Nonlinear quantum interferometry with Josephson junction based parametric circuits*

Classical interferometers are indispensable tools in experiments which require accurate estimations of various physical quantities. Their respective accuracy is bound by the standard quantum limit, which, nevertheless, can be overcome by using quantum states or nonlinear quantum building blocks. Such nonlinear interferometers have been thoroughly investigated at optical frequencies, while leaving the microwave domain largely unexplored. Meanwhile, quantum microwave sensing represents a novel and quickly growing field, which is important for various applications in quantum information processing or quantum field theory. In this context, we realize and investigate a nonlinear interferometer in the microwave regime. The circuit consists of two cryogenic 180° hybrid ring beam splitters combined with superconducting flux-driven Josephson parametric amplifiers. We experimentally test a transformation implemented by this nonlinear microwave interferometer and demonstrate sub-Poissonian photon statistics for specific parameter regimes. Furthermore, we identify a low-gain operation regime of the interferometer, which is useful for achieving the theoretical 3 dB quantum advantage in quantum illumination protocols. Our findings demonstrate the versatility of nonlinear parametric interferometers in the microwave regime, which can be applied further in the fields of quantum metrology and sensing, as well as in quantum information processing.