  An excited emitter decays by radiating a photon into a quantized mode of the
electromagnetic field, a process known as spontaneous emission. If the emitter
is driven to a higher excited state, it radiates multiple photons in a cascade
decay. Atomic and biexciton cascades have been exploited as sources of
polarization-entangled photon pairs. Because the photons are emitted
sequentially, their intensities are strongly correlated in time, as measured in
a double-beam coincidence experiment. Perhaps less intuitively, their phases
can also be correlated, provided a single emitter is deterministically prepared
into a superposition state, and the emitted radiation is detected in a
phase-sensitive manner and with high efficiency. Here we have met these
requirements by using a superconducting artificial atom, coherently driven to
its second-excited state and decaying into a well-defined microwave mode. Our
results highlight the coherent nature of cascade decay and demonstrate a novel
protocol to generate entanglement between itinerant field modes.
