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arXiv:2603.16522 · Physical Review Research

Stroboscopic detection of itinerant microwave photons

Hanna Zeller, Lukas Danner, Max Hofheinz, Ciprian Padurariu, Joachim Ankerhold, Björn Kubala

quant-phcond-mat.mes-hallcond-mat.supr-conSubmitted Mar 17, 2026• Announced Mar 18, 2026• 0 citations
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Abstract

We present a novel scheme to detect itinerant microwave radiation at the single photon level. Using existing Josephson-photonics devices, where two microwave cavities are coupled by a dc-voltage biased superconducting junction, we theoretically show how to implement a stroboscopically repeated, near-projective measurement of a photon impinging on one of the cavities. Optimizing rate, duration, and strength of the measurement by flux control of the junction and developing a threshold protocol to detect the photon from a homodyne measurement of the radiation output of the other cavity, we achieve highly efficient detection with low dark counts. By cascading the detector with a preamplifier, where a similar two-cavity Josephson-photonics device acts as a photon multiplier, we can further improve the device to reach a detection efficiency of $88.5 \%$ with a dark count rate of $\sim10^{-4} γ_a$, set by the resonance width $γ_a$ of the absorbing cavity. These results for a multiplication factor of two suggest that near-unity efficiencies may be reached for higher multiplication factors.

Journal reference
Phys. Rev. Research 8, 033145 (2026)
DOI
10.1103/xnm9-98cm
Comments
13 pages, 12 figures

