Josephson Arbitrary Waveform Synthesizer Research Articles

Nb/a-Si/Nb-junction Josephson arbitrary waveform synthesizers for quantum information.

We demonstrate Josephson arbitrary waveform synthesizers (JAWS) with increased operating temperature range for temperatures below 4 K. These JAWS synthesizers were fabricated with externally-shunted Nb/a-Si/Nb junctions whose critical current exhibits improved temperature stability compared to the self-shunted Nb/Nb0.15Si0.85/Nb junctions typically used. Vertical stud resistors made of 230 nm of PdAu were developed to provide the milliohm shunt resistance required for junction overdamping while maintaining a small footprint suitable for high-density series arrays embedded in a coplanar waveguide. We evaluated the performance of these resistors from 3.8 K down to 20 mK. We designed, fabricated and tested a JAWS circuit with 4650 externally shunted Nb/a-Si/Nb JJs with a critical current density () of 0.12 and critical current () of 3 mA. This circuit was designed to be mounted to the 3 K stage of a dilution refrigerator and used to control and calibrate a qubit mounted at the 10 mK stage. To increase the circuit density of the JAWS circuits we made arrays of two-junction vertical stacks. Current-voltage () curves of this JAWS circuit with stacked junctions under microwave excitation show Shapiro steps with quantum-locking ranges similar to those of JAWS circuits used for qubit control.

Sub-GHz resolution line-by-line pulse shaper for driving superconducting circuits

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.

Bipolar Waveform Synthesis With an Optically Driven Josephson Arbitrary Waveform Synthesizer

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.

RF Josephson Arbitrary Waveform Synthesizer With Integrated Superconducting Diplexers

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{\Omega }$</tex-math></inline-formula> 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.

A Microwave Quantum-Defined Millivolt Source

We demonstrate a tenfold increase in the amplitude of microwave-frequency waveforms generated by a quantum-defined superconducting voltage source, with an open-circuit signal of 17.56 mV rms at 1.005 GHz. The voltage source is an RF Josephson arbitrary waveform synthesizer (RF-JAWS) that utilizes a circuit that is cooled to 4 K and is composed of an array of 4500 Josephson junctions. These junctions are connected in series along the center conductor of a 50- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> superconducting coplanar waveguide transmission line. We introduce a new zero-forcing equalization technique for reducing distortion in drive current pulse patterns. This technique allows an increase in the amplitude of the quantum-based voltage waveforms while suppressing parasitic feedthrough signals to −75 dBc. Synthesizing a two-tone delta–sigma waveform, we monitor an audio-frequency 10-kHz tone of less than 100- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{V}$ </tex-math></inline-formula> rms amplitude while simultaneously measuring the 1.005-GHz tone of −28.12-dBm power in a 50- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> environment. The two-tone synthesis allows simultaneous verification of correct operation of the voltage source using time-efficient low-frequency measurement techniques as well as slower microwave measurements.

Cryogenic Characterization of a Superconductor Quantum-Based Microwave Reference Source for Communications and Quantum Information

We are developing a new instrument, the RF Josephson arbitrary waveform synthesizer (RF-JAWS), for communications metrology and quantum information applications. An important aspect of the RF-JAWS design is the accurate and traceable characterization of its superconducting devices. In this article, we present a procedure for characterizing microwave superconducting devices in a cryogenic RF probe station via a vector network analyzer (VNA) calibrated with a custom cryogenic calibration kit colocated with the superconducting device under test (DUT) in the cryogenic environment. By de-embedding lossy and dispersive RF interconnects linking the superconducting DUT to the measurement apparatus at room temperature, we characterize the DUT exactly at the cryogenic on-wafer reference plane. More importantly, we operate our VNA with an external modulated source and our procedure features metrology-grade multiline thru-reflect-line calibration and absolute power and phase corrections, as opposed to the more common relative scattering-parameter correction. In addition, we apply an X -parameter model to account for impedance mismatch in cryogenic Josephson microwave sources. Our techniques are also suitable for cryogenic characterization of microwave superconducting devices for solid-state quantum computers and could help to optimize the quantum-classical interfaces in these systems.

