  Mediated photon-photon interactions are realized in a superconducting
coplanar waveguide cavity coupled to a superconducting charge qubit. These
non-resonant interactions blockade the transmission of photons through the
cavity. This so-called dispersive photon blockade is characterized by measuring
the total transmitted power while varying the energy spectrum of the photons
incident on the cavity. A staircase with four distinct steps is observed and
can be understood in an analogy with electron transport and the Coulomb
blockade in quantum dots. This work differs from previous efforts in that the
cavity-qubit excitations retain a photonic nature rather than a hybridization
of qubit and photon and provides the needed tolerance to disorder for future
condensed matter experiments.
