Interaction-Free Quantum Optical Fredkin Gates in $\chi ^{(2)}$ Microdisks

We present novel “interaction-free” realizations of quantum optical Fredkin gates that do not rely on direct physical coupling between the target light (signal) and the control light (pump). The interaction-free feature of such gates allow to overcome the fundamental limits of photon loss and quantum-state decoherence imposed by the signal-pump coupling. This advantage, together with the low inherent quantum-noise level in χ⁽²⁾ microdisks, gives rise to substantially improved performance over the existing Fredkin-gate designs. Explicitly using lithium-niobate mircrodisks, we present two kinds of interaction-free Fredkin gates, a phase gate and an optical-path gate, both of which are designed with telecom-band applications in mind. For both gates, the threshold pump peak power to achieve a gate contrast >;100 and a signal loss <;10% is hundreds of microwatts for practical parameters of the devices.