Nucleation of vortex-antivortex pairs (VAPs) is believed to play a central role in the photon detection mechanism of superconducting detectors; however, their direct dynamic observation has remained challenging. Here, we report the direct observation of photon-induced VAP dynamics in a current-carrying superconductor as quantized voltage signals following photon absorption. The observed signals are interpreted as discrete phase-slip events, where each vortex traversal induces a 2-pi phase change of the superconducting order parameter, resulting in a quantized voltage pulse whose time integral is given by the magnetic flux quantum. We analyze the resulting quantized signals as a function of bias current, base temperature, and input photon-number states, and find that the number of VAPs generated per absorbed photon becomes effectively stabilized under specific conditions. Under these conditions, we demonstrate photon-number-resolving capability by directly counting phase-slip-induced voltage quanta. Our results reveal a detection mechanism governed by phase dynamics rather than conventional resistive transitions. We further show that photon-number resolution emerges when the fluctuation of photon-induced vortex-antivortex pair generation becomes statistically suppressed. These findings establish a new route toward photon-number-resolving detection based on phase-slip counting and open opportunities for high-speed superconducting detectors for quantum optics and photonic quantum technologies.
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Submitted to Physical Review Applied. Presented at SPW 2026
Nucleation of vortex-antivortex pairs (VAPs) is believed to play a central role in the photon detection mechanism of superconducting detectors; however, their direct dynamic observation has remained challenging. Here, we report the direct observation of photon-induced VAP dynamics in a current-carrying superconductor as quantized voltage signals following photon absorption. The observed signals are interpreted as discrete phase-slip events, where each vortex traversal induces a 2-pi phase change of the superconducting order parameter, resulting in a quantized voltage pulse whose time integral is given by the magnetic flux quantum. We analyze the resulting quantized signals as a function of bias current, base temperature, and input photon-number states, and find that the number of VAPs generated per absorbed photon becomes effectively stabilized under specific conditions. Under these conditions, we demonstrate photon-number-resolving capability by directly counting phase-slip-induced voltage quanta. Our results reveal a detection mechanism governed by phase dynamics rather than conventional resistive transitions. We further show that photon-number resolution emerges when the fluctuation of photon-induced vortex-antivortex pair generation becomes statistically suppressed. These findings establish a new route toward photon-number-resolving detection based on phase-slip counting and open opportunities for high-speed superconducting detectors for quantum optics and photonic quantum technologies.
Nucleation of vortex-antivortex pairs (VAPs) is believed to play a central role in the photon detection mechanism of superconducting detectors; however, their direct dynamic observation has remained challenging. Here, we report the direct observation of photon-induced VAP dynamics in a current-carrying superconductor as quantized voltage signals following photon absorption. The observed signals are interpreted as discrete phase-slip events, where each vortex traversal induces a 2 π phase change of the superconducting order parameter, resulting in a quantized voltage pulse whose time integral is given by the magnetic flux quantum Φ 0 . We analyze the resulting quantized signals as a function of bias current, base temperature, and input photon-number states and find that the number of VAPs generated per absorbed photon becomes effectively stabilized under specific conditions. Under these conditions, we demonstrate photon-number-resolving capability by directly counting phase-slip-induced voltage quanta. Our results reveal a detection mechanism governed by phase dynamics rather than conventional resistive transitions and represent the first demonstration of photon-number resolution based on VAP counting, enabling fast multi-photon-resolving superconducting detectors for quantum optics.
To elucidate the photon detection mechanism of superconducting single-photon detectors, we theoretically examine the dynamics of type-II superconductors with a bias current using the two-dimensional time-dependent Ginzburg–Landau and the Maxwell equations. The photon injection that weakens the superconducting order parameter is treated phenomenologically as a local temperature increase, and the injected energy is controlled by the initial hotspot radius. The photon is detected by the voltage change between two electrodes attached to the left and right edges of the superconductor. We find that the detection dynamics in certain parameter ranges can be explained by the conventional hotspot model, whereas those in other parameter ranges are governed by the formation and subsequent dynamics of superconducting vortex and antivortex pairs. The photon detection is possible for an initial hotspot radius that exceeds a threshold value. We find that the generation of a vortex–antivortex pair occurs near the threshold. The flow of the pair perpendicular to the current direction finally creates a normal region for the photon detection. The voltage change for the Ginzburg–Landau parameter close to the transition point from type-II to type-I superconductor shows anomalous behavior that is not associated with the dynamics of the vortex–antivortex pair. We also examine the effects of spatially non-uniform current density on the voltage change and the superconducting order parameter to provide a hint to understand the behavior of wide-strip single-photon detectors. The estimated values of incident photon energy and response time for photon detection are reasonable in comparison with experiments. The present analysis provides useful guidelines for flexible design of device structures.
We propose a novel quantum detection mechanism for photon absorption in a two-dimensional superconductor that exhibits a vortex-unbinding transition. Well below the transition, absorption of a single photon of energy hf can result in the creation of a vortex-antivortex pair, which can be broken apart in an applied current, thus transferring a single flux quantum ${\mathrm{\ensuremath{\Phi}}}_{0}$ across the film. This results in a quantum-limited voltage responsivity ${\mathrm{\ensuremath{\Phi}}}_{0}$/hf=1/2ef, and may account for some reports of enhanced nonbolometric detection of infrared radiation in thin granular superconducting films.
Strong interests on optical quantum based metrology, quantum information and particularly in quantum cryptography are continuously growing. The main limitations to the developments in these fields are due to non-ideal devices: both single photon sources and single photon detectors. In these field of applications, detectors require to be able to resolve the number of photons in a light pulse. Presently state of the art indicates that classical semiconductor light detectors (i.e. avalanche photodiode or single photon avalanche diode) are not able to discriminate the number of photon arriving at the same time. In the meanwhile, superconducting devices have shown the possibility to resolve single photon pulses. One of the most promising superconducting detectors is the Transition-Edge Sensor (TES): a microcalorimeter that takes advantage of the sharp transition (few millikelvin) from the superconducting to the normal phase; for this reason it is sometimes called Superconductive Phase Thermometer (SPT). In the ultraviolet (UV) to infrared (IR) wavelength range, the photons are absorbed directly by the superconductive thin film and the absorbed energy induces an increase of the TES resistance. Thanks to the applied bias voltage, which maintains the device in the transition region the photon absorption induces a decrease of the TES current, measured by a dc-SQUID amplifier, and the pulse integral of the bias power reduction corresponds to the absorbed energy. This means that TESs have the very interesting properties to be able to detect single photons with an intrinsic energy resolution, without filters or gratings, that limit the quantum efficiency. By contrary of classical detectors, if monochromatic light irradiates TESs, as usually happens in communication systems, they show the photon-number resolving (PNR) capability and due to the good signal to noise ratio TESs are almost free from dark counts. Moreover, in the superconducting detector family, TESs are the only true photon-number resolving detectors operating in the VIS-NIR range. Together with quantum information science, the PNR property results useful even for optical radiometry too. In the optical community, the candela - the International System (SI) unit for the luminous intensity - has not a common consensus whether its present definition fully satisfies the current and future needs of growing associated technology. Furthermore, actually there are substantial efforts directed toward a new definitions of four base SI units: the proposal wants to link the SI units to fundamental constants, leaving f.i. material artifact. Considering the recent advances in optical radiometry and in quantum technologies, for the candela world it means redefine its unit linking to the Planck constant and consequently expressing the luminous intensity unit in terms of photon number rather than optical power. This challenge has been accepted by several national metrology institutes to demonstrate the feasibility of redefining the candela. Inside this research project called `qu-candela', the TES PNR capability has been considered to build the bridge between the quantum and classical world of radiometry: i.e. the detector possibility to measure optical powers from one single photon per second to the lower limits of cryogenic radiometry, 104 photons per second. The theme of this work of thesis is to investigate both optical and electrical characterization of different kind of TESs based on a titanium/gold multilayer film, produced and developed at the National Institute of Metrological Research (INRIM) of Torino. Thanks to the proximity effect, the multilayer allows to lower with continuity the critical temperature from that of the Ti bulk (Tc ~ 390 mK) to those of interest: ~ 300 mK and ~ 100 mK. Detectors with higher Tc have shown a faster response pulse with a relaxing time constant of the order of 200 ns, while for the lower Tc sensors, the time constant is about 10 µs. By contrary to the response time, the detector intrinsic energy