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IEEE Workshop on Low Temperature Electronics (WOLTE)

Analysis of Josephson Junction Lifetimes for the Detection of Single Photons in a Thermal Noise Background

Alex Stephane Piedjou Komnang, Claudio Guarcello, C. Barone, S. Pagano, Giovanni Filatrella

Published Apr 12, 2021• 5 citations
Publisher

Abstract

This work deals with the numerical analysis of the zero-voltage state lifetimes distribution of an underdamped Josephson junction used for the detection of single microwave photons in the presence of thermal noise. The analysis considers the switching probabilities of a JJ subjected to a train of current pulses, which simulates a weak photon field. To characterize the detection, we take advantage of a statistic tool, the Kumar-Carroll (KC) index, which is a good proxy of the signal-to-noise-ratio. It can be, therefore, exploited to identify the proper device fabrication parameters and the optimal operation point of the junction.

DOI
10.1109/wolte49037.2021.9555447

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This work deals with the numerical analysis of the zero-voltage state lifetimes distribution of an underdamped Josephson junction used for the detection of single microwave photons in the presence of thermal noise. The analysis considers the switching probabilities of a JJ subjected to a train of current pulses, which simulates a weak photon field. To characterize the detection, we take advantage of a statistic tool, the Kumar-Carroll (KC) index, which is a good proxy of the signal-to-noise-ratio. It can be, therefore, exploited to identify the proper device fabrication parameters and the optimal operation point of the junction.
We propose a scheme for the detection of microwave-induced photons through a current-biased Josephson junction, from the point of view of the statistical decision theory. Our analysis is based on the numerical study of the zero-voltage lifetime distribution in response to a periodic train of pulses, that mimics the absorption of photons. The statistical properties of the detection are retrieved comparing the thermally induced transitions with the distribution of the switchings to the finite voltage state due to the joint action of thermal noise and of the incident pulses. The capability to discriminate the photon arrival can be quantified through the Kumar-Caroll index, which is a good indicator of the signal-to-noise ratio. The index can be exploited to identify the system parameters best suited for the detection of weak microwave photons.
The performances of a Josephson junction employed to reveal a train of pulses (a rough model for single photon detection) are analyzed with a theoretical estimate that exploits an index employed in statistical decision theory, the Kumar–Carroll index. The approximate analysis compares the numerically simulated performances of the device through the receiver operating characteristics, that offer an overview of the rate of false detection, as well as the probability to miss a signal (in this case, a pulse train). It is thus demonstrated the usefulness and the limits of the succinct Kumar–Carroll parameter. On the first side, it is proven that an increase of the parameter corresponds to an improvement of the detection. However, on the side of the limitations, the expected performances are not quite accurate, for the actual performances are systematically worse than the theoretical estimates. The results may be relevant to characterize Josephson junctions as detectors of weak signals, as those stemming from axions.
We demonstrate the narrow switching distribution of an underdamped Josephson junction from the zero to the finite voltage state at millikelvin temperatures. We argue that such junctions can be used as ultrasensitive detectors of the single photons in the GHz range, operating close to the quantum limit: a given initial (zero voltage) state can be driven by an incoming signal to the finite voltage state. The width of the switching distribution at a nominal temperature of about T = 10 mK was 4.5 nA, which corresponds to an effective noise temperature of the device below 60 mK.
An aluminium Josephson junction (JJ), with a critical current suppressed by a factor of three compared with the maximal value calculated from the gap, is experimentally investigated for application as a threshold detector for microwave photons. We present the preliminary results of measurements of the lifetime of the superconducting state and the probability of switching by a 9 GHz external signal. We found an anomalously large lifetime, not described by the Kramers’ theory for the escape time over a barrier under the influence of fluctuations. We explain it by the phase diffusion regime, which is evident from the temperature dependence of the switching current histograms. Therefore, phase diffusion allows for a significant improvement of the noise immunity of a device, radically decreasing the dark count rate, but it will also decrease the single-photon sensitivity of the considered threshold detector. Quantization of the switching probability tilt as a function of the signal attenuation for various bias currents through the JJ is observed, which resembles the differentiation between N and N + 1 photon absorption.
In this Letter, we experimentally demonstrated that Josephson threshold detectors (JTDs) could be developed to implement the sensitive detection of broadband microwave photons. Beginning with the numerical simulations of the damped dynamics for the macroscopic phase particle generated by a Josephson junction (JJ), we showed that the time-domain threshold voltage state switched measurements of the JJ driven by a low-frequency triangular wave current, which could be utilized to implement the sensitive microwave photons detection. The detectable signal power can be determined by using the Kumar–Caroll index to quantify the distinguishability between two statistical distributions on the measured threshold switched durations of the JJ with and without the signal input. Experimentally, we fabricated the Al/AlOx/Al JJ and measured its threshold responses, at 50 mK temperature, to the input microwave photons at the frequency of ∼5 GHz. The experimental results indicated that the weak microwave signals, which are phenomenologically threatened by the additional thermal noise that modifies the damped phase dynamics of the JJ, can be detected by the fabricated JTD. The detectable power of the microwave signals demonstrated here was calibrated as about −92 dBm (corresponding to the photons rate of ∼2×108 photons/ms). Based on the numerical simulations for optimizing the relevant performance indicators of the detectors, we further argue that the JTDs could be utilized to achieve the sensitive detection of broadband microwave photons at the single-photon level.
Abstract Josephson junctions, in appropriate configurations, can be excellent candidates for detection of single photons in the microwave frequency band. Such possibility has been recently addressed in the framework of galactic axion detection. Here are reported recent developments in the modelling and simulation of dynamic behaviour of a Josephson junction single microwave photon detector. For a Josephson junction to be enough sensitive, small critical currents and operating temperatures of the order of ten of mK are necessary. Thermal and quantum tunnelling out of the zero-voltage state can also mask the detection process. Axion detection would require dark count rates in the order of 0.001 Hz. It is, therefore, is of paramount importance to identify proper device fabrication parameters and junction operation point.