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We present a novel scheme to detect itinerant microwave radiation at the single photon level. Using existing Josephson-photonics devices, where two microwave cavities are coupled by a dc-voltage biased superconducting junction, we theoretically show how to implement a stroboscopically repeated, near-projective measurement of a photon impinging on one of the cavities. Optimizing rate, duration, and strength of the measurement by flux control of the junction and developing a threshold protocol to detect the photon from a homodyne measurement of the radiation output of the other cavity, we achieve highly efficient detection with low dark counts. By cascading the detector with a preamplifier, where a similar two-cavity Josephson-photonics device acts as a photon multiplier, we can further improve the device to reach a detection efficiency of 88.5%88.5 \%88.5% with a dark count rate of ∼10−4γa\sim10^{-4} γ_a∼10−4γa​, set by the resonance width γaγ_aγa​ of the absorbing cavity. These results for a multiplication factor of two suggest that near-unity efficiencies may be reached for higher multiplication factors.
Single-photon detectors are an essential part of the toolbox of modern quantum optics for implementing quantum technologies and enabling tests of fundamental physics. The low energy of microwave photons, the natural signal path for superconducting quantum devices, makes their detection much harder than for visible light. Despite impressive progress in recent years and the proposal and realization of a number of different detector architectures, the reliable detection of a single itinerant microwave photon remains an open topic. Here, we investigate and simulate a detailed protocol for single-photon multiplication and subsequent amplification and detection. At its heart lies a Josephson-photonics device which uses inelastic Cooper-pair tunneling driven by a dc bias in combination with the energy of an incoming photon to create multiple photons, thus compensating for the low-energy problem. Our analysis provides clear design guidelines for utilizing such devices, which have previously been operated in an amplifier mode with a continuous wave input, for counting photons. Combining a formalism recently developed by Mølmer to describe the full quantum state of in- and outgoing photon pulses with stochastic Schrödinger equations, we can describe the full multiplication and detection protocol and calculate performance parameters, such as detection probabilities and dark count rates. With optimized parameters, a high population of a single output mode can be achieved that can then be easily distinguished from vacuum noise in heterodyne measurements of quadratures with a conventional linear amplifier. Realistic devices with two multiplication stages with multiplication of 161616 reach for an impinging Gaussian pulse of length TTT a detection probability of 84.5%84.5\%84.5% with a dark count rate of 10−3/T10^{-3}/T10−3/T, and promise to outperform competing schemes.
At its heart, a Josephson-photonics device combines macroscopic superconducting electronics and microscopic quantum optics. It consists of a dc-voltage biased Josephson junction that is connected in series to one or a few microwave cavities. Cooper pairs can tunnel incoherently across the junction by depositing their energy 2eVdc in the microwave cavities, creating photonic excitations in them. Many parameters, such as the eigenfrequencies ∝ (LC)^(−1/2) or zero-point fluctuations ∝ (L/C)^(1/4) of the microwave cavities, can be experimentally designed; other parameters, such as the strength of the Josephson nonlinearity and the dc voltage are easily modified in situ. In this way, Josephson-photonics devices constitute a versatile source of microwave photons with a wide variety of features extending from the classical to the deep quantum regime. To make them of use for quantum technological applications that rely on a well-defined phase of the microwave light, a crucial drawback must be overcome. The dc voltage does not provide a stable reference phase to Josephson-photonics devices, as it is subject to experimental noise, such that all phase information is lost. In this thesis, we develop the field of Josephson photonics in two directions: As first main result, we resolve the issue of phase instability in Josephson photonics. The phase can be stabilized either by injection locking to a small external signal with a stable and well-defined reference phase or by mutual synchronization to a second device. An alternative approach mitigates the issue for some use cases by optimizing an ansatz to reconstruct the undiffused stationary quantum state from experiments with phase diffusion. Secondly, we show how Josephson-photonics devices can be used for the challenging task of reliably detecting single itinerant microwave photons. The “Inelastic Cooper Pair Tunneling Photon Multiplier” exploits a resonance condition, where the energy provided by the dc voltage enables a multiplication process from one incoming to n outgoing photons. This process can be staged to reach a large number of outgoing photons. Here, we model itinerant Gaussian single-photon pulses of length T with Mølmer’s approach. Further, we define a detection scheme based on heterodyne quadrature measurement of the output signal. Most importantly, we show that realistic devices can achieve a detection efficiency of 84.5% with a small dark-count rate of 10^(−3)/T, promising to outperform competing schemes.
The detection of single microwave photons is becoming a cornerstone of fundamental experiments in circuit quantum electrodynamics and quantum sensing. Experiments in cavity quantum electrodynamics, photon-mediated entanglement, dark-matter axion searches and quantum thermodynamics increasingly rely on single-photon sensitivity. Current technologies exploit superconducting devices, including Josephson parametric detectors, and transmon-based non-demolition counters for dark-matter haloscopes. Hybrid double quantum dot-Josephson systems reach interesting levels of efficiency, while current-biased Josephson junctions show potential for near-quantumlimited resolution. Despite impressive progress, challenges remain in reducing dark counts, improving reset speed, and scaling for multiplexed arrays. Continued advances in superconducting materials, qubit coherence, and hybrid semiconductor-superconductor designs promise to extend detection efficiency and bandwidth. These developments are poised to enable the next generation of quantum-enabled experiments, from foundational tests in quantum optics to searches for new physics.
Axions detection requires the ultimate sensitivity down to the single-photon limit. In the microwave region, this corresponds to energies in the yJ range. This extreme sensitivity has to be combined with an extremely low dark-count rate since the probability of axions conversion into microwave photons is supposed to be very low. To face this complicated task, we followed two promising approaches that both rely on the use of superconducting devices based on the Josephson effect. The first one is to use a single Josephson junction (JJ) as a switching detector (i.e., exploiting the superconducting to normal state transition in the presence of microwave photons). We designed a device composed of a coplanar waveguide terminated on a current-biased JJ. We tested its efficiency to pulsed (pulse duration 10 ns) microwave signals since this configuration is closer to an actual axions search experiment. We show how our device is able to reach detection capability of the order of ten photons with the frequency of 8 GHz. The second approach is based on an intrinsically quantum device formed by two resonators coupled only via a superconducting qubit network. This approach relies on quantum nondemolition measurements of the resonator photons. We show that by injecting radiofrequency power into the resonator, the frequency position of the resonant drop in the transmission coefficient (S21) can be modulated up to 4 MHz. We anticipate that, once optimized, both the devices have the potential to reach single-photon sensitivity.
We propose a viable design of a microwave two-photon threshold detector. In essence, the considered scheme is an extension of the existing single-photon detector—a Josephson photomultiplier (JPM)—an absorbing microwave detector based on a capacitively shunted rf superconducting quantum interference device (SQUID). To implement a two-photon threshold detector, we utilize a dimer of resonators—two lumped-element resonators interacting via an asymmetric dc SQUID, with one of the resonators capacitively coupled to the JPM. By specific tuning of the resonator frequencies and the external flux through the dc SQUID coupler, we engineer a nonperturbative two-photon coupling between the resonators. This coupling results in the coherent conversion of a photon pair from one resonator into a single photon in another resonator, enabling selective response to quantum states with at least two photons. We also consider an extended coupler design that allows on-demand switching of two-photon coupling. In addition, we propose the modified JPM design to improve its performance. Our calculations demonstrate that, for realistic circuit parameters, we can achieve more than 99 % fidelity of photon pair detection in less than 50 ns. The considered scheme may serve as a building block for the implementation of efficient photon-number-resolving detectors in circuit QED architecture.
We use a semiclassical formalism to optimize a microwave single-photon detector based on switching events of a current-biased Josephson junction coupled to a resonator. To detect very rare events, the average time between dark counts ${\ensuremath{\tau}}_{\mathrm{dark}}$ should be maximized taking into account that the switching time ${\ensuremath{\tau}}_{\mathrm{sw}}$ should be sufficiently small. We demonstrate that these times can be tuned in a wide range by changing the junction parameters, and ${\ensuremath{\tau}}_{\mathrm{dark}}/{\ensuremath{\tau}}_{\mathrm{sw}}\ensuremath{\sim}{10}^{9}$ can be achieved. Therefore, a junction-resonator arrangement can be used to detect extremely low photon fluxes (e.g., for searching for galactic axions).