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Optics & Laser Technology

Evaluation of detection efficiency of a transition edge sensor at C-band wavelength

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

Published Jul 25, 2025• 5 citations
Publisher

Abstract

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.

DOI
10.1016/j.optlastec.2025.113414

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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.
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.
We have realized a high-detection-efficiency photon number resolving detector at an operating wavelength of about 850 nm. The detector consists of a titanium superconducting transition edge sensor in an optical cavity, which is directly coupled to an optical fiber using an approximately 300-nm gap. The gap reduces the sensitive area and heat capacity of the device, leading to high photon number resolution of 0.42 eV without sacrificing detection efficiency or signal response speed. Wavelength dependent efficiency in fiber-coupled devices, which is due to optical interference between the fiber and the device, is also decreased to less than 1% in this configuration. The overall system detection efficiency is 98%±1% at wavelengths of around 850 nm, which is the highest value ever reported in this wavelength range.
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).
A longstanding goal in quantum optics has been to realize a photon-number-resolving detector that efficiently counts the number of photons in an optical field. This goal has been largely met with the development of transition edge sensors which can count up to roughly 20 photons with efficiencies over 95%. This thesis presents three experiments that employ these detectors to characterize and prepare quantum states of light. Firstly, we develop a weak-field homodyne detector. By replacing the photodiodes conventionally used in homodyne detection with transition edge sensors, we experimentally implement a versatile measurement device that can tune between photon counting and quadrature measurements. We study the transition between these complementary measurement regimes and determine the minimum local oscillator strength needed to perform quadrature measurements. Secondly, we use the weak-field homodyne detector as a quantum state engineering tool. We propose a scheme to prepare a wide range of definite parity states, including two- and four-component Schrödinger cat states of arbitrary size with nearly perfect fidelity. Thirdly, we perform optical interferometry using quantum states of light with the aim of surpassing the maximal precision achievable with classical light, i.e. the shot-noise limit. We propose and experimentally implement a scheme that uses high-gain squeezed vacuum sources and transition edge sensors to prepare loss-tolerant entangled states containing up to 8 photons. While our achieved precision does not unconditionally (i.e. without post-selecting on certain measurement trials) surpass the shot-noise limit, our results do demonstrate the robustness of these entangled states to loss despite their size.