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IEEE Transactions on Applied Superconductivity

Nb/a-Si/Nb-Junction Josephson Arbitrary Waveform Synthesizers for Quantum Information

David I. Olaya, John Biesecker, Manuel A. Castellanos-Beltran, Adam J. Sirois, Logan A. Howe, Paul D. Dresselhaus, Samuel P. Benz, P. F. Hopkins

Published Feb 24, 2023• 6 citations
Publisher

Abstract

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/$\boldsymbol{a}$-Si/Nb junctions whose critical current exhibits improved temperature stability compared to the self-shunted Nb/Nb$\boldsymbol{ _{0.15} }$Si$\boldsymbol{ _{0.85} }$/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/$\boldsymbol{a}$-Si/Nb JJs with a critical current density ($\boldsymbol{J}_{\mathbf{c}}$) of 0.12 mA/$\boldsymbol{\mu }$m$\boldsymbol{^{2}}$and critical current ($\boldsymbol{I}_{\mathbf{c}}$) 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 (I-V) 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.

DOI
10.1109/tasc.2023.3249141

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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\boldsymbol{a}a-Si/Nb junctions whose critical current exhibits improved temperature stability compared to the self-shunted Nb/Nb0.15\boldsymbol{ _{0.15} }0.15​Si0.85\boldsymbol{ _{0.85} }0.85​/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\boldsymbol{a}a-Si/Nb JJs with a critical current density (Jc\boldsymbol{J}_{\mathbf{c}}Jc​) of 0.12 mA/μ\boldsymbol{\mu }μm2\boldsymbol{^{2}}2and critical current (Ic\boldsymbol{I}_{\mathbf{c}}Ic​) 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 (I-V) 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.
This paper describes the status of developing Josephson arbitrary waveform synthesizer (JAWS) chips at NIM (National Institute of Metrology, China). To obtain high junction integration density and fewer data input channels, the chip employs an on-chip Wilkinson power divider and inside/outside dc blocks, enabling both arrays to be driven by a single pulse-generator channel. In addition, the tapered coplanar waveguide structure is used to ensure the microwave uniformity of the long-junction array. Each array consisted of 4000 double-stack Nb/NbxSi1−x/Nb junctions, and 16,000 junctions are integrated in the chip in total. The JAWS chip demonstrates good performance, capable of synthesizing a 300 mV root mean square (rms) voltage with exceptionally low harmonic distortion. Dc and ac voltage-current characteristics measurements indicate that the junctions are with a critical current of 2.5 mA, and a normal-state resistance of 4.5 mΩ per junction. Contact aligners are manually operated to fabricate the chips, and process errors in the fabrication are estimated in this paper.
We report on the design, fabrication, and measurement of a very high frequency band Josephson arbitrary waveform synthesizer (VHF-JAWS) at frequencies from 1 kHz to 50.05 MHz. The VHF-JAWS chip is composed of a series array of 12 810 Josephson junctions (JJs) embedded in a superconducting coplanar waveguide. Each JJ responds to a pattern of current pulses by creating a corresponding pattern of voltage pulses, each with a time-integrated area related to fundamental constants ash/2e{{h/2e}}h/2e. The pulse patterns are chosen to produce quantum-based single-tone voltage waveforms with an open-circuit voltage of 50 mV rms (–19.03 dBm output power into 50Ω\OmegaΩload impedances) at frequencies up to 50.05 MHz, which is more than twice the voltage that has been generated by previous RF-JAWS designs at 1 GHz. The VHF-JAWS is “quantum-locked,” that is, it generates one quantized output voltage pulse per input current pulse per JJ while varying the dc current through the JJ array by at least 0.4 mA and the amplitude of the bias pulses by at least 10 %. We use the large bias pulse quantum-locking range to investigate one source of error in detail: the direct feedthrough of the current bias pulses into the DUT at VHF frequencies, which adds an unwanted, in-band component to the measured voltage. We reduce this error by high-pass filtering the current bias pulses and measure the error as a function of input pulse amplitude using two techniques: 1) by measuring small changes over the quantum-locking range and 2) by passively attenuating the input pulse amplitude so that the nonlinear JJs no longer generate voltage pulses while the error is only linearly scaled.
We employ externally shunted Nb-AlOx_xx​-Nb Josephson junctions for demonstrating a circuit that is suitable for an optically driven Josephson Arbitrary Waveform Synthesizer (JAWS). This technology enables overdamped junctions with characteristic frequencies above 100 GHz and critical currents of the order of 100 μμμA, which is promising, e.g., for low-dissipation optical control of quantum circuits such as superconducting quantum bits. Here we utilize a double-pulse technique to experimentally determine the maximum rate at which optical pulse data can be reliably delivered to the superconducting circuit. We demonstrate the feasibility of data transfer up to 60 Gbit/s, which is about factor 4 higher than for typical JAWS.
The PTB Josephson Arbitrary Waveform Synthesizer (JAWS) enables the generation of arbitrary waveforms up to voltages of 70 mVRMS (199 mVPP) using two Josephson arrays in series containing 4000 Josephson junctions each. The SNS-like double-stacked junctions are based on NbxSi1-x as barrier material. While the JAWS system is typically operated using a Dewar with liquid helium, the operation in a closed-cycle pulse-tube cryocooler at temperatures around 4.2 K range was here investigated and successfully demonstrated. For this purpose a special designed cryoprobe was used to provide high quality pulses to the Josephson arrays.
The output voltage of Josephson arbitrary waveform synthesizers (JAWS) is limited by the number of Josephson junctions (JJs) that can be driven by a single pulse-generator channel. Here, we double the number of JJs driven by one generator channel to 51 200 JJs by distributing the pulse bias between four JJ arrays by use of two layers of Wilkinson dividers. We use this single bias to generate a voltage at 1 kHz with an rms magnitude of 1 V. This voltage is quantum-accurate over an operating current range of 1.4 mA. For comparison, the operating current range of a recent design that uses a single layer of Wilkinson dividers is twice as large, but requires two pulse-bias channels to generate 1 V. We also show that we can recover this performance by incorporating in the pulse generator a finite-impulse response (FIR) filter that acts as an equalizer. The FIR filter creates a custom transfer function that compensates for the bandwidth-limited transfer function of the Wilkinson dividers. Optimizing the FIR filter parameters increases the operating current range from 1.4 to 2.7 mA. This ability to drive additional JJ arrays with a single pulse-generator channel will enable future JAWS chips and systems to achieve significantly larger output voltages. This will increase the voltage range for JAWS calibrations of ac thermal converters and improve precision voltage measurements that require quantum-accurate, stable, and distortion-free waveforms with a large signal-to-noise ratio.