  Single-photon devices at microwave frequencies are important for applications
in quantum information processing and communication in the microwave regime. In
this work, we describe a proposal of a multi-output single-photon device. We
consider two superconducting resonators coupled to a gap-tunable qubit via both
its longitudinal and transverse degrees of freedom. Thus, this qubit-resonator
coupling differs from the coupling in standard circuit quantum-electrodynamic
systems described by the Jaynes-Cummings model. We demonstrate that an
effective quadratic coupling between one of the normal modes and the qubit can
be induced, and this induced second-order nonlinearity is much larger than that
for conventional Kerr-type systems exhibiting photon blockade. Assuming that a
coupled normal mode is resonantly driven, we observe that the output fields
from the resonators exhibit strong sub-Poissonian photon-number statistics and
photon antibunching. Contrary to previous studies on resonant photon blockade,
the first-excited state of our device is a pure single-photon Fock state rather
than a polariton state, i.e., a highly hybridized qubit-photon state. In
addition, it is found that the optical state truncation caused by the strong
qubit-induced nonlinearity can lead to an entanglement between the two
resonators, even in their steady state under the Markov approximation.