resolution is proportional to its film critical temperature. Our sensors work to discriminate incident photon from UV wavelengths to those typical of the telecommunications, 1310 nm and 1550 nm. Irradiating a TES with an active area of 10x10 µm^2 by incident photons of 0.79 eV (corresponds to a wavelength 1570 nm), the best energy resolution obtained has been 0.18 eV. Detectors with higher active area 20x20 µm^2 have a worse energy resolution, because it is also proportional to the material film heat capacity. In the meanwhile due to the same reason these kind of sensors present a bigger saturation energy. This has allowed to investigate on the TES capability to discriminate up to 29 incident photons simultaneously. Until now, such count represents the bigger amount of photons discriminated by single photon detectors, without reaching the device saturation, with a linear behaviour. From this count it has been estimated 12 photons on average, per pulse, at 9 kHz repetition rate; this results in a photon flux of about 105 photons/s, demonstrating the possibility of having a detector able to work from low flux regime to 1 photon/s to flux measurable by conventional semiconductor device (f.i. single photon avalanche detector SPAD). An innovative absolute calibration technique for PNR detector has been demonstrated. The absolute technique is based on the Klyshko's efficient solution to measure detection efficiency in photon counting rate and well know for common click-no-click detector. In fact, exploiting the recent developments in quantum state world, it is possible to work with quasi single photon state, by using a parametric down conversion heralded single photon source, and calibrate PNR detectors without requiring reference standards. The best detection efficiency, of ca. 50%, has been reached by coupling the smaller active area detectors with a 9 µm core optical fiber, single mode at telecom wavelengths
Single photon detectors based on meanders from 5-nm thin B1 niobium nitride nanostrips show moderate spectral resolution along with the spectral cut-off of the quantum efficiency occurring in the near-infrared spectral range. Beyond the cut-off there is a gradual decrease of the quantum efficiency. To describe the response beyond the cut-off we combine the previously developed hot-spot detection mechanism with the photon-induced unbinding of the vortex-antivortex pairs, which appear in the superconducting film below the Kosterlitz-Thouless phase transition. The detector responds to the absorption of a single photon with a voltage pulse whose amplitude depends on the photon energy. We report the observation of a photon-energy dependent statistical distribution of the pulse amplitude that defines the energy resolution of the detector. We analyzed the detector response to continuous and femtosecond-pulse radiation using broadband microwave amplifiers and a fast single-shot oscilloscope as well as integrating SQUID amplifiers. Our analysis suggests that both the amplitude and the duration of the response pulses are jointly controlled via the kinetic inductance of the meander line and the Joule power dissipated in the meander by the bias current.
Advantage of superconducting photon detectors is a much lower noise in comparison to semiconductor counterparts. The purpose of the present work is to advance understanding of the physics of noises in a superconducting nanostructures. We have studied the rate and spectrum of dark counts of an 80-nm wide, 5-nm thick superconducting NbN meander-line and analyzed experimental data considering various noise mechanisms: quantum phase-slips, discrete thermodynamic fluctuations of the superconducting order parameter, and topological fluctuations in the two-dimensional vortex gas. The latter mechanism, i.e. Kosterlitz-Thouless phase transition, is the only one adequately describing the observed noise performance. Besides that, this approach provides clear explanation of the peculiarities of the resistive transition. The other two mechanisms would result in a much stronger current and temperature dependence of the dark count rate than the experiment shows. Basing on our understanding of the noise source, we propose a novel concept of a superconductor submillimeter direct detector. The detector operates in the superconducting state and utilizes current-dependent high-frequency electrical noise that changes under irradiation. The novel aspect is the use of the noise, which generally hampers the performance of conventional detectors, as the physical quantity that itself senses radiation. Predicted noise-equivalent power is 10_-13 W Hz_-1/2 at 4 K and should improve at lower temperatures.