Abstract
A Josephson radiation threshold detector (JRTD) that is based on the threshold behaviour of a current bias Josephson junction (CBJJ) is designed and fabricated for infrared radiation (IR@1550nm) detection at low temperatures. To achieve the optimal performance, we develop a binary hypothesis detection method to calibrate Josephson threshold behaviours (i.e. the switching current distributions of the CBJJ with the Al/AlOx/Al junction) in the absence and presence of radiation. In the absence of IR radiation, the junction transitioned with a measurable voltage drop across the junction, and this signal was treated as the events of hypothesis H0. The events of junction transition observed in the presence of the IR radiation served as hypothesis H1. Considering the usual Gaussian noise and based on statistical decision theory, the accumulated data of the measured switching current distributions are processed, and the threshold sensitivity of the demonstrated JRTD device is estimated. The minimum detectable IR radiation power of the proposed detector is approximately 0.74 pW, which corresponds to the photon rate of 5.692 × 106 photons/second. Further optimisation of JRTDs to implement the desired binary detection of a single photon is still a subject of argument, at least theoretically.
Similar content being viewed by others
Introduction
The development of superconducting electronic devices has facilitated the very sensitive detection of photons and particles. Desirably, the single-photon detectors for different practical applications are expected to possess (i) a wide waveband response, (ii) a shorter response time, (iii) higher quantum efficiency1,2,3,4 and the ability to count single photons5. Amongst various devices that demonstrate single-photon detection, the use of superconducting Josephson junctions (JJs) as single-photon detectors is particularly desirable and have been investigated extensively owing to their theoretically good energy resolution, high responsivity and high count-rate capabilities6,7,8,9,10. Physically, if the energy of the applied photon is larger than the superconducting gap, then Cooper pairs in the superconductor can be broken, and the quasiparticles can be generated consequently. This phenomenon might lead to relevant observable effects and thus can be utilised to implement the detection of illuminating photons. Indeed, the JJ-based axion detection11,12,13, superconducting nanowire single-photon detectors14,15,16,17,18,19, transition-edge sensors20,21,22, microwave kinetic inductance detectors23,24 and the superconducting qubit detectors25,26,27,28, are under development for astronomic observations, axion searches29,30,31,32,33,34,35, quantum optical communication36,37 and optical quantum computation38,39.
Physically, any radiation-induced threshold behaviour of the device can be utilised to generate the photon detectors40,41,42,43,44 (i.e. the threshold detector (TD)). These devices can possess numerous notable features45,46, including their ability to operate at high speeds, minimal resource demands and high efficiency in detecting signals. In fact, this technology has been applied in multisensor networks or distributed intelligent systems41,43, as well as weak sinusoidal signal detection in marine environment44. For example, a maximum posteriori probability detector demonstrated in Ref.41 utilised two-state threshold nonlinearity. Even in the presence of non-Gaussian noise, the TD can enhance the performance of signal detection compared with the linear detector47. Basically, threshold detection benefits from the ability to determine the existence of a signal by observing the shifts from one metastable condition to another48,49. Specifically, the JRTD possesses (i) a binary capability to distinguish between two states with or without the radiation; (ii) a feasible technique to trigger the transition from one state to the other and (iii) the possibility to identify these transitions from the superconducting-to-resistive state by observing whether the junction switching current behaviours cross the detector threshold level or not50. A CBJJ can be depicted as a phase particle trapped in a metastable state of a cosine potential28,51,52; it can ‘escape’ if the bias current, Ib, approaches the critical current of the JJ. As a consequence, a switching event (i.e. from the zero-voltage state to a finite-voltage state) can be observed, and thus, relevant physical quantities, such as the switching currents, can be measured53,54. Due to the presence of Gaussian noise, the switching current measurement should show certain statistical distributions. CBJJs provide a feasible platform to investigate macroscopic quantum tunnelling (MQT)55,56, thermal activation (TA)57 and phase diffusion58,59. Therefore, by monitoring the changes in these statistical distributions under the applied IR radiation power, CBJJ can be regarded as a threshold detector to implement photon detection4,60. JJs can be regarded as JRTD detectors that provide a readily observable signal when exposed to a disturbance of radiation energy that is equivalent to a typical threshold61,62. Indeed, the CBJJ-based photon detectors, including the Josephson escape detectors63,64, graphene-based CBJJ detectors9,65,66 and microwave single-photon detectors67,68,69, have received extensive attention in recent years. Indeed, the JJ serves as an intrinsic threshold detector that has been applied to implement the current fluctuation detection70,71,72. The test methodology described in73 utilises the declared temperature dependence of the critical currents of JJs, which must still be optimised for the sensitive radiation detection.
In this paper, based on binary detection theory, we designed and fabricated the JRTD to demonstrate IR@1550nm radiation detection at low temperatures. We address the issues of the Josephson radiation threshold circuit (JRTC) to solve the fast binary hypothesis detection problem. We optimise the proposed JRTD through the analysis of the experimentally measured switching current distributions of the (Al/AlOx/Al) CBJJ. In the absence of IR radiation (i.e. dark count), the bias current Ib is gradually increased from 0–25 µA, the junction transition from superconducting-to-resistive state with a measurable voltage drop across the junction can be observed, and the switching current distribution mimics hypothesis H0. Meanwhile, in the presence of an IR@1550nm radiation with the power being 740 nW, the junction transition from superconducting-to-resistive state is observed again, and the switching current distributions mimics hypothesis H1. Considering the effects of Gaussian noise, a method based on standard statistical decision theory is developed to process the accumulated data of the switching current distributions to estimate the threshold control functions, namely, Th1 and Th2, and thus the detection sensitivity. Furthermore, the numerical processing of the detected data can be further optimised to improve the quality of the detector.
Model and method
The CBJJs are used to implement the binary detection74 of the infrared photons. Figure 1 illustrates the components of the JRTD and provides a comprehensive explanation of the control mechanisms for governing the input/output signals (e.g. the bias voltage, current, resistance and waveforms), as well as the characteristics of the IR@1550nm radiation power and the threshold switching current value. The JRTD operation is presented as follows: Initially, let the CBJJ be biased at Ib < Isw. Next, increase the bias current gradually until the junction transition with a measurable voltage drop can be observed across the junction75. This state mimics hypothesis H0. Then, illuminate the device with the IR@1550nm radiation power via the fibre focus and increase the bias current gradually until the junction transition with a measurable voltage drop can be observed across the junction again. This state mimics hypothesis H1. The input and output signals are passed via a low-pass filter (LPF) to separate the noise component. Subsequently, the output signal is amplified by a power amplifier with a gain of 103 before being inputted into the JRTC for the binary hypothesis detection process. The measurement of the switching current distributions of the CBJJ is conducted by carefully probing the abrupt transition from the zero-voltage state to a non-zero finite voltage state. This transition is also influenced by the fluctuations in TA and MQT. Certainly, under radiation power, the absorbed IR@1550nm illumination would break the Cooper pairs in the superconductor and thus generate quasiparticles, which might reduce the switching current compared with the first case.
CBJJ’s detection
Firstly, let the CBJJ be a biased current Ib0, which is far from the switching current, and the voltage across the junction is kept at zero state. As seen in Fig. 2a, a current-biased JJ can be described by a resistively and capacitively shunted junction (RCSJ) circuit model76, which consists of four parallel components, namely, resistor, capacitor, pure JJ and the current sources Ib and In being the bias and noise currents, respectively. Also, as shown in Fig. 2b, the CBJJ can be described physically by a phase particle trapped in a minimum of the potential28,77 \(;{\mathrm{ U}\left(\varphi \right)=-{\text{E}}}_{{\text{J}}}[{\text{cos}}\varphi +({{\text{I}}}_{{\text{b}}}/{{\text{I}}}_{{\text{c}}})\mathrm{\varphi }]\), where U(φ) is the washboard potential, EJ is the JJ coupling energy, φ is the phase difference across the junction, and Ic is the critical current of the JJ.
The dynamics of such phase particle can be described by the following 2nd-order differential equation:
This equation is a Langevin-type calculation with stochastic noise current, In71,78, where ħ = h/2π is the reduced Planck constant; e is the electron charge; and CJ and RJ are the junction capacitance and junction shunt resistance, respectively. When the bias current gradually increases from a fixed value Ib0 to a certain value Isw within the duration t, the phase particle can escape, either through TA or MQT79, from the minimum potential barrier. Thus, a finite voltage state can be observed across the junction. The (I–V) curve of the JJ is measured by connecting the JJ with a variable AC power supply (function generator). Suppose that the bias current flowing through JJ is evenly distributed in the junction. When the current density is less than the critical current density jc, the AC Josephson effect relation \({{\text{I}}={\text{I}}}_{{\text{c}}}{\text{sin}}\varphi\) is maintained. Thus, the Cooper pairs that flow through the JJ generate the supercurrent (I) without voltage across the junction. However, if the current density is greater than the critical current density (i.e. j > jc), then the relation \({{\text{I}}={\text{I}}}_{{\text{c}}}{\text{sin}}\varphi\) does not hold, which means that the tunnelling particles are not the Cooper pairs but the quasiparticles, and thus a voltage drop signal appears across the junction. Therefore, the I–V curve of the CBJJ should be characterised as follows: i) if Ib is sufficiently less than Ic, then a zero-voltage signal exists and ii) for Ib ≥ Ic, the voltage signal shows a finite value; until the I–V relation describes the normal-state resistance behaviour80,81. Schematically, Fig. 3a shows the measured non-hysteretic I-V curve of the CBJJ by measuring the junction capacitance and resistance using a digital multi-meter that shows the values of CJ ~ 4.4 nf and RJ ∼ 160 Ω, respectively. Due to the presence of noise and bias currents, the measured switching current shows the relevant distribution in Fig. 3b with an estimated value (Isw ~ 9.95 µA). For the above measurements without the IR illumination (i.e. dark count), the CBJJ can be applied to implement the desired weak radiation detection, in principle, by comparing the measured signals under the weak IR radiation power to those without IR radiation4,9.
Secondly, the device is illuminated with IR@1550 nm radiation power using the fibre focus, and the bias current is incrementally increased until a nonzero voltage signal becomes detectable. We performed numerous measurements under identical conditions. Each iteration began with a bias current that is less than Ic and proceeded to record the occurrence of switching current distribution, Isw.
JRTC
The JRTC refers to a device that is utilised to determine the presence or absence of a finite voltage state, which is achieved by subjecting the junction current to the pre-threshold system Th1, followed by the aggregation of the data samples. Then, the cumulative value of these samples is assessed to ascertain whether it surpasses the threshold Th2 or not. The primary purpose of this circuit is to facilitate binary hypothesis detection, specifically to distinguish between H0 and H1. Figure 4 presents the binary hypothesis detection82,83 issue, wherein the obtained histogram exhibits compatibility with two critical outcomes, namely, the only existence of noise (referred to as hypothesis H0) or the occurrence of the IR@1550nm radiation power absorption within a backdrop of noise (referred to as hypothesis H1). The issue may be formulated using two hypotheses in a binary test74,84:
The first hypothesis, denoted as H0 or the null hypothesis, posits that escapes are only induced by the noise. The second hypothesis, denoted as H1 or the alternative hypothesis, suggests that escapes are induced by noise and the occurrence of IR@1550nm radiation power. In this context, the Isw[n] represents the switching current value, whereas s[n] denotes the IR@1550nm radiation power. The detection scheme can be elucidated in Fig. 4, to use the Gaussian distribution function and the central limit theorem to determine the optimal decision rule for detecting the IR@1550nm radiation power.
Mathematically, the switching probability without radiation power P (Isw)0 and with IR radiation power P (Isw)1 can be described by:
and
respectively, where \({{I}_{sw}}_{0}\) is the switching current in the absence of IR radiation, and \({{I}_{sw}}_{1}\) is the switching current in the presence of IR radiation power. µ, σ and, σ2 are the mean value, standard deviation and variance of the switching current, respectively. To ascertain the switching current value, the initial step involves the calculation of the disparities between the switching probabilities with and without IR radiation power. The schematic of the JRTC used for signal detection is shown in Fig. 5. H1 decision is made if K < Th2. Note that Th1 and Th2 are different thresholds. Th2 is the threshold used to decide H0 or H1 (binary detection threshold), whilst Th1 is the pre-threshold to separate between the escape induced only by the noise and escape induced by the noise and the arrival of IR@1550nm radiation power (Fig. 4).
The JRTD performance is sensitive to Th1, which requires accurate computation47,82. Then, we can calculate the pre-threshold bound of the switching current Th1:
The false detection probability and the alternative probability limitations can be derived using the interval probability for Isw being in the interval [α, β] as:
Where erf is the error function, α and β factors are related to the false detection probability of the noise that induces escapes and that of the noise and the arrival of IR@1550nm radiation power, respectively. The switching probability of the binary detection can be estimated by85:
Note that the switching current distribution (Isw) measurements presented here demonstrate that the detection of weak radiation is also possible when the Gaussian noise is comparable61,86.
