  The ability to generate light in a pure quantum state is essential for
advances in optical quantum technologies. However, obtaining quantum states
with control in the photon-number has remained elusive. Optical light fields
with zero and one photon can be produced by single atoms, but so far it has
been limited to generating incoherent mixtures, or coherent superpositions with
a very small one-photon term. Here, we report on the on-demand generation of
quantum superpositions of zero, one, and even two photons, via pulsed coherent
control of a single artificial atom. Driving the system up to full atomic
inversion leads to the generation of quantum superpositions of vacuum and one
photon, with their relative populations controlled by the driving laser
intensity. A stronger driving of the system, with $2\pi$-pulses, results in a
coherent superposition of vacuum, one and two photons, with the two-photon term
exceeding the one-photon component, a state allowing phase super-resolving
interferometry. Our results open new paths for optical quantum technologies
with access to the photon-number degree-of-freedom.

Quantum Physics