Calibration of the dual-mode auto-calibrating resistance thermometer with few-parts-per-million uncertainty

The dual-mode auto-calibrating resistance thermometer (DART) has recently been proposed for highly accurate temperature measurement based on noise thermometry. In this paper, it is demonstrated that calibration and operation of the DART at part-per-million (ppm) level should be possible with the hardware developed. For this purpose, we have extensively tested a representative signal path comprising the basic DART components. This includes a low-noise amplifier connected to a 24-bit ADC and a metrology-grade voltage reference. A Josephson arbitrary waveform synthesizer (JAWS) generates a pseudo-noise consisting of low-distortion multitones superimposed on a low-frequency square-wave reference voltage. Using this signal, a fast and efficient calibration scheme for the signal path gain is demonstrated. The reference voltage stabilizes the gain at ppm level. We observed gain fluctuations within over a period of 19 d, a temperature coefficient of , and insignificant nonlinearity within an uncertainty band of for rms input levels between 5 µV and 80 µV. The behavior of the signal path with a 300 Ω resistor as a noise source was also investigated. From the observed stability of the voltage reference and flatness of the noise gain between 10 kHz and 225 kHz, we estimate that the presented hardware components are suitable for temperature measurements with systematic uncertainties well below .

Driving a low critical current Josephson junction array with a mode-locked laser

We report proof-of-concept experiments on an optically driven Josephson voltage standard based on a mode-locked laser (MLL), a time-division multiplexer, and a cryogenic ultrafast photodiode driving an overdamped Josephson junction array (JJA). Our optical pulse pattern generator (PPG) concept builds on the capability of MLLs to produce trains of picosecond-wide optical pulses with little amplitude and temporal spread. Our present setup enables multiplication of the original 2.3 GHz pulse repetition frequency by a factor of 8. A commercial photodiode converts the optical pulses into about 25 ps wide electrical pulses in liquid helium several cm from the JJA. Using a custom-made MLL, we can drive a JJA with a low critical current of 360 μA at multiple Shapiro steps. We have performed experiments with pulse pairs whose time interval can be set freely without distorting the shapes of individual pulses. Experimental results are in qualitative agreement with theoretical simulations, and they demonstrate, e.g., crossover in the Shapiro step pattern when the time interval between the pulses is approximately equal to the inverse of the characteristic frequency of the JJA. However, there are quantitative discrepancies, which motivate an improved integration of photodiodes and JJAs to improve both the understanding and fidelity of Josephson Arbitrary Waveform Synthesizers. Considering future quantum technologies in a wider perspective, our optical approach is a potential enabler for fast and energy-efficient pulse drive without an expensive high-bandwidth electrical PPG and without high-bandwidth electrical cables that yield too high thermal conductance between cryogenic and room temperatures.

Linearity measurements of critical Johnson noise thermometer components with low-distortion multitones from a Josephson arbitrary waveform synthesizer

Quantum-based and low-distortion multitone signals from a Josephson arbitrary waveform synthesizer are used to calibrate critical noise thermometer components between 8 and 240 kHz at increased input noise levels. The example signal path includes a 24-bit ΣΔ analog-to-digital converter (ADC) and a prototype amplifier for Physikalisch-Technische Bundesanstalt’s new noise thermometer. The signals consist of odd harmonics of the pattern repetition frequency with growing tone spacing, minimizing the influence of intermodulation distortion during calibration. After a detailed description of the calibration procedure, we compare the multitone spectra with growing tone spacing to ones with equally spaced tones. For the example signal path, gain nonlinearities better than ±2 µV V−1 at input rms noise levels between 9.7 and 465 µV are experimentally demonstrated. Furthermore, we investigate the effect of dither and applied offset voltage on the non-linearity of the ADC.

Stacked Josephson Junction Arrays for the Pulse-Driven AC Josephson Voltage Standard

We developed a fabrication process to establish large arrays of up to 5-stacked Josephson junctions for the Josephson Arbitrary Waveform Synthesizer (JAWS). SNS-type Josephson junctions with Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> barriers are used for this application. By modifying our standard window process, e.g. to add a CMP (chemical mechanical polishing) and an ALD (atomic layer deposition) step, the yield of this process was increased. An output voltage of 1 V RMS could be achieved by using 4 JAWS arrays in series with a total number of 60,000 5-stacked junctions. The investigation of the current-voltage characteristics (IVC) showed an interesting and potentially useful feature. The required pulse amplitude per junction for getting the maximum Shapiro step width reduces for higher junction stacks. We found that the pulse power linearly reduces with the square of the junction number in the array. The origin of this effect might be a strong neighbour-neighbour interaction of the junctions, which are closely arranged within the stacked configuration. This might generate a strong self-synchronization of the junctions.

