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arXiv:2510.08030

Amplification and Detection of Single Itinerant Microwave Photons

Lukas Danner, M. Hofheinz, Nicolas Bourlet, Ciprian Padurariu, Joachim Ankerhold, Björn Kubala

Published Oct 9, 2025• 0 citations
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Abstract

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 $16$ reach for an impinging Gaussian pulse of length $T$ a detection probability of $84.5\%$ with a dark count rate of $10^{-3}/T$, and promise to outperform competing schemes.

DOI
10.48550/arxiv.2510.08030

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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.
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.
The interaction between propagating microwave fields and Cooper-pair tunneling across a DC-voltage-biased Josephson junction can be highly nonlinear. We show theoretically that this nonlinearity can be used to convert an incoming single microwave photon into an outgoing nnn-photon Fock state in a different mode. In this process, the electrostatic energy released in a Cooper-pair tunneling event is transferred to the outgoing Fock state, providing energy gain. The created multiphoton Fock state is frequency entangled and highly bunched. The conversion can be made reflectionless (impedance matched) so that all incoming photons are converted to nnn-photon states. With realistic parameters, multiplication ratios n>2n>2n>2 can be reached. By two consecutive multiplications, the outgoing Fock-state number can get sufficiently large to accurately discriminate it from vacuum with linear postamplification and power measurement. Therefore, this amplification scheme can be used as a single-photon detector without dead time.
We experimentally demonstrate a microwave photon-multiplication scheme which combines the advantages of a single-photon detector and a power meter by multiplying the incoming photon number by an integer factor. Our first experimental implementation achieves an n = 3 -fold multiplication with 0.69 efficiency in a 116 MHz bandwidth up to an input photon rate of 400 MHz. It loses phase information but does not require any dead time or time binning. We expect an optimized device cascading such multipliers to achieve number-resolving measurement of itinerant photons with low dark count, which would offer new possibilities in a wide range of quantum-sensing and quantum-computing applications. Published by the American Physical Society 2024
While single-photon counting is routinely achieved in the optical domain, operational single microwave photon detectors (SMPDs) have only recently been demonstrated. SMPDs are critical for sensing weak signals from incoherent emitters, with applications ranging from the detection of individual electron spins and dark-matter candidates to advancements in hybrid quantum devices and superconducting quantum computing. These detectors offer a substantial advantage over quantum-limited amplification schemes by bypassing the standard quantum limit for power detection, therefore further reductions in their intrinsic noise are essential for advancing quantum sensing at microwave frequencies. Several SMPD designs utilize the state of a superconducting qubit to encode the detection of an itinerant photon, and rely on a non-destructive photon-qubit interaction. Here, we leverage this Quantum-Non-Demolition feature by repeatedly measuring the impinging photon with cascaded Four-Wave-Mixing processes and encoding the detection on several qubits. This cascaded detector mitigates the intrinsic local noise of individual qubits, achieving a two-order-of-magnitude reduction in intrinsic detector noise at the cost of halving the efficiency. We report an intrinsic sensitivity of 8(1)×10−24W/Hz8(1)\times10^{-24}\text{W}/\sqrt{\text{Hz}}8(1)×10−24W/Hz​, with an operational sensitivity of 5.9(6)×10−23W/Hz5.9(6)\times 10^{-23}\text{W}/\sqrt{\text{Hz}}5.9(6)×10−23W/Hz​ limited by thermal photons in the input line.
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.