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The detection of microwave fields at single-photon power levels is a muchsought-after technology, with practical applications in nanoelectronics andquantum information science. Here we demonstrate a simple yet powerfulcriticality-enhanced method of microwave photon detection by operating amagnetic-field tunable Kerr Josephson parametric amplifier near a first-orderquantum phase transition. We obtain a 73% efficiency and a dark-count rate of167 kHz, corresponding to a responsivity of $1.3 \times10^{17}~\mathrm{W}^{-1}$ and noise-equivalent power of 3.28 zW/$\sqrt{\rm Hz}$.We verify the single-photon operation by extracting the Poissonian statisticsof a coherent probe signal.

Microwave photon detection at parametric criticality