  Photons are ideal carriers for quantum information as they can have a long
coherence time and can be transmitted over long distances. These properties are
a consequence of their weak interactions within a nearly linear medium. To
create and manipulate nonclassical states of light, however, one requires a
strong, nonlinear interaction at the single photon level. One approach to
generate suitable interactions is to couple photons to atoms, as in the strong
coupling regime of cavity QED systems. In these systems, however, one only
indirectly controls the quantum state of the light by manipulating the atoms. A
direct photon-photon interaction occurs in so-called Kerr media, which
typically induce only weak nonlinearity at the cost of significant loss. So
far, it has not been possible to reach the single-photon Kerr regime, where the
interaction strength between individual photons exceeds the loss rate. Here,
using a 3D circuit QED architecture, we engineer an artificial Kerr medium
which enters this regime and allows the observation of new quantum effects. We
realize a Gedankenexperiment proposed by Yurke and Stoler, in which the
collapse and revival of a coherent state can be observed. This time evolution
is a consequence of the quantization of the light field in the cavity and the
nonlinear interaction between individual photons. During this evolution
non-classical superpositions of coherent states, i.e. multi-component
Schroedinger cat states, are formed. We visualize this evolution by measuring
the Husimi Q-function and confirm the non-classical properties of these
transient states by Wigner tomography. The single-photon Kerr effect could be
employed in QND measurement of photons, single photon generation, autonomous
quantum feedback schemes and quantum logic operations.

Quantum Physics;Superconductivity