they do not form an orthogonal basis, no photon number states can be obtained from it by linear optics. Here we demonstrate the reverse, by manipulating a random continuous single-photon stream using quantum interference in an optical Sagnac loop, we create engineered quantum states of light with tunable photon statistics, including approximate weak coherent states. We demonstrate this experimentally using a true single-photon stream produced by a semiconductor quantum dot in an optical microcavity, and show that we can obtain light with $g^{(2)}(0)\rightarrow1$ in agreement with our theory, which can only be explained by quantum interference of at least 3 photons. The produced artificial light states are, however, much more complex than coherent states, containing quantum entanglement of photons, making them a resource for multi-photon entanglement.