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Superconductor Science and Technology

Four-quadrant flux quanta counting for wide-range SQUID amplifiers

M. Kiviranta, Nikolai Beev

Published Jun 5, 2014• 5 citations
Publisher

Abstract

We have studied flux quanta counting in an open loop as a way to implement superconducting quantum interference device (SQUID) amplifiers with a large dynamic range and small power dissipation simultaneously. Good signal-to-noise ratio at all flux values is provided by using two SQUIDs, one yielding sin(ϕ) and the other cos(ϕ) proportional signals. In principle, the lack of feedback lifts the slew rate limitation due to the loop causality present in previously implemented flux quanta counters. Experimental results are shown for up to 180 Φ0 peak-to-peak flux ranges with a 1.5 μΦ0 Hz−1/2 noise floor, dominated by the digitizer noise. The SQUID and low-noise amplifier would allow a 0.07 μΦ0 Hz−1/2 noise floor with a more silent digitizer. Operation up to a 13 Φ0 μs−1 slew rate was demonstrated, but this is not a fundamental limitation. In our experiment, the mismatch between the sin(ϕ) and cos(ϕ) channels limited the practically achievable slew rate.

DOI
10.1088/0953-2048/27/7/075005

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We have studied flux quanta counting in an open loop as a way to implement superconducting quantum interference device (SQUID) amplifiers with a large dynamic range and small power dissipation simultaneously. Good signal-to-noise ratio at all flux values is provided by using two SQUIDs, one yielding sin(ϕ) and the other cos(ϕ) proportional signals. In principle, the lack of feedback lifts the slew rate limitation due to the loop causality present in previously implemented flux quanta counters. Experimental results are shown for up to 180 Φ0 peak-to-peak flux ranges with a 1.5 μΦ0 Hz−1/2 noise floor, dominated by the digitizer noise. The SQUID and low-noise amplifier would allow a 0.07 μΦ0 Hz−1/2 noise floor with a more silent digitizer. Operation up to a 13 Φ0 μs−1 slew rate was demonstrated, but this is not a fundamental limitation. In our experiment, the mismatch between the sin(ϕ) and cos(ϕ) channels limited the practically achievable slew rate.
User-friendly ultra-high-speed readout electronics for dc superconducting quantum interference devices (SQUIDs) are presented. To maximize the system bandwidth, the SQUID is directly read out without flux modulation. A composite preamplifier is used consisting of a slow dc amplifier in parallel with a fast ac amplifier. In this way, excellent dc precision and a high amplifier bandwidth of 50 MHz are achieved, simultaneously. A virtual 50 Ω amplifier input resistance with negligible excess noise is realized by active shunting, i.e., by applying feedback from preamplifier output to input via a high resistance. The white voltage and current noise levels are 0.33 nV Hz −1 and 2.6 pA Hz −1/2 , respectively. The electronics is fully computer controlled via a microcontroller integrated into the flux-locked loop (FLL) board. Easy-to-use software makes the various electronic settings accessible. A wide bias voltage range of 1.3 mV enables the readout of series SQUID arrays. Furthermore, additional current sources allow the operation of two-stage SQUIDs or transition edge sensors. The electronics was tested using various SQUIDs with input inductances between 30 nH and 1.5 µH. Typically, the maximum FLL bandwidth was 20 MHz, which is close to the theoretical limit given by transmission line delay within the FLL. Slew rates of up to 4.6 Φ 0 µs −1 were achieved with series SQUID arrays. Current noise levels as low as 0.47 pA Hz −1/2 and coupled energy sensitivities between 90 h and 500 h were measured at 4.2 K, where h is the Planck constant. The noise did not degrade when the system bandwidth was increased to the maximum value of about 20 MHz. With a two-stage set-up, intrinsic white energy sensitivities of 30 h and 2.3 h were measured at 4.2 and 0.3 K, respectively.
Digital superconducting quantum interference devices (SQUIDs) based on single-flux quantum (SFQ) logic have attractive characteristics such as wide dynamic ranges and high slew rates. However, the resolution of a typical digital SQUID is limited by SFQ feedback. To realize lower magnetic field noise by magnetometers using digital SQUIDs, we have adopted two feedback combinations: one, utilizing the SFQ input/output for a main loop and the other, using a mutually coupled loop. The main loop receives direct Φ0feedback and subflux quantum feedback Φ0/n, where n is an integer from the mutually coupled loop. The flux resolution for the digital SQUID shows improvement with increasing n and reaches below 40 mΦ0at n = 210; however, the slew rate decreases with increasing n and reaches 1.22 × 106Φ0/s at fc= 1.25 GHz and n = 210. For a magnetometer using a digital SQUID with a pickup loop, we confirmed a magnetic field noise of less than 100 fT/√Hz with a signal bandwidth of 1 MHz for operation frequency fcof 20 GHz.