In the context of the performance evaluation for a JRTD detector, the commonly used metrics include the detection probability, PD, and the false probability of switching, PFS. With regard to the provided test in Fig. 5 and the observation \({\text{I}}\left[{\text{n}}\right],\mathrm{ n}\in [0,\mathrm{ N}-1]\), calculating the test statistic K is possible. If L (K) < Th2, then the decision H1 is made, where \({\text{L}}\left({\text{K}}\right)= \frac{{f}_{K}(k;{H}_{1})}{{f}_{K}(k;{H}_{0})}\) is the likelihood ratio test on K, and \({f}_{K}\left(k;{H}_{i}\right), i=\mathrm{0,1}\) represents the probability density functions of K according to the two hypotheses (for each possible value k). Consequently, Th2 can be computed (for a given value PFS = γ) by using the following equations:
Consequently, the detection probability PD can be calculated as
To estimate \({f}_{K}\left(k;{H}_{0}\right) \,and \,{f}_{K}\left(k;{H}_{1}\right)\), let \({f}_{I}\left(i;{H}_{0}\right) \,and \,{f}_{I}\left(i;{H}_{1}\right)\) represent the probability density function of a sample in \({\text{I}}\left[{\text{n}}\right],\mathrm{ n}\in [0,\mathrm{ N}-1]\) under H0 and H1 conditions, respectively. Given a threshold Th1 for the pre-threshold system (Eq. 5), we confirm that Isw = isw [n] is a binary random variable with the values 0 or 1. Therefore, Isw, regarded as a result of the noise, leads to Escape (0), and the occurrence of IR@1550nm radiation power leads to Escape (1). This experimental setup is often referred to as the Bernoulli trial87. The probability \({\text{P}}\left({{\text{I}}}_{{\text{sw}}}=0; {{\text{H}}}_{0}\right)\) refers to the probability that Isw = 0 given by H0. The probabilities \({\text{P}}\left({{\text{I}}}_{{\text{sw}}}=1; {{\text{H}}}_{0}\right),\mathrm{ P}\left({{\text{I}}}_{{\text{sw}}}=0; {{\text{H}}}_{1}\right)\mathrm{ and P}\left({{\text{I}}}_{{\text{sw}}}=1; {{\text{H}}}_{1}\right)\) are defined similarly and calculated as follows:
where \({{\text{a}}}_{0}+{{\text{b}}}_{0}=1,\mathrm{ and }{{\text{a}}}_{1}+{{\text{b}}}_{1}=1\). b0 and b1 are the probabilities of Isw = 1 under H0 and H1 conditions, respectively. Considering that the IR@1550nm radiation is present, the detectable IR@1550nm signal amplitude is AIR > 0, which can be verified. \({f}_{I}\left(i; {H}_{1}\right)\) is a left-side shift of \({f}_{I}\left(i; {H}_{0}\right),\) and the pre-threshold system is employed, and thus b1 > b0 is accurate. For \({\text{I}}\left[{\text{n}}\right],\mathrm{ n}=[0, 1,\dots ,{\text{N}}-1]\) under H0, we let \(m\in [0, N]\) be the number of detecting IR@1550nm radiation signals (i.e. Isw [n] = 1 when I [n] is applied to the pre-threshold system). The binomial distribution represents the discrete probability distribution of the number of occurrences of detecting IR@1550nm radiation power. The probability mass function associated with the variable m is denoted as \({f}_{M}\left(m\right)=\left(\genfrac{}{}{0pt}{}{N}{m}\right) {b}_{0}^{m} {a}_{0}^{N-m}\). Subsequently, we obtain:
where \({f}_{K}\left(k;{H}_{i}\right), i=\mathrm{0,1}\) is discrete because N and Nk are positive integers; k = m/N; m = 0, 1, …, N, the JRTC operating feature that has the shape of a staircase with the width of each rung varying with the value of N. If the value of N is high, then the staircase may be compacted, and the proof is exact. To avoid the discreteness impact of N, we utilise the continuous version of Eq. (14) for theoretical exposition, as follows:
where \({\text{N}},{{\text{N}}}_{{\text{k}}}\mathrm{ \epsilon R}, 0\le {{\text{N}}}_{{\text{k}}}\le \mathrm{N and \delta }(.)\) is the Delta function defined as \(\updelta \left({\text{N}}\right)={\int }_{0}^{\infty }{{\text{I}}}^{{\text{n}}-1} {{\text{e}}}^{-{\text{I}}}\mathrm{ dI}\). In Eq. (15), N is a scaling factor that causes the integral to be equal to 1. In a similar vein, we obtain:
Using Eqs. (15) and (16), we can calculate the likelihood ratio test L (k) as follows:
Given that b1/b0 > 1 due to AIR > 0, we have a1/a0 < 1. Thus, \({(\frac{{b}_{1}}{{b}_{0}})}^{{N}_{k}} \,and \,{ (\frac{{a}_{1}}{{a}_{0}})}^{{N-N}_{k}}\) rise monotonically as a function of k. Therefore, L (k) is consistently growing with respect to k, and the decision H1 is taken when k < Th2, which is determined by Eqs. (8) and (9)47. To determine Th2 threshold, the detection signals that correspond to each of the two hypotheses are set as follows: H1: K = m—n, and H0: K = n, where K is the test statistic value of the average switching current Isw[n] that is examined by the binary detection threshold Th2 (Fig. 5), and n is the Gaussian noise with zero mean and variance σ2. For hypothesis H0:
Consequently, the test statistic value K of the average Isw[n] under Hypothesis H1 is:
The likelihood ratio is expressed as:
The likelihood ratio can be simplified by taking a logarithm of both sides of Eq. (20), which yields:
where η = P(H0) / P(H1) is the minimum probability threshold. The comparable test after arranging terms is presented as:
The decision regions (H0 and H1) are shown in Fig. 4, the probabilities of no signal (i.e. without IR radiation) and with the IR@1550nm radiation power are:
and
respectively. Finally, the optimal decision rule under Hypothesis H0 (i.e. the noise alone induces escapes) is determined by:
where \({{i}_{sw}}_{k}\) is a sequence of test statistic values of the average switching current Isw[n]. Given that the Kth detection signal is assumed to be Gaussian with mean m and variance σ2, the optimum decision rule can be obtained as follows:
Given that the noise samples (without IR radiation) are statistically uncorrelated, the joint density function of the K values is the product of each of the density functions:
with Π representing the product, and \({\prod }_{{\text{k}}}{{\text{e}}}^{{\text{x}}}{\text{k}}= {{\text{e}}}^{{\sum }_{{\text{k}}}{{\text{x}}}_{{\text{k}}}}\). Consequently, the likelihood ratio becomes:
By applying the natural logarithm to both sides of the equation, the likelihood ratio becomes
After arranging the terms, we yield:
