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IEEE Transactions on Applied Superconductivity

Branching-Ratio-Based Detection Efficiency Calibration of Transition-Edge Sensors at C-Band Wavelengths

Tetsuya Tsuruta, Takeshi Jodoi, M. Rajteri, Daiji Fukuda

Published May 25, 2026• 0 citations
Publisher

Abstract

We characterize a detection efficiency calibration system with a wavelength-tunable pulsed photon source for single photon detectors or photon number resolving detectors covering the telecommunication range from 1510 nm to 1570 nm, with measurements performed at the representative wavelength of 1550 nm. The source employs an external cavity diode laser and acousto-optic modulator for pulse generation with controlled mean photon number. By implementing a branching-ratio monitoring scheme instead of direct power monitoring, we achieved a relative Allan deviation below 0.02% at an averaging time of 10000 seconds, representing a tenfold improvement in long-term stability. This stability enables extended calibration measurements while maintaining consistent photon flux determination. Using photon-number-resolving detection with transition edge sensors, we measured second- and third-order intensity correlation functions from single datasets. The light source maintained Poisson distribution at repetition rates below 1 MHz, with weak bunching (g⁽²⁾ ≈ 1.05,g⁽³⁾ ≈ 1.16) observed at higher frequencies. The measured correlations satisfied the theoretical relation for weak bunching, indicating a single dominant mechanism, likely background light from the finite AOM extinction ratio. While we cannot entirely exclude potential contributions from the detector's response characteristics, the systematic frequency dependence and consistency with the weak bunching model strongly suggest the light source as the primary factor. The demonstrated stability and characterized photon statistics confirm the suitability of this source for detector calibration at repetition rates up to 1 MHz. These performance metrics meet the requirements for calibrating photon-number resolving detectors used in quantum state characterization and quantum information applications.

DOI
10.1109/tasc.2026.3696394

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We characterize a detection efficiency calibration system with a wavelength-tunable pulsed photon source for single photon detectors or photon number resolving detectors covering the telecommunication range from 1510 nm to 1570 nm, with measurements performed at the representative wavelength of 1550 nm. The source employs an external cavity diode laser and acousto-optic modulator for pulse generation with controlled mean photon number. By implementing a branching-ratio monitoring scheme instead of direct power monitoring, we achieved a relative Allan deviation below 0.02% at an averaging time of 10000 seconds, representing a tenfold improvement in long-term stability. This stability enables extended calibration measurements while maintaining consistent photon flux determination. Using photon-number-resolving detection with transition edge sensors, we measured second- and third-order intensity correlation functions from single datasets. The light source maintained Poisson distribution at repetition rates below 1 MHz, with weak bunching (g⁽²⁾ ≈ 1.05,g⁽³⁾ ≈ 1.16) observed at higher frequencies. The measured correlations satisfied the theoretical relation for weak bunching, indicating a single dominant mechanism, likely background light from the finite AOM extinction ratio. While we cannot entirely exclude potential contributions from the detector's response characteristics, the systematic frequency dependence and consistency with the weak bunching model strongly suggest the light source as the primary factor. The demonstrated stability and characterized photon statistics confirm the suitability of this source for detector calibration at repetition rates up to 1 MHz. These performance metrics meet the requirements for calibrating photon-number resolving detectors used in quantum state characterization and quantum information applications.
Photon-number-resolving detectors face strict demands regarding detection efficiency to meet the needs of quantum information processing. We constructed a system that can accurately evaluate system detection efficiency of a photon-number-resolving detector. We generated an optical pulse containing an arbitrary number of photons for the initial states by attenuated laser light; this pulse was used to evaluate the detection efficiency of the device under test. To generate this pulse, we modulated a continuous wavelength tunable laser using an acoustic optical modulator. From the photon statistics of the initial states, we found a second-order correlation function that was almost 1 at any wavelength, and these photon statistics followed a Poisson distribution. For the device under test, we evaluated the detection efficiency of a transition edge sensor and we employed two methods to calculate the number of detected photons. This value was calculated based on each photon state (method 1) or based on the zero photon state by assuming a Poisson distribution (method 2). Although the results of both methods were comparable within the range of uncertainty, method 2 yielded smaller uncertainty than method 1. We found that the wavelength-dependent detection efficiency was explained by the photon absorptance characteristics of the device under test. Additionally, the system detection efficiency varied from approximately 87 % to 93 %, and the expanded uncertainty values of methods 1 and 2 were 4.1 % and 1.5 %, respectively. This system enables the accurate evaluation of quantum states of photons at various wavelengths. • We developed a calibration system for the C-band wavelength using laser pulses. • Initial states were generated via laser by switching acoustic optical module. • Input state photon statistics were evaluated by a second-order correlation function. • Wavelength-dependent detection efficiency was precisely determined. • Detection efficiency was evaluated by comparing experimental and simulation values.
Optical transition-edge sensors (TESs) that can resolve the energy of a single photon have been proven useful in quantum information and biology. TESs can provide spectra ranging from near-infrared to visible regions and have the potential to reveal new phenomena in biology. In this paper, we have investigated the responses of TESs to photons at near-infrared and visible wavelengths, from 450 to 1000 nm in 10-nm increments using a supercontinuum laser and a tunable bandpass filter, which converted the multichromatic light source into monochromatic light. The system detection efficiency of an optical TES optimized for photon detection at 950 nm was nearly 100% at some wavelengths and was more than 10% for the overall bandwidth. We found that the detector responses strongly depended on the wavelengths. A spectrum of the filtered light at shorter wavelengths was more likely to show a second peak with energy lower than that of the primary peak.
Optical transition edge sensors (TESs) which can resolve an energy of a single photon have proven desirable in quantum information and biology. TESs can provide spectra ranging from near-infrared to visible regions, and have the potential to reveal new phenomena in biology. To obtain reliable spectra, wavelength dependence of the system detection efficiency should be calibrated. The dependence is due to a cavity structure of the detector, consisting of an anti-reflection coating and a mirror. We will present a calibration using a supercontinuum laser and acousto-optic tunable filters (AOTF).
Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols.
The quantum efficiency of photon counters can be measured with standard uncertainty below 1% level using correlated photon pairs generated through spontaneous parametric down-conversion process. Normally a laser in UV, blue or green wavelength range with sufficient photon energy is applied to produce energy and momentum conserved photon pairs in two channels with desired wavelengths for calibration. One channel is used as the heralding trigger, and the other is used for the calibration of the detector under test. A superconducting nanowire single photon detector with advantages such as high photon counting speed (<20 MHz), low dark count rate (<50 counts per second), and wideband responsivity (UV to near infrared) is used as the trigger detector, enabling correlated photons calibration capabilities into shortwave visible range. For a 355nm single longitudinal mode pump laser, when a superconducting nanowire single photon detector is used as the trigger detector at 1064nm and 1560nm in the near infrared range, the photon counting efficiency calibration capabilities can be realized at 532nm and 460nm. The quantum efficiency measurement on photon counters such as photomultiplier tubes and avalanche photodiodes can be then further extended in a wide wavelength range (e.g. 400-1000nm) using a flat spectral photon flux source to meet the calibration demands in cutting edge low light applications such as time resolved fluorescence and nonlinear optical spectroscopy, super resolution microscopy, deep space observation, and so on.
Characterizing the temporal response function of single-photon detectors (SPDs) is essential for quantum communication protocols and time-resolved measurements. Typically, this characterization is obtained from the arrival time statistics of photons from a pulsed laser. In this work, we present an alternative approach using time-correlated photon pairs generated in spontaneous parametric down-conversion (SPDC). We demonstrate a continuous wavelength-tunability from 526 nm to 661 nm for one photon of the pair, and 1050 nm to 1760 nm for the other photon a range comparable to existing pulsed-laser systems. With this source, we characterized single-photon avalanche detectors sensitive to the two distinct wavelength bands, one based on Silicon, the other based on Indium Gallium Arsenide.