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