where the JRTC is a device that aggregates K data samples and evaluates if their cumulative value is above the threshold Th2 or not, as determined by \({{\text{Th}}}_{2}=(\frac{{\sigma }^{2}}{m}\mathit{ln}\eta + \frac{Km}{2})\). When the prior probabilities are identical, the threshold is equivalent to one. Additionally, when using the log-likelihood ratio, the threshold is set at zero. Hence, this particular form effectively demonstrates the computation of posteriori probabilities, P(H0|Isw) and P(H1|Isw) to ascertain the detection of IR radiation power85. Subsequently, the hypothesis associated with the highest signal is selected37,84. The JRTC is designed by adhering to an optimal decision rule88, and the circuit calculates the probabilities of maximum switching current P(Hi | Isw), i = 0, 1, 2,…, M − 1. Subsequently, the JRTD detector selects the hypothesis associated with the highest switching probability as the preferred decision through the threshold control function. In Fig. 5, the threshold control functions are used for estimation and adjustment. Specifically, the pre-threshold system (Th1) is utilised to delineate and differentiate between the switching of the noise and the switching of arrival IR@1550nm radiation. Furthermore, the test statistic threshold (Th2) serves as the discriminant between hypotheses H0 and H1. In this study, we provide two distinct experimental distributions of switching probabilities that pertain to a specific collection of system characteristics. These distributions are differentiated based on the presence or absence of the IR@1550nm radiation power. According to Eq. (7), the superior value is determined by selecting the lower of the two values of α and β. In cases where the two distributions exhibit clear differentiation, identifying an appropriate threshold (Th1) becomes feasible. This threshold serves the purpose of achieving a low level of significance, such as α ≤ 1%, which effectively eliminates the likelihood that the observed outcomes are solely attributable to Gaussian noise. Additionally, Th1 is selected to ensure a high test power, specifically 1 − β ≥ 99%, thereby guaranteeing the detection of the IR@1550nm radiation signal61.
Experimental setup
The terminated Al/AlOx/Al junction is fabricated in our laboratory by using laser beam lithography (Microlab model) and electron beam double-angle evaporation techniques. Firstly, start with the Dolan bridge structure process: (Coating the bottom film—1st Photoresist (RZJ-390)—photolithography—development (RZX-3038)—etching (NaOH)—degumming—2nd Photoresist (LOR 10B)—photolithography—development (RZX-3038)). Secondly, the JJ fabrication process: Place the sample in the coating machine, in the position of the first evaporation angle (θ1 = + 54°), then begin coating the lower Al film (thickness = 100 nm). The AlOx layer was obtained by oxidising the top of the first Al film in pure oxygen at a pressure of 3.2 mbar for 10 min89. Then, switch the sample position to the second evaporation angle (θ2 = − 54°) and start coating the upper Al film (thickness = 120 nm), as shown in Fig. 6. The fabricated JJ area is approximately 30 μm2, and the junction has been built on a 0.5 mm-thick, 6 mm × 6 mm silicon substrate. Figure 1 shows our experimental setup for the proposed JRTD measurements; The measured JJ is placed in an aluminium sample box (27.5 mm long, 26.5 mm wide, and 11 mm thick), and the box is placed in a dilution refrigerator (Leiden Cryogenics B.V.; CRYOGEN-FREE DILUTION REFRIGERATOR, CF-CS50 model) at the mixing chamber. To prevent and dampen thermal noise, twisted-pair copper cables are used to link the AC and RF lines. At a temperature of 42 mK, the IV curve of the device is measured by using four probe methods. The measurements revealed non-hysteretic IV curve behaviour (Fig. 3a), because of small JJ capacitance, thereby causing the McCumber–Stewart dam** parameter to be less than unity (βc < 1)90. The function generator can generate a sinusoidal voltage signal, which is applied to the bias resistor (100 KΩ) to drive the bias current, Ib through the junction. All electrical lines that link the sample box to the operating electronics at room temperature 300 k are filtered by using RC low-pass filters (home-made RC filters) with a cutoff frequency of 10 kHz. A laser diode source (S/N: 141,014-10) is used to provide a consistent infrared radiation beam with a wavelength of 1550 nm.
The JJ is lighted using a single-mode optical fibre cable (SMF-28), and the IR@1550nm radiation that passes through an optical radiation attenuator (8156A OPTICAL ATTENUATOR model) has regulated attenuation from 740 nW to the minimum obtainable radiation power 0.74 pW. The IR@1550nm radiation power is focused onto the upper surface of the JJ superconducting electrode by means of a hole located in the lid of the sample box that contains the JJ at the mixing chamber of the dilution refrigerator. Meanwhile, the output signals are passed via a LPF (RC) to separate the noise component. Subsequently, they are amplified by a power amplifier (home-made) with a gain of 103 before being inputted into the JRTC for the binary hypothesis detection process (Fig. 5).
Results and discussions
The statistics of photon noises govern the seeming uncontrolled switching with IR@1550nm radiation signal. We created a histogram of switching occurrences in Fig. 7a, as predicted for uncorrelated switching events. A Poisson distribution of the switching current distribution, Isw is shown, for two cases: (i) no signal, see the blue histogram, and the peak is at 9.95 μA (this case mimics the hypothesis H0, i.e., the noise alone induces escapes), and (ii) under IR@1550nm radiation with the power 740 nW, see the green histogram, and the peak is at 9.34 μA (this case mimics Hypothesis H1, the noise and radiation induce the escapes). The noisy environment (i.e., Gaussian noise and measurement noise) affects the histogram of switching current distributions without IR radiation ‘No signal’. Meanwhile, the width of the green curve is the same as that of the blue curve, but the edges of the latter are sharp and vibrated (Fig. 7b).
