Flux-ramp Modulation Research Articles

Online Demodulation and Trigger for Flux-ramp Modulated SQUID Signals

Due to the periodic characteristics of SQUIDs, a suitable linearization technique is required for SQUID-based readout. Flux-ramp modulation is a common linearization technique and is typically applied for the readout of a microwave SQUID multiplexer as well as since recently also for dc-SQUIDs. Flux-ramp modulation requires another stage in the signal processing chain to demodulate the SQUID output signal before further processing. For cryogenic microcalorimeters, the signal contains events that are given by a fast exponentially rising and slowly exponentially decaying pulses shape. The events shall be detected by a trigger engine and recorded by a storage logic. Since the data rate can be decreased significantly by demodulation and event detection, it is desirable to do both steps on the deployed fast FPGA logic during measurement before passing the data to a general-purpose processor. In this contribution, we show the implementation of efficient multi-channel flux-ramp demodulation computed at run-time on a SoC-FPGA. Furthermore, a concept and implementation for an online trigger and buffer mechanism with its theoretical trigger loss rates depending on buffer size is presented. Both FPGA modules can be operated with up to 500 MHz clock frequency and can efficiently process 32 channels. Correct functionality and data reduction capability of the modules are demonstrated in measurements utilizing magnetic microcalorimeter irradiated with an Iron-55 source for event generation and read out by a microwave SQUID multiplexer.

Flux ramp modulation based hybrid microwave SQUID multiplexer

We present a hybrid microwave superconducting quantum interference device (SQUID) multiplexer that combines two frequency-division multiplexing techniques to allow multiplexing a given number of cryogenic detectors with only a fraction of frequency encoding resonators. Similar to conventional microwave SQUID multiplexing, our multiplexer relies on inductively coupling non-hysteretic, unshunted rf-SQUIDs to superconducting microwave resonators as well as applying flux ramp modulation for output signal linearization. However, instead of utilizing one resonator per SQUID, we couple multiple SQUIDs to a common readout resonator and encode the SQUID input signals in sidebands of the microwave carrier by varying the flux ramp modulation frequency for each SQUID. We prove the suitability of our approach using a prototype device and argue by means of fundamental information theory that our approach is particularly suited for reading out large cryogenic bolometer arrays.

Flux ramp modulation based MHz frequency-division dc-SQUID multiplexer

We present a MHz frequency-division direct-current superconducting quantum interference device (dc-SQUID) multiplexer that is based on flux ramp modulation and a series array of N identical current-sensing dc-SQUIDs with tightly coupled input coil. By running a periodic, sawtooth-shaped current signal through additional modulation coils being tightly but non-uniformly coupled to the individual SQUIDs, the voltage drop across the array changes according to the sum of the flux-to-voltage characteristics of the individual SQUIDs within each cycle of the modulation signal. In this mode of operation, an input signal injected in the input coil of one of the SQUIDs and being quasi-static within a time frame adds a constant flux offset and leads to a phase shift of the associated SQUID characteristics. The latter is proportional to the input signal and can be inferred by channelizing and down-converting the sampled array output voltage. Using a prototype multiplexer as well as custom readout electronics, we demonstrate the simultaneous readout of four signal sources with MHz bandwidth per channel.

Readout of Energy Pulses on Microwave SQUID Multiplexer: A Sensor Array-Based Approach

Suitable techniques for reading out large arrays of metallic magnetic calorimeters are very challenging and demand optimal performance in each system stage to preserve intrinsic fast signal rise time, excellent energy resolution, large energy dynamic range, and highly linear detector response. A multiplexer based on superconducting quantum interference device is the key component in achieving this goal. Linearity of the response requires a technique called flux-ramp modulation, which generates a phase-modulated complex waveform according to the sensor signal. At the end-cap of the signal processing chain it is currently recovered by a demodulation process referred to as Fourier measurement. In this letter, we prove that the mentioned method is equivalent to a maximum likelihood estimation, build an analogy to the sensor array-based direction of arrival estimation, propose an alternative approach based on the eigenvalue decomposition of a correlation matrix, present the mathematical formulation, discuss the results, and compare both methods. Our method is robust against transients due to flux ramp returning point and allows proper estimation in large phase ranges.

Expanding the Capability of Microwave Multiplexed Readout for Fast Signals in Microcalorimeters.

Microwave SQUID multiplexing has become a key technology for reading out large arrays of X-ray and gamma-ray microcalorimeters with mux factors of 100 or more. The desire for fast X-ray pulses that accommodate photon counting rates of hundreds or thousands of counts per second per sensor drives system design toward high sensor current slew rate. Typically, readout of high current slew rate events is accomplished by increasing the sampling rate, such that rates of order 1MHz may be necessary for some experiments. In our microwave multiplexed readout scheme, the effective sampling rate is set by the frequency of the flux-ramp modulation (f r) used to linearize the SQUID response. The maximum current slew rate between samples is then nominally Φ 0 f r/2M in (where M in is the input coupling) because it is generally not possible to distinguish phase shifts of > π from negative phase shifts of < -π. However, during a pulse, we know which direction the current ought to be slewing, and this makes it possible to reconstruct a pulse where the magnitude of the phase shift between samples is > π. We describe a practical algorithm to identify and reconstruct pulses that exceed this nominal slew rate limit on the rising edge. Using pulses produced by X-ray transition-edge sensors, we find that the pulse reconstruction has a negligible impact on energy resolution compared to arrival time effects induced by under-sampling the rising edge. This technique can increase the effective slew rate limit by more than a factor of two, thereby either reducing the resonator bandwidth required or extending the energy range of measurable photons. The extra margin could also be used to improve crosstalk or to decrease readout noise.

Transformer Coupling and Its Modelling for the Flux-Ramp Modulation of rf-SQUIDs

Microwave SQUID (Superconducting QUantum Interference Device) multiplexