Accurate S-parameter calibrations at cryogenic temperatures are essential for using the Josephson arbitrary waveform synthesizer (JAWS) as a quantum-based power standard in the microwave regime. At NIST, we are developing multiple approaches to cryogenic calibration. One effort focuses on a new multi-impedance-state line (MISL) technique that allows in-situ on-chip calibration at 4 K, without the need for cryogenic switches or a probe station (J. N. Thomas et al., “Cryogenic On-Chip In Situ S-Parameter Calibration Using Superconducting Coplanar Waveguides,” in IEEE Transactions on Microwave Theory and Techniques, doi: 10.1109/TMTT.2025.3585803). The approach uses coplanar waveguide (CPW) models based on various impedance states of niobium (Nb), which is superconducting below 9 K and has a monotonically increasing resistance above 10 K. By varying stage temperature and current bias, multiple impedance states of the same CPW are accessed and used as calibration standards within a fixed cryogenic signal path. A least-squares analysis of these states solves the full eight-term error model. Validation against typical calibration algorithms performed using a cryogenic probe station show transmission agreement within the uncertainties of the measurement, with nominal differences below 0.2 dB, up to the maximum measurement frequency of 26.5 GHz. We further demonstrate the technique in a separate cryostat with fixed wire-bonded connections, applying it to Nb CPWs with and without embedded Josephson junctions (JJs).

To avoid degradation of circuit performance, fabrication processes for niobium-based superconductive electronics are typically limited to temperatures below 150 °C. In this study, we investigated protective dielectric capping layers that preserve the superconducting properties of Niobium (Nb) wiring at processing temperatures as high as 400 °C. To assess the thermal stability of Nb films, 400 nm thick Nb layers were deposited on oxidized silicon wafers and were either left uncapped or were intentionally capped with selected dielectric materials. The samples were subjected to postdeposition annealing in an argon atmosphere for comparison. Samples were annealed up to 450 °C, and changes in room temperature sheet resistance were used as a proxy for film degradation and checked with cryogenic measurements of samples annealed up to 400 °C. A sharp increase in room temperature sheet resistance, and a resulting decrease in residual resistivity ratio was observed in pristine Nb films above 300 °C. We found that the ex-situ deposition of insulating covering ("cap") reduces the onset of degradation. Notably, silicon oxide (SiO x ) capping shows significant improvement and silicon nitride (Si x N y ) capped samples exhibit minimal changes in resistance across the full annealing range. These results suggest that Si x N y encapsulation as a dielectric "cap" preserves superconductive properties and offers an expanded thermal budget for Nb-based superconductive electronics, with implications for multilayer integration and scalable fabrication.

This work presents the results of evaluating and measuring the dc leakage effects associated with programmable Josephson voltage standards (PJVSs) caused by unintended currents flowing in the circuit. Two types of leakage error can occur in PJVS systems: (1) involves leakage currents to Earth ground, which typically result from the finite resistance of cable insulation and the bias electronics, and (2) leakage paths on the precision output leads giving rise to a voltage divider effect between the leads and the load impedance. Both effects impact the PJVS's measurement accuracy and must be monitored regularly. We have developed assessment methods, including both manual and automated measurements, that should be applied to any disseminated PJVS systems currently in use. If these recommended techniques are followed and the leakage current to Earth ground remains below 150 pA when the PJVS array is biased at 10 V, the resulting voltage error at the room-temperature terminals will be less than 0.2 nV.

This article presents a new multiimpedance-state line (MISL) in situ scattering parameter (S-parameter) calibration technique using on-chip superconducting transmission lines at 4 K that enables cryogenic calibration in a fixed signal path without the need for cryogenic switches or a cryogenic probe station. The method uses coplanar waveguide (CPW) models based on various impedance states of niobium (Nb), which has zero dc resistance below 9 K and a monotonically increasing resistance from 10 K to room temperature. The different impedance states are accessed by heating the 4 K stage of a cryostat and injecting up to 245 mA of current into the line. Using these states, we solve for the unknowns in an eight-term error model through a least-squares analysis. We first validate the MISL calibration technique by comparing it with short-open-load-reciprocal (SOLR) calibrated measurements in a cryogenic probe station, finding transmission agreement within 0.2 dB and uncertainty overlap for nearly all frequencies up to 26.5 GHz. We then apply the method to calibrate Nb CPWs with and without embedded Josephson junctions (JJs), using a fixed wire bonded connection, and without the use of cryogenic switches or movable probes. Strong agreement with the CPW models is demonstrated, with uncertainty overlap and differences below 0.1 dB up to 4.6 GHz without JJs and up to 2.4 GHz with JJs; resonances cause interruptions beyond these frequencies.

This article presents a 2-V programmable Josephson voltage standard (PJVS) with dual microwave frequency inputs and multiple output taps. The design provides three main features: 1) output voltages with nanovolt resolution; 2) the ability to perform a microwave frequency self-check based on a null voltage measurement; and 3) additional voltage output taps providing simultaneous 10:1 (or 5:1) divided voltage reference for resistive divider calibration. With low heat dissipation, this device is well suited for implementation with a compact cryocooler as a turnkey traveling system.

The voltage errors related to ac leakage currents in Josephson arbitrary waveform synthesizer (JAWS) systems are significant contributors to the overall system accuracy. These ac leakage currents flow through paths (typically to ground) that are not part of the intended measurement circuit. This article examines output voltage discrepancies between two different but nominally identical circuit halves on a single JAWS circuit and shows that this discrepancy is dominated by ac leakage currents through the stray capacitance in the compensation leads. Methods to minimize these voltage errors will be discussed along with their associated limitations.

We report on the design, fabrication, and measure-ment of a very high frequency band Josephson arbitrary waveformsynthesizer (VHF-JAWS) at frequencies from 1 kHz to 50.05 MHz.The VHF-JAWS chip is composed of a series array of 12 810Josephsonjunctions(JJs)embeddedinasuperconductingcoplanarwaveguide. Each JJ responds to a pattern of current pulses bycreating a corresponding pattern of voltage pulses, each with atime-integrated area related to fundamental constants ash/2e.Thepulse patterns are chosen to produce quantum-based single-tonevoltage waveforms with an open-circuit voltage of 50 mV rms (-19.03 dBm output power into 50 Omega load impedances) at frequenciesup to 50.05 MHz, which is more than twice the voltage that has beengenerated by previous RF-JAWS designs at 1 GHz. The VHF-JAWSis "quantum-locked," that is, it generates one quantized outputvoltage pulse per input current pulse per JJ while varying the dccurrent through the JJ array by at least 0.4 mA and the amplitudeof the bias pulses by at least 10 %. We use the large bias pulsequantum-locking range to investigate one source of error in detail:the direct feedthrough of the current bias pulses into the DUT atVHF frequencies, which adds an unwanted, in-band componentto the measured voltage. We reduce this error by high-pass filter-ing the current bias pulses and measure the error as a functionof input pulse amplitude using two techniques: 1) by measuringsmall changes over the quantum-locking range and 2) by passivelyattenuating the input pulse amplitude so that the nonlinear JJsno longer generate voltage pulses while the error is only linearlyscaled.

This paper describes differential sampling measurements of an ac source and a Josephson arbitrary waveform synthesizer (JAWS). A new iterative approach for aligning the phases of the JAWS and the source waveforms was implemented to minimize the differential voltage at the digitizer. A type-A uncertainty of 45 nV/V after 10 min was measured for a commercial ac source at 1 V rms amplitude and 1 kHz.

This article examines the non-linearity and gain error of a commercial digitizer on the 100 mV range with a Josephson Arbitrary Waveform Synthesizer (JAWS) as a reference. Different digitizer input filter settings were studied, and the shortest aperture of the digitization window was chosen to maximize the processing speed. The results revealed a maximum non-linearity of 0.3 mu V on the 100 mV range with the digitizer filter frequency set to 100 kHz. A gain stability over 12 hours was determined to be 0.92 mu V/ V.

This article presents a superconducting voltage source that generates modulated microwave waveforms with quantum-based stability. The voltage source—an RF Josephson Arbitrary Waveform Synthesizer (RF-JAWS)—uses a superconducting IC with an array of 4500 series-connected Josephson junctions (JJs) that are embedded in a coplanar waveguide (CPW) transmission line. The JJs are driven with 100-ps wide current pulses that force each JJ to generate voltage pulses with a quantized integrated area. A pulse sequence is created using a delta-sigma ( $\Delta $ – $\Sigma $ ) algorithm to generate a 101-tone waveform with a 40-MHz instantaneous bandwidth around 1005 MHz with a flat power distribution of −53 dBm and a Schroeder phase distribution. The JJ's quantum-based nonlinearity produces an amplitude stability with respect to various drive and bias parameters of ±0.005 dB and a detrended phase stability of ±0.05°. The stability of the source is verified without the need for calibrated measurements. Another $\Delta $ – $\Sigma $ pulse sequence generates a 10-MHz quadrature-phase shift-keying (QPSK) waveform on a 1005-MHz carrier that has the same stability and the mean error vector magnitude (EVM) of −48 dB. This work is a step toward creating a quantum-based reference source for power and cross-frequency phase calibrations, as well as a reference-modulated signal source for calibrating telecommunication links.

Delta-sigma modulator algorithms determine the desired sequence of quantum-based voltage pulses used by the Josephson Arbitrary Waveform Synthesizer (JAWS) to create calculable, quantum-based voltage waveforms. We describe typical settings used for synthesizing JAWS audio-frequency waveforms and important additions to the pattern generation algorithm that improve the spectral purity of the JAWS waveforms.

The performance of programmable voltage signals that exploit the quantum behavior of superconducting Josephson junctions continues to improve and enhance measurements in metrology, communications, and quantum control. We review advances in pulse-driven digital synthesis techniques with Josephson-junction-based devices. Quantum-based synthesis of voltage waveforms has been demonstrated at frequencies up to 3 GHz and rms amplitudes up to 4 V. Josephson pulse generators have also been used to control and characterize superconducting qubits.

We demonstrate the use of a Josephson Arbitrary Waveform Synthesizer (JAWS) for linearity measurements of two instruments: an RF power sensor and a fast ADC. The VHF-JAWS source consists of a chip with 12,810 Josephson junctions located in a cryocooler and driven to produce quantum-based ac waveforms at frequencies up to 50.05 MHz and power up to -19 dBm. We first confirm that the device is operating correctly by measuring the dc bias current quantum-locking range and then measure the system output power with an RF power sensor and a high-speed digitizer. After removing an overall scale factor, the ten-nanowatt scale differences between the programmed JAWS values and the measured values indicate better than +/- 0.5 % DUT linearity for frequencies in the VHF band.

We demonstrate a sub-GHz resolution, fully programmable Fourier-domain pulse shaper capable of generating arbitrary optical pulse patterns for superconducting circuit platforms. This high resolution allows line-by-line pulse shaping of a 1 GHz-spaced comb, and the pulse shaper can accommodate an optical bandwidth as large as 1 THz, which represents the highest resolution programmable line-by-line pulse shaping to our knowledge. Linear optical sampling with a dual-comb system confirms independent control of 1 GHz-spaced optical lines, and the low phase noise of the pulse shaper is characterized. We apply the pulse shaper as an optical drive for an array of Josephson junctions operating at a temperature of 4 K, where cryogenic photodetection of pulse doublets with user-defined separation characterizes the Josephson junction response. Furthermore, we demonstrate a pulse-density modulation pattern of 4 ps duration optical pulses that can serve as the high bandwidth drive of a quantum-based Josephson arbitrary waveform synthesizer. By leveraging the exquisite control, large bandwidth, and low noise of photonics, this represents an important advance toward the realization of high power and high spectral purity AC voltage standards at gigahertz frequencies without requiring 100 GHz bandwidth driving electronics.

Superconducting optoelectronic hardware is being explored as a path towards artificial spiking neural networks with unprecedented scales of complexity and computational ability. Such hardware combines integrated-photonic components for few-photon, light-speed communication with superconducting circuits for fast, energy-efficient computation. Monolithic integration of superconducting and photonic devices is necessary for the scaling of this technology. In the present work, superconducting-nanowire single-photon detectors are monolithically integrated with Josephson junctions for the first time, enabling the realization of superconducting optoelectronic synapses. We present circuits that perform analog weighting and temporal leaky integration of single-photon presynaptic signals. Synaptic weighting is implemented in the electronic domain so that binary, single-photon communication can be maintained. Records of recent synaptic activity are locally stored as current in superconducting loops. Dendritic and neuronal nonlinearities are implemented with a second stage of Josephson circuitry. The hardware presents great design flexibility, with demonstrated synaptic time constants spanning four orders of magnitude (hundreds of nanoseconds to milliseconds). The synapses are responsive to presynaptic spike rates exceeding 10 MHz and consume approximately 33 aJ of dynamic power per synapse event before accounting for cooling. In addition to neuromorphic hardware, these circuits introduce new avenues towards realizing large-scale single-photon-detector arrays for diverse imaging, sensing, and quantum communication applications.

We demonstrate a decade-passband superconducting diplexer operating from dc to 27 GHz, integrated in a niobium, Josephson junction (JJ) compatible process. Both low-and high-pass branches of the diplexer are singly-terminated 5-pole Butterworth filters with a 2.5 GHz cutoff. Several diplexer test circuits were characterized with on-wafer cryogenic two-port calibration by terminating the third port of the device. Insertion loss below 0.8 dB are measured across the entire frequency range. Good agreement between measurements and simulations up to 27 GHz suggests that the upper diplexer band extends to the over-a-decade simulated 40 GHz. This device can be integrated in large-scale superconducting JJ-based quantum processors, broadband sensors, amplifiers and sources.

An array of Josephson junctions (JJs) was driven with photonically generated current pulses to synthesize a high-fidelity 1 kHz bipolar voltage waveform with a quantum-based amplitude that can be directly related to fundamental constants. A photodiode capable of producing high average photocurrent was used to generate large-amplitude current pulses that were ac-coupled to a JJ array. The resulting bipolar current pulses have enabled the first demonstration of quantum-based bipolar waveform synthesis with an optical drive. We measured the quantum locking range with respect to several operating parameters, including 1.2 mA with respect to a dc bias current applied to the array, confirming the robust synthesis of bipolar waveforms.

We present the design and characterization of a broadband RF Josephson arbitrary waveform synthesizer (RF-JAWS) with a series array of 4500 Josephson junctions (JJs) and integrated low-pass/high-pass five-pole superconducting diplexers. The integrated diplexers enable broadband filtering of the feedthrough signal components in the drive-current pulses with decade-wide instantaneous bandwidth. The diplexers have at least 30 GHz passband with less than 0.8 dB insertion loss. The JJ array is driven with a delta-sigma pulse sequence that encodes 10 kHz and 1.005 GHz tones, and generates an open-circuit voltage of 22 mV rms (−26.18 dBm available power assuming a 50 $\mathrm{\Omega }$ Thevenin equivalent source) at 1.005 GHz—a 25% increase compared to the state of the art. The drive current pulses undergo a three-step equalization to compensate for the linear distortion of the room-temperature electronics, the on-chip diplexers, and the remaining on- and off-chip components. The measured parasitic feedthrough voltages at 1.005 GHz are around −33 dBc, and their effect on the quantum locking ranges (QLRs) is quantified by measurements. The results demonstrated in this article show a significant step toward a broadband, integrated, quantum-based microwave voltage source with useful power above −30 dBm.

Superconducting optoelectronic hardware could be used to create large-scale and computationally powerful artificial spiking neural networks. The approach combines integrated photonic components that offer few-photon, light-speed communication with superconducting circuits that offer fast, energy-efficient computation. However, the monolithic integration of photonic and superconducting devices is needed to scale this technology. Here we report superconducting optoelectronic synapses that are created by monolithically integrating superconducting nanowire single-photon detectors with Josephson junctions. The circuits perform analogue weighting and the temporal leaky integration of single-photon presynaptic signals. Synaptic weighting is implemented in the electronic domain allowing binary, single-photon communication to be maintained. Records of recent synaptic activity are locally stored as current in superconducting loops, and dendritic and neuronal nonlinearities are implemented with a second stage of Josephson circuitry. This hardware offers synaptic time constants spanning four orders of magnitude (hundreds of nanoseconds to milliseconds). The synapses are responsive to presynaptic spike rates exceeding 10 MHz and consume approximately 33 aJ of dynamic power per synapse event before accounting for cooling. This demonstration also introduces new avenues for realizing large-scale single-photon detector arrays.

We construct cosmic microwave background lensing mass maps using data from the 2014 and 2015 seasons of observations with the Atacama Cosmology Telescope (ACT). These maps cover 2100 square degrees of sky and overlap with a wide variety of optical surveys. The maps are signal dominated on large scales and have fidelity such that their correlation with the cosmic infrared background is clearly visible by eye. We also create lensing maps with thermal Sunyaev-Zel'dovich contamination removed using a novel cleaning procedure that only slightly degrades the lensing signal-to-noise ratio. The cross-spectrum between the cleaned lensing map and the BOSS CMASS galaxy sample is detected at 10 sigma significance, with an amplitude of A = 1.02 +/- 0.10 relative to the Planck best-fitting Lambda cold dark matter cosmological model with fiducial linear galaxy bias. Our measurement lays the foundation for lensing cross-correlation science with current ACT data and beyond.