We adopt artificial <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Lambda $ </tex-math></inline-formula> -type three-level system with superconducting devices for microwave signal detection, where the signal intensity reaches the level of discrete photons instead of continuous waveform. Based on the state transition principles of the three-level system, we propose a statistical model for microwave signal detection. In addition, achievable transmission rates and signal detection based on the proposed statistical models are investigated for low temperature conditions in deep space communication scenario. It is predicted that high sensitivity can be achieved by the proposed system. We further characterize the received signal considering the saturation phenomenon of three-level system, which reveals negligible performance degradation caused by saturation under weak received power regime.