Investigation of Broadband Wilkinson Power Dividers for Pulse-Driven Josephson Voltage Standards

This paper describes recent developments for increasing the output voltage of the Josephson Arbitrary Waveform Synthesizer (JAWS) at PTB. For this purpose, we developed modified broadband Wilkinson power dividers, which enable the operation of two or four Josephson junction series arrays per RF channel of the pulse pattern generator and thus the generation of increased output voltages. In detail, we designed and investigated two different Wilkinson power dividers: the one-stage three-section Wilkinson power divider with extended bandwidth and the two-stage single-section Wilkinson divider with more outputs to combine four parallel series arrays. They were both integrated with triple-stacked Josephson junction series arrays. Additionally, a new modulator pulse amplifier was introduced into the JAWS set-up to provide sufficient power for all the junction arrays. Our measurement results show that spectrally pure sinusoidal waveforms were successfully generated with both types of power dividers. With the one-stage three-section Wilkinson power divider, we obtained RMS voltages of nearly 53 mV at a clock-frequency of 15 GHz combined with a test array of 3000 Josephson junctions. As for the two-stage single-section Wilkinson power divider combined with a test array of 6000 Josephson junctions, we synthesized RMS output voltages of about 105 mV. These test results show a promising prospect for quantum voltage standard applications.

Evaluation of a Josephson Arbitrary Waveform Synthesizer at Low Voltages for the Calibration of Lock-In Amplifiers.

We have evaluated a Josephson arbitrary waveform synthesizer (JAWS) in the voltage range from 1 μV to 1 mV at frequencies from 60 to 1000 Hz for the use in the calibration of lock-in amplifiers. The uncertainty contribution from the JAWS system is 45 nV for 1 mV at 1000 Hz and k = 2.0. We anticipate that the JAWS will help extend the lower voltage and frequency range of ac voltage metrology and improve the uncertainties by one order of magnitude compared to conventional techniques.

Comparison of AC Power Referenced to Either PJVS or JAWS

The results of a comparison on active power meter calibrations at the National Institute of Standards and Technology (NIST) using a source of ac power referenced to either a programmable Josephson voltage standard (PJVS) or a Josephson arbitrary waveform synthesizer (JAWS) is presented. The measurements were made at 60 V rms, 5 A rms, and 50 Hz at a power factor of 1.0. The estimated uncertainty of the active power applied to a meter under test (MUT) of the two system configurations is within $2~\mu \text{W}$ /VA ( $k = 1$ ), and the comparison results demonstrate that the two system configurations agree to within 1 part in $10^{6}$ for applied voltage, current, and phase. A discussion of the measurement techniques and major sources of error is given for applied power signals over the 50-Hz–6-kHz frequency range.

Dual Josephson impedance bridge: towards a universal bridge for impedance metrology

This paper presents a full characterization of a Dual Josephson Impedance Bridge (DJIB) at frequencies up to 80 kHz by using the DJIB to compare the best available impedance standards that are (a) directly traceable to the quantum Hall effect, (b) used as part of international impedance comparisons, or (c) believed to have calculable frequency dependence. The heart of the system is a dual Josephson Arbitrary Waveform Synthesizer (JAWS) source that offers unprecedented flexibility in high-precision impedance measurements. The JAWS sources allow a single bridge to compare impedances with arbitrary ratios and phase angles in the complex plane. The uncertainty budget shows that both the traditional METAS bridges and the DJIB have comparable uncertainties in the kilohertz range. This shows that the advantages of the DJIB, including the flexibility which allows the comparison of arbitrary impedances, the wide frequency range and the automated balancing procedure, are obtained without compromising the measurement uncertainties. These results demonstrate that this type of instrument can considerably simplify the realization and maintenance of the various impedance scales. In addition, the DJIB is a very sensitive tool for investigating the frequency-dependent systematic-errors that can occur in impedance construction and in the voltage provided by the JAWS source at frequencies greater than 10 kHz.

Measurement and analysis of high-frequency voltage errors in the Josephson arbitrary waveform synthesizer

This paper reports on the comparison of two Josephson arbitrary waveform synthesizers for frequencies up to 500 kHz. Both independent pulse-driven Josephson arrays produce a 10 mV RMS sinusoidal voltage. They are alternately connected to an analog-to-digital converter which serves as a transfer standard. The setup is capable to of synthesizing quantum-based waveforms using two different pulse-bias techniques. We use the Zero-Compensation method and a two-pole high-pass filter structure in the pulse-bias configuration of one system (the reference) to minimize the amplitude error for signal frequencies up to 500 kHz. Consequently, we are able to directly detect the high-frequency voltage errors in the other system (the device under test). The setup is used to measure differences between both systems, and the influence of parameter variation on the results with Type A uncertainties of 0.4 µV/V (k = 1) in measurement times of 60 s. We find that the dominant sources of deviations above 10 kHz can be traced to the influence of the output cabling and the pulse bias on the synthesized voltage signal. Our analysis explains the origin and the reduction of these high-frequency voltage errors.