Statistical decision theory41,69 is used to examine the observed data for the switching current distribution to determine an appropriate decision rule for our proposed JRTD. To achieve the optimum design of the JRTD, one determines the probability P0 (Isw) and P1 (Isw) that a switch will occur after and before the threshold Th1 for each of the binary hypotheses H0, and H1, respectively. To determine the probability of switching events:
where the switching probability with ‘no signal’ is \({\text{P}}{\left({{\text{I}}}_{{\text{sw}}}\right)}_{0}\), and \({\text{P}}{\left({{\text{I}}}_{{\text{sw}}}\right)}_{1}\) is the switching probability in the presence of an IR radiation@1550nm with the power set to 740 nW. Solve Eq. (31) by substituting \({\text{P}}{\left({{\text{I}}}_{{\text{sw}}}\right)}_{\mathrm{0,1}}\) from Eqs. (3) and (4). We can write the two possible hypotheses (H0 | H1) probabilities as follows:
The output of the JRTC exhibits two distinct scenarios: In the first scenario, we consider the null hypotheses: H0, Eq. (32a) indicating the switching occurred in the absence of the radiation signal, given a measured value of Isw0 = 9.95 µA, surpassing thresholds Th1 and Th2. In the subsequent scenario, we consider alternative hypothesis H1, and Eq. (32b) suggests that the switching occurred in the presence of IR radiation@1550nm with the power 740 nW, and the measured value Isw1 = 9.34 µA, is smaller than those of thresholds Th1 and Th2. The suggested JRTD aims to determine the optimal decision by formulating certain hypotheses that are derived from the switching probabilities of the received IR radiation signals. The threshold switching current Th1 for the transition between states H0 and H1 was measured as 9.72 μA. This measurement was conducted in the absence of radiation, and under the influence of a 740 nW IR@1550nm radiation power. The limit of the switching current induced by Gaussian noise: H0 is \({{({\text{I}}}_{{\text{sw}}})}_{{\text{Null}}}>9.72 \mu {\text{A}}\). Similarly, the switching current induced by the Gaussian noise and the arrival of IR@1550nm radiation power H1 is \({{({\text{I}}}_{{\text{sw}}})}_{{\text{Alter}}.}<9.72 \mu {\text{A}}\). Furthermore, the detection of the switching current in response to IR radiation is within the range of \({{8.59 \mu {\text{A}}<({\text{I}}}_{{\text{sw}}})}_{{\text{Alter}}.}<9.72 \mu {\text{A}}\). Based on the findings obtained from these experimental results, the minimum obtainable radiation power of our instrumentation is 0.74 pW. Additionally, the corresponding minimum switching current is \({{({\text{I}}}_{{\text{sw}}})}_{{\text{Min}}}=9.91 \mu {\text{A}}\), as seen in Fig. 8. Meanwhile, the noise results in the generation of escape amounts α = 8.99 µA, whereas the noise combined with the arrival of IR@1550nm radiation power leads to β = 10.40 µA. These values of α and β were extracted directly from the figure properties window in the 'MATLAB' software that we used to generate the switching current histograms.
The optimal design of JRTD is supposed to detect a single IR photon energy, E = h/cλ; where E is the photon energy, h is Planck’s constant, λ is the wavelength, and c is the speed of light in vacuum. This energy is calculated as 0.7999 eV (1.28 × 10−19 J)91,92. The minimum detectable power of the proposed JRTD can be estimated as 0.74 pW by reducing the IR radiation power to the minimum obtainable radiation power of our instrumentation that causes JJ transition. We achieved this process by using an optical radiation attenuator, coupled in series with the IR radiation source. This attenuator reduces the IR radiation power from 740 nW to 0.74 pW by adding a calibrated amount of power loss in decibel units (0–60 dB) to the IR radiation generated by the IR radiation source. Figure 9a illustrates the relationship between the attenuated IR@1550nm radiation and the switching current distributions by gradually decreasing the IR radiation power from 740 nW to 0.74 pW, which is comparable with the attenuator range from 0 to 60 dB whilst maintaining the same junction under test but with different measurement parameters. The linear relationship between the switching current and the attenuated IR radiation power within the range of 0 dB to 10 dB, equal to 740 nW to 74 nW, is evident. The switching current varies from 8.6 µA to 9.696 µA, including an average range of 1.096 µA. After this region (10 dB), the curve stability for the IR radiation power lower than 74 nW (10 dB) to the minimum radiation level applied from the IR radiation source, which is 0.74 pW (60 dB), the equivalent switching current values varied from 9.696 µA to 9.715 µA. Despite the small displacement that occurred in the values of the switching currents, the minimum obtainable radiation power of our instrumentation (0.74pW) is also obtained in this different measurement method.
The JRTD minimum detectable power depends on the junction characteristics, the IR radiation source and the attenuator loss gain. Our studies were performed with a minimum detectable power of 0.74 pW, and the rate of detecting photons from IR radiation was 5.692 × 106 photons per second according to; Rph = Pmin / E, where Rph is the photon rate, Pmin is the minimum detectable power, and E = hv is the energy of each photon. Based on these results, the presence of noise in the transmission of the IR@1550nm radiation has an effect on the precision of measurements and the value of the switching current. For computing the JRTD performance parameters, we evaluate the minimum attainable sensitivity of the JRTD as the IR radiation signal required to equal the minimum JRTD noise power (Noise equivalent power (NEP)) according to; \({\text{NEP}}/\Delta V=\sqrt{6}{\left(\frac{\mathrm{\hbar }{\omega }_{{\text{IR}}}}{2{{\text{eR}}}_{{\text{J}}}{{\text{I}}}_{{\text{c}}}}\right)}^{2}\sqrt{4{k}_{B}T{R}_{J}}\) , where ωIR is the IR radiation frequency, kB is Boltzmann constant, and T is the working temperature93,94. The NEP estimated to be (~ 2.85 × 10−13 W Hz−1/2) is a clear indication of the high sensitivity of the proposed JRTD. Moreover, to estimate the performance of the JRTD, we calculated the Kumar-Caroll (KC) index dKC, which is a signal-to-noise ratio (SNR) indicator95. We obtained that through the analysis of the switching currents (Isw) of the JJ transition with and without IR@1550nm illumination as follows:
where \({\langle {I}_{sw}\rangle }_{1}=\frac{1}{N}\sum_{i=1}^{N}{{I}_{sw}}_{i}{|}_{1}\) is the average value of the Isw in the presence of the IR@1550nm radiation power and noise, \({\langle {I}_{sw}\rangle }_{0}\) describes the Isw in the absence of the IR@1550nm radiation and the presence of the noise alone, and \({\sigma }^{2}{\left({I}_{sw}\right)}_{1}=\frac{1}{N(N-1)} \sum_{i=1}^{N}{({{I}_{sw}}_{i}-{\langle {I}_{sw}\rangle }_{1})}^{2}\) is the variance of the average Isw96. Figure 9b shows the dKC index analysis, which agrees very well with the experimental results of switching current distribution vs. attenuated IR@1550nm radiation power in dB. We can observe that the dKC parameter values are higher in the window of 740 nW (0 dB) to 74 nW (10 dB), which confirms the experimental results in Fig. 9a. We conclude that the proposed JRTD can detect lower IR radiation if radiation source lower than 0.74 pW is provided, and the Gaussian noise is further suppressed.
Conclusions
In summary, we designed and fabricated the JRTD that utilises the CBJJ at cryogenic temperatures, thereby serving as an infrared radiation sensor capable of binary detection. The binary hypothesis detection problem can be effectively addressed by utilising the JRTC. Furthermore, we have conducted an experimental analysis on the switching current distributions of the Al/AlOx/Al CBJJ to investigate the anticipated responses of the JRTD. Considering the effects of the Gaussian noise, a method based on standard statistical decision theory84,96 is developed to process the accumulated data of the switching current distributions for calibrating threshold control functions (Th1 and Th2). The results prove that the device can be used for the binary detection of the photons. Given the quality of the fabricated CBJJ can be further improved, and the numerical approaches to processing the detected data can also be further optimised, and the proposed JRTD based on the CBJJs can be used to implement the sensitive detection of photons (NEP ~ 2.85 × 10−13 W Hz−1/2) in a noisy environment. Furthermore, our results suggest a potential to enhance the minimum detectable power of the suggested JRTD detector by using radiation source lower than 0.74 pW and reducing the Gaussian noise of the junction. Finally, the JRTD performance is evaluated through the SNR indicator (dKC), which shows a maximum value of 44.3 at 740 nW, which confirms our experimental results.
Data availability
The datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request.
Change history
11 March 2024
A Correction to this paper has been published: https://doi.org/10.1038/s41598-024-56375-w
References
Perryman, M. A. C., Foden, C. L. & Peacock, A. Optical photon counting using superconducting tunnel junctions. Nucl. Inst. Methods Phys. Res. A 325, 319–325 (1993).
Peacock, T. et al. Superconducting tunnel junctions as detectors for ultraviolet, optical, and near infrared astronomy. Astron. Astrophys. Suppl. Ser. 123, 581–587 (1997).
Bai, P., Zhang, Y. H. & Shen, W. Z. Infrared single photon detector based on optical up-converter at 1550 nm. Sci. Rep. 7, 1–12 (2017).
Wang, Y. et al. Photon-detections via probing the switching current shifts of Josephson junctions. Phys. C Supercond. Appl. 515, 49–53 (2015).
Kuzmin, L. S. et al. Single photon counter based on a josephson junction at 14 GHz for searching galactic axions. IEEE Trans. Appl. Supercond. 28, 1–5 (2018).
Verhoeve, P. et al. Superconducting tunnel junctions as photon counting detectors in the infrared to the ultraviolet. IEEE Trans. Appl. Supercond. 7(2), 3359–3362 (1997).
Rando, N. et al. The properties of niobium superconducting tunneling junctions as X-ray detectors. Nucl. Inst. Methods Phys. Res. A 313, 173–195 (1992).
Guo, Q. et al. Single photon detector with high polarization sensitivity. Sci. Rep. 5, 1–5 (2015).
Walsh, E. D. et al. Josephson junction infrared single-photon detector. Science 372, 409–412 (2021).
Giazotto, F., Heikkilä, T. T., Luukanen, A., Savin, A. M. & Pekola, J. P. Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications. Rev. Mod. Phys. 78, 217–274 (2006).
Grimaudo, R., Valenti, D., Spagnolo, B., Filatrella, G. & Guarcello, C. Josephson-junction-based axion detection through resonant activation. Phys. Rev. D 105, 033007 (2022).
Grimaudo, R., Valenti, D., Filatrella, G., Spagnolo, B. & Guarcello, C. Coupled quantum pendula as a possible model for Josephson-junction-based axion detection. Chaos Solitons and Fractals 173, 113745 (2023).
Grimaudo, R. et al. Axion field influence on Josephson junction quasipotential. Materials (Basel). 16, 5972 (2023).
Natarajan, C. M., Tanner, M. G. & Hadfield, R. H. Superconducting nanowire single-photon detectors: Physics and applications. Supercond. Sci. Technol. 25, 063001 (2012).
Engel, A., Renema, J. J., Il’In, K. & Semenov, A. Detection mechanism of superconducting nanowire single-photon detectors. Supercond. Sci. Technol. 28, 114003 (2015).
You, L. Superconducting nanowire single-photon detectors for quantum information. Nanophotonics 9, 2673–2692 (2020).
Esmaeil Zadeh, I. et al. Superconducting nanowire single-photon detectors: A perspective on evolution, state-of-the-art, future developments, and applications. Appl. Phys. Lett. 118, 190502 (2021).
Dauler, E. A. et al. Review of superconducting nanowire single-photon detector system design options and demonstrated performance. Opt. Eng. 53, 081907 (2014).
Vodolazov, D. Y., Korneeva, Y. P., Semenov, A. V., Korneev, A. A. & Goltsman, G. N. Vortex-assisted mechanism of photon counting in a superconducting nanowire single-photon detector revealed by external magnetic field. Phys. Rev. B 92, 104503 (2015).
Alesini, D. et al. Status of the SIMP project: Toward the single microwave photon detection. J. Low Temp. Phys. 199, 348–354 (2020).
Ullom, J. N. & Bennett, D. A. Review of superconducting transition-edge sensors for x-ray and gamma-ray spectroscopy. Supercond. Sci. Technol. 28, 84003 (2015).
Paolucci, F. et al. Development of highly sensitive nanoscale transition edge sensors for gigahertz astronomy and dark matter search. J. Appl. Phys. 128, 194502 (2020).
Zmuidzinas, J. Superconducting microresonators: Physics and applications. Annu. Rev. Condens. Matter. Phys. 3, 169–214 (2012).
Peltonen, J. T. et al. Hybrid rf SQUID qubit based on high kinetic inductance. Sci. Rep. 8, 6–13 (2018).
Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y. X. & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718, 1–102 (2017).
Braginski, A. I. Superconductor electronics: Status and outlook. J. Supercond. Nov. Magn. 32, 23–44 (2019).
Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).
Wendin, G. & Shumeiko, V. S. Quantum bits with Josephson junctions (Review Article). Low Temp. Phys. 33, 724–744 (2007).
Beck, C. Possible resonance effect of axionic dark matter in josephson junctions. Phys. Rev. Lett. 111, 1–5 (2013).
Graham, P. W., Irastorza, I. G., Lamoreaux, S. K., Lindner, A. & Van Bibber, K. A. Experimental searches for the axion and axion-like particles. Annu. Rev. Nucl. Part. Sci. 65, 485–514 (2015).
Asztalos, S. J. et al. SQUID-based microwave cavity search for dark-matter axions. Phys. Rev. Lett. 104, 1–4 (2010).
Anghel, D. V., Kulikov, K., Galperin, Y. M. & Kuzmin, L. S. Electromagnetic radiation detectors based on Josephson junctions: Effective Hamiltonian. Phys. Rev. B 101, 024511 (2020).
Peccei, R. D. & Quinn, H. R. CP conservation in the presence of pseudoparticles. Phys. Rev. Lett. 38, 1440–1443 (1977).
Ellis, J. & Gaillard, M. K. No new light boson?. Phys. Lett. B 74, 374–376 (1978).
Wilczek, F. Problem of strong P and T invariance in the presence of instantons. Phys. Rev. Lett. 40, 279–282 (1978).
Barnett, S. M., Pegg, D. T., Jeffers, J., Jedrkiewicz, O. & Loudon, R. Retrodiction for quantum optical communications. Phys. Rev. A 62, 022313 (2000).
Mičuda, M. et al. Noiseless loss suppression in quantum optical communication. Phys. Rev. Lett. 109, 1–5 (2012).
O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007).
Ralph, T. C. & Pryde, G. J. Optical quantum computation. In Progress in Optics Vol. 54 (Elsevier, 2010).
Thomas, J. B. Nonparametric detection. Proc. IEEE 58(5), 623–631 (1970).
Chapeau-Blondeau, F. Nonlinear test statistic to improve signal detection in non-Gaussian noise. IEEE Signal Process. Lett. 7, 205–207 (2000).
Guerriero, M., Marano, S., Matta, V. & Willett, P. Stochastic resonance in sequential detectors. IEEE Trans. Signal Process. 57(1), 2–15 (2008).
Papadopoulos, H. C., Wornell, G. W. & Oppenheim, A. V. Low-complexity digital encoding strategies for wireless sensor networks. Proc. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing. Vol. 6, 3273–3276 (1998).
Saha, A. A. & Anand, G. V. Design of detectors based on stochastic resonance. Signal Process. 83, 1193–1212 (2003).
Galdi, V., Pierro, V. & Pinto, I. M. Evaluation of stochastic-resonance-based detectors of weak harmonic signals in additive white Gaussian noise. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 57, 6470–6479 (1998).
Bulsara, A. R. et al. Signal detection via residence-time asymmetry in noisy bistable devices. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 21 (2003).
Guo, G. & Mandal, M. On optimal threshold and structure in threshold system based detector. Signal Process. 92, 170–178 (2012).
Bulsara, A. R. & Zador, A. Threshold detection of wideband signals: A noise-induced maximum in the mutual information. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 54, 2185–2188 (1996).
Novotný, T. Josephson junctions as threshold detectors of full counting statistics: open issues. J. Stat. Mech. Theory Experiment https://doi.org/10.1088/1742-5468/2009/01/P01050 (2009).
Addesso, P., Filatrella, G. & Pierro, V. Characterization of escape times of Josephson junctions for signal detection. Phys. Rev. E - Stat. Nonlinear Soft Matter. Phys. 85, 016708 (2012).
Voutilainen, J., Laakso, M. A. & Heikkilä, T. T. Physics of proximity Josephson sensor. J. Appl. Phys. 107, 064508 (2010).
Guarcello, C., Braggio, A., Solinas, P. & Giazotto, F. Nonlinear critical-current thermal response of an asymmetric Josephson tunnel junction. Phys. Rev. Appl. 11, 1 (2019).
Oelsner, G. et al. Underdamped Josephson junction as a switching current detector. Appl. Phys. Lett. 103, 1–4 (2013).
Pountougnigni, O. V., Yamapi, R., Tchawoua, C., Pierro, V. & Filatrella, G. Detection of signals in presence of noise through Josephson junction switching currents. Phys. Rev. E 101, 52205 (2020).
Clarke, J., Cleland, A. N., Devoret, M. H., Esteve, D. & Martinis, J. M. Quantum mechanics of a macroscopic variable: The phase difference of a Josephson junction. Science 239, 992–997 (1988).
Hartmann, M. J. Quantum simulation with interacting photons. J. Opt. (United Kingdom) 18, 104005 (2016).
Fulton, T. A., Dunkleberger, L. N. & Dynes, R. C. Quantum interference properties of double Josephson junctions. Phys. Rev. B 6, 855–875 (1972).
Krasnov, V. M. et al. Collapse of thermal activation in moderately damped Josephson junctions. Phys. Rev. Lett. 95, 93–96 (2005).
Männik, J. et al. Crossover from Kramers to phase-diffusion switching in moderately damped Josephson junctions. Phys. Rev. B Condens. Matter Mater. Phys. 71, 2–5 (2005).
Poudel, A., McDermott, R. & Vavilov, M. G. Quantum efficiency of a microwave photon detector based on a current-biased Josephson junction. Phys. Rev. Condens. B Matter. Mater. Phys. 86, 1–4 (2012).
Piedjou Komnang, A. S. et al. Analysis of Josephson junctions switching time distributions for the detection of single microwave photons. Chaos Solitons Fractals 142, 104005 (2021).
Revin, L. S. et al. Microwave photon detection by an Al Josephson junction. Beilstein J. Nanotechnol. 11, 960–965 (2020).
Paolucci, F. et al. Hypersensitive tunable josephson escape sensor for gigahertz astronomy. Phys. Rev. Appl. 14, 1 (2020).
Yablokov, A. A. et al. Resonant response drives sensitivity of Josephson escape detector. Chaos Solitons and Fractals 148, 111058 (2021).
Walsh, E. D. et al. Graphene-based Josephson junction single photon detector. Phys. Rev. Appl. 8(2), 024022 (2017).
Lee, G. H. et al. Graphene-based Josephson junction microwave bolometer. Nature 586, 42–46 (2020).
Astafiev, O. et al. Single-photon detector in the microwave range. Appl. Phys. Lett. 80, 4250–4252 (2002).
Inomata, K. et al. Single microwave-photon detector using an artificial Λ-type three-level system. Nat. Commun. 7, 1–7 (2016).
Pankratov, A. L. et al. Towards a microwave single-photon counter for searching axions. NPJ Quantum Inf. 8, 61. https://doi.org/10.1038/s41534-022-00569-5 (2022).
Guarcello, C., Valenti, D., Spagnolo, B., Pierro, V. & Filatrella, G. Josephson-based threshold detector for Lévy-distributed current fluctuations. Phys. Rev. Appl. 11, 1 (2019).
White, R. M. Physics and Applications of the Josephson Effect by A. Barone and G. Paterno. J. Vacuum Sci. Technol. 21 (1982).
Guarcello, C., Filatrella, G., Spagnolo, B., Pierro, V. & Valenti, D. Voltage drop across Josephson junctions for Lévy noise detection. Phys. Rev. Res. 2, 43332 (2020).
Guarcello, C., Braggio, A., Solinas, P., Pepe, G. P. & Giazotto, F. Josephson-threshold calorimeter. Phys. Rev. Appl. 11, 1 (2019).
Addesso, P., Pierro, V. & Filatrella, G. Interplay between detection strategies and stochastic resonance properties. Commun. Nonlinear Sci. Numer. Simul. 30, 15–31 (2016).
Devoret, M. H., Esteve, D., Martinis, J. M., Cleland, A. & Clarke, J. Resonant activation of a Brownian particle out of a potential well: Microwave-enhanced escape from the zero-voltage state of a Josephson junction. Phys. Rev. B 36, 58–73 (1987).
Ponta, L., Carbone, A., Gilli, M. & Mazzetti, P. Resistively and capacitively shunted Josephson junctions model for unconventional superconductors. Proc. Canadian Confernce on Electrical and Computer Engineering 000644–000647. https://doi.org/10.1109/CCECE.2011.6030531 (2011).
Guarcello, C., Valenti, D. & Spagnolo, B. Phase dynamics in graphene-based Josephson junctions in the presence of thermal and correlated fluctuations. Phys. Rev. Condens. B Matter. Mater. Phys. 92, 1–17 (2015).
Ben-Jacob, E. & Bergman, D. J. Thermal noise effects on the microwave-induced steps of a current-driven Josephson junction. Phys. Rev. A 29(4), 2021 (1984).
Guarcello, C. Lévy noise effects on Josephson junctions. Chaos Solitons Fractals 153, 111531 (2021).
Shapovalov, A. P. et al. Low-capacitance Josephson junctions. Prog. Phys. Met. 21, 3–25 (2020).
Couëdo, F. et al. Dynamic properties of high-Tc superconducting nano-junctions made with a focused helium ion beam. Sci. Rep. 10(1), 10256. https://doi.org/10.1038/s41598-020-66882-1 (2020).
Kay, S., Michels, J. H., Chen, H. & Varshney, P. K. Reducing probability of decision error using stochastic resonance. IEEE Signal Process. Lett. 13(11), 695–698 (2006).
Chen, H., Member, S., Varshney, P. K., Kay, S. M. & Michels, J. H. Theory of the stochastic resonance effect in signal detection: Part I—fixed detectors. IEEE Trans. Signal Process. 55, 3172–3184 (2007).
Addesso, P., Filatrella, G. & Pierro, V. Escape time of Josephson junctions for signal detection. In Spontaneous Symmetry Breaking, Self-Trap**, and Josephson Oscillations 657–678 (Springer, 2012).
Fallis, A. Signal Detection and Estimation, Second Edition, Journal of Chemical Information and Modeling vol. 53 (2013).
Yablokov, A. A., Mylnikov, V. M., Pankratov, A. L., Pankratova, E. V. & Gordeeva, A. V. Suppression of switching errors in weakly damped Josephson junctions. Chaos Solitons and Fractals 136, 109817 (2020).
Papoulis, A. & Pillai, U. Probability, Random Variables and Stochastic Processes 4th edn. (McGraw Hill, 2002).
Chapeau-Blondeau, F. Stochastic resonance and optimal detection of pulse trains by threshold devices. Digital Signal Process. 9(3), 162–177 (1999).
Moskalev, D. O. et al. Optimization of shadow evaporation and oxidation for reproducible. Sci. Rep. 13, 1–7 (2023).
Hansma, P. K. & Rochlin, G. I. Josephson weak links: Shuntedjunction and mechanicalmodel results. J. Appl. Phys. 43, 4721 (1972).
Chang, J. et al. Efficient mid-infrared single-photon detection using superconducting NbTiN nanowires with high time resolution in a Gifford-McMahon cryocooler. Photonics Res. 10, 1063 (2022).
Semenov, A. D. et al. Energy resolution of a superconducting nanowire single-photon detector. J. Low Temp. Phys. 151, 564–569 (2008).
Richards, P. L. The Josephson junction as a detector of microwave and far-infrared radiation. Proc. Semiconductors and Semimetals, vol. 12, 395-440, Elsevier (1977).
Holdengreber, E. et al. THz radiation measurement with HTSC Josephson junction detector matched to planar antenna. Appl. Sci. 10(18), 6482 (2020).
Kumar, B. V. K. V. & Carroll, C. W. Performance of Wigner distribution function based detection methods. Opt. Eng. 23, 732 (1984).
Guarcello, C. et al. Josephson-based scheme for the detection of microwave photons. Phys. Rev. Appl. 16(5), 054015. https://doi.org/10.1103/PhysRevApplied.16.054015 (2021).
Acknowledgements
This work was partially supported by the National Key Research and Development Program of China (NKRDC) under Grant No. 2021YFA0718803 and the National Natural Science Foundation of China (NSFC) under Grant No. 11974290.
Author information
Authors and Affiliations
Contributions
S.A., P.H.O. and L.F.W. proposed and conceptualised the ideas of the project and the design. J.X.H. and Y.Q.C. fabricated experimental samples and made electrical measurements. L.F.W. and S.A. analysed the results and co-wrote the original draft and reviewed and edited the manuscript. L.F.W. supervised the project. All authors have contributed to the information and material submitted for publication, and all authors have read and approved the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The original online version of this Article was revised: In the original version of this Article, P. H. Ouyang was incorrectly listed as a corresponding author. The correct corresponding author for this Article is L. F. Wei. Correspondence and request for materials should be addressed to lfwei@swjtu.edu.cn.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Ali, S., Ouyang, P.H., He, J.X. et al. Josephson radiation threshold detector. Sci Rep 14, 2531 (2024). https://doi.org/10.1038/s41598-024-52684-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598-024-52684-2
- Springer Nature Limited