Measurements of extremely weak magnetic fields in unshielded environments require sensors providing a high dynamic range and slew rate while maintaining a high resolution. At present, analog Superconducting Quantum Interference Devices (SQUIDs) are the most sensitive sensors for magnetic flux. Due to their room-temperature feedback electronics necessary to maintain a stable point of operation, slew rates of those sensors are limited. The dynamic range is usually restricted by the resolution of classical analog to digital converters. The digital SQUID follows a different approach: a change of the magnetic field penetrating the pickup loop is translated by the sensor into a stream of voltage pulses. Each pulse represents the change of the magnetic flux inside the pickup loop by one flux quantum Φ0. By fast counting of these flux quanta, it is possible to outperform the analog SQUID in terms of dynamic range and maximum slew rate. We present our latest results with respect to the internal mechanisms of the digital SQUID and present a method to compensate the main source for nonlinear behavior of the sensor. The analyzed circuit was fabricated by FLUXONICS Foundry (1) in a 1 kA/cm² niobium fabrication process.
Digital SQUIDs based on the single flux quantum (SFQ) logic have attractive characteristics, such as wide dynamic range and high slew rate. However, the resolution of digital SQUIDs is limited to SFQ. To realize sub-flux quantum resolution for these SQUIDs, we have adopted two types of feedback combinations: one with the SFQ input/output for a main loop and the other with a mutually coupled loop. The main loop receives direct Φ0feedback and sub-flux quantum feedback Φ0/n, where n is an integer, from the mutually coupled loop. We confirmed the correct operation of our device at a clock frequency of 1.25 GHz for a digital SQUID with a sub-Φ0flux feedback resolution of Φ0/8 from circuit simulation. The slew rate is found to be 1.56×108Φ0/s in this simulation (fc=1.25 GHz, n=8). The flux resolution for the digital SQUID shows improvement with increasing n and reached below 40 mΦ0with n=210; however the slew rate is decreased with increasing n and reached 1.22×106Φ0/swith fc=1.25 GHz and n=210.
We have fabricated and tested thin film, niobium edge junction, double transformer, dc superconducting quantum interference devices (SQUID’s) that were stable under room-temperature storage and thermal cycling and that had very good noise performance. The input inductance, approximately 1.7 μH, was large enough to facilitate good matching to many experiments. When the SQUID was operated as a small-signal amplifier, the minimum detectable energy per unit bandwidth (Se) was 5×10−33 J/Hz at 100 kHz, referred to the SQUID loop (uncoupled). The minimum detectable energy per unit bandwidth was 1.8×10−31 J/Hz at 100 kHz, referred to the input coil. The SQUID’s had good characteristics for flux-locked operation since the small signal Se was low over a substantial range of bias current and magnetic flux. For operation in a flux-locked feedback circuit, Se was 6×10−32 J/Hz at 1 kHz.
A digital double relaxation oscillation (DROS) superconducting quantum interference device (SQUID) has the potential for a very large dynamic range and a slew rate that is orders of magnitude larger than that of conventional SQUID systems. This is, for example, advantageous when using the SQUID in an unshielded environment. An important characteristic of the digital DROS is that the feedback flux is quantized since this flux is supplied by a superconducting up-down counter. Together with the clock frequency, the quantization unit of the feedback flux determines the maximum slew rate. In an optimized design, the quantization unit is adapted to the broadband flux noise of the DROS, so that the slew rate is maximized without compromising the sensitivity. Simulations on our optimized digital DROS showed proper operation for slew rates up to 5×10 6 Φ 0 s -1 . The relaxation oscillations generated at a frequency of 100 MHz deliver an on-chip clock signal, so that no external clock is required. Slew rates up to 10 8 Φ 0 s -1 can be achieved by increasing the relaxation oscillation frequency to a few GHz. This means that sub-µm 2 Josephson junctions with high critical current densities are required. The first experiments using low- T c ramp-type Josephson junctions are presented in this paper.