Development of RF Power Dividers for the Josephson Arbitrary Waveform Synthesizer

To make the experimental setup of the Josephson arbitrary waveform synthesizer less complex by reducing the number of RF cables between room and cryogenic temperature, we developed on-chip RF power dividers. By integration of these components, we can eventually increase the number of Josephson junctions operated by one single pulse-pattern generator channel, and thus reduce the costs of the setup. At Physikalisch-Technische Bundesanstalt, we designed, fabricated, and investigated the performance of two different RF power dividers types: the serial–parallel and the Wilkinson power divider. Spectrally pure sinusoidal waveforms were successfully synthesized with both types of power dividers. With the Wilkinson power divider, we obtained 17.55 mV (rms) at a clock frequency of 15 GHz combined with a test array of 1000 Josephson junctions. As for the serial–parallel power divider combined with a test array of 2000 Josephson junctions, we synthesized rms output voltages of 19.0 mV.

Load compensation bridge for Josephson arbitrary waveform synthesizers

The Josephson arbitrary waveform synthesizer is a quantum-based voltage source that can generate arbitrary waveforms with quantum accuracy. However, these state-of-the-art performances are drastically decreased by the wiring connecting the source to the device under test. This wiring introduces deviations from the Josephson voltage which scale quadratically with frequency.This paper describes a load compensation bridge that fully compensates the load of the Josephson arbitrary waveform synthesizer by the input impedance of the device under test and completely suppresses the frequency dependence up to a frequency of 80 kHz with an overall uncertainty of 2.8 V V−1.

Josephson Microwave Sources Applied to Quantum Information Systems

Quantum computers with thousands or millions of qubits will require a scalable solution for qubit control and readout electronics. Colocating these electronics at millikelvin temperatures has been proposed and demonstrated, but there exist significant challenges with power dissipation, reproducibility, fidelity, and scalability. In this article, we experimentally demonstrate the use of a Josephson arbitrary waveform synthesizer (JAWS) to generate control signals at 4 K and perform spectroscopy of two components of a typical superconducting quantum information system: a linear resonator and a (nonlinear) transmon qubit. By locating the JAWS chip at 4 K and a qubit at 0.1 K, the direct path for quasi-particle poisoning from the JAWS chip to the qubit is broken. We demonstrate the stable, self-calibrated, and reproducible output signal of the JAWS when operated in its quantum locking range, a feature that allows these synthesizers to be replicated and scaled in the cryostat, all with identical on-chip, quantized, outputs. This is a proof-of-concept demonstration to generate signals at 4 K using driven superconducting electronics to control qubits at lower temperatures.

RF Waveform Synthesizers With Quantum-Based Voltage Accuracy for Communications Metrology

We review our development of Josephson-junction-based programmable reference sources to synthesize spectrally pure waveforms with quantum-based voltage accuracy for characterizing and improving future communication devices and systems. The goal is to provide sources that together span the entire radio frequency band, equivalent to seven orders of magnitude in frequency (20 kHz to 300 GHz). To synthesize waveforms in the microwave frequency band, we are extending the existing Josephson arbitrary waveform synthesizer (JAWS) technology used for ac voltage metrology at audio frequencies (<;20 kHz). Using new microwave circuits and experimental techniques, we demonstrate JAWS-based synthesis of single-tone waveforms at 1 GHz, with -49 dBm output power and 79 dBc spur-free dynamic range (SFDR). To synthesize waveforms in the millimeter-wave frequency band, we are exploiting single flux quantum (SFQ) superconducting digital technology to design circuits that amplify SFQ pulses using a network of pulse splitters. With our initial SFQ-based circuit, we demonstrate synthesis of a 4-GHz sine wave with -74 dBm output power and 70 dBc SFDR.

Optical Pulse-Drive for the Pulse-Driven AC Josephson Voltage Standard

We developed an optical pulse-drive for the operation of the Josephson Arbitrary Waveform Synthesizer (JAWS) using a fast photodiode (PD) operated at 4 K, close to the JAWS chip. The optical pulses are transmitted to the PD by an easily removable optical fiber attached to it. A bare-lensed PD is mounted by flip-chip technique to a custom-made silicon-carrier chip. This carrier chip is equipped with coplanar waveguides to transmit the electrical pulses from the PD to the JAWS chip mounted on a separate printed circtuit board (PCB). The main components of this optical setup are a laser source, a high-speed Mach–Zehnder modulator, and the modulator driver. The waveform pattern is supplied by a commercial pulse pattern generator providing up to 15 GHz electrical return-to-zero (RTZ)-pulses. Unipolar sinusoidal waveforms were synthesized. Using a JAWS array with 3000 junctions, an effective output voltage of 6.6 mV root mean square (RMS) at the maximum available clock-frequency of 15 GHz was achieved. Higher harmonics were suppressed by more than 90 dBc at laser-bias operation margins of more than 1 mA.