Detection of single-mode thermal microwave photons using an underdamped Josephson junction

Introduction

Photons, the quanta of light, are massless particles whose energy E is related to their frequency f by Planck’s constant h, through the relation E = hf ¹. The most energetic photons ever recorded, with E > 100 TeV, belong to the class of gamma rays, which extend down to E ~ MeV². Lower energy photons, such as X-rays, have energies around E ~ keV^{3, 4–5}. Single photons in the gamma and X-ray ranges are detected using high-energy physics techniques, such as crystal scintillators and photomultiplier tubes⁶. In the optical domain, where photons typically have energies of E ~ eV, single-photon detection is well-established, utilizing devices like photomultipliers and avalanche photodiodes⁷. Advancements in superconducting technologies have enabled photon detection in the infrared range (E ~ meV), employing methods such as nanowires^8,9, transition-edge sensors¹⁰, kinetic inductance detectors⁵, and Josephson junctions⁴.

The microwave range, with photon energies around E ~50 μeV ( ~10 yJ), represents the frontier of single-photon detection¹¹. This range has been explored using quantum dots¹² and bolometric schemes^{13, 14–15}. The development of single-photon detectors (SPDs) in the microwave range has drawn significant interest from the field of quantum technologies. Circuit quantum electrodynamics schemes¹⁶ have been proposed^17,18 and implemented with qubits^{19, 20, 21, 22, 23, 24, 25–26}.

The demand for microwave SPDs is exemplified in dark matter searches, such as those for axions^{27, 28–29}. In particular, dark matter haloscopes^{30, 31, 32–33} rely on precision power measurements using low-noise amplifiers. Transitioning to photon detectors is crucial^34,35 as they outperform quantum-limited amplifiers and quantum-enhanced measurement techniques, especially at higher frequencies (above a few GHz) where the standard quantum limit of linear amplification significantly hinders sensitivity^34,36.

The axion signal, characterized by a stochastic emission of rare photons at frequency f_a, depends on the unknown axion mass and has a narrow bandwidth of 10⁻⁶f_a²⁷. Consequently, suitable photon detectors must exhibit a low dark count rate, wide spectral range, high efficiency, and continuous operation capabilities. Existing microwave photon detectors generally fall short of these requirements, although some recent...