We present a superconducting noise bolometer for terahertz radiation, which is suitable for large-format arrays. It is based on an antenna-coupled superconducting micro-bridge embedded in a high-quality factor superconducting resonator for a microwave bias and readout with frequency-division multiplexing in the GHz range. The micro-bridge is kept below its critical temperature and biased with a microwave current of slightly lower amplitude than the critical current of the micro-bridge. The response of the detector is the rate of superconducting fluctuations, which depends exponentially on the concentration of quasiparticles in the micro-bridge. Excess quasiparticles are generated by an incident THz signal. Since the quasiparticle lifetime increases exponentially at lower operation temperature, the noise equivalent power rapidly decreases. This approach allows for large arrays of noise bolometers operating above 1 K with sensitivity, limited by 300-K background noise. Moreover, the response of the bolometer always dominates the noise of the readout due to relatively large amplitude of the bias current. We performed a feasibility study on a proof-of-concept device with a ${1.0times 0.5 rm mu m^{2}}$ micro-bridge from a 9-nm thin Nb film on a sapphire substrate. Having a critical temperature of 5.8 K, it operates at 4.2 K and is biased at the frequency 5.6 GHz. For the quasioptical input at 0.65 THz, we measured the noise equivalent power ${approx 3times 10^{-12}rm W/sqrt Hz}$ , which is close to expectations for this particular device in the noise-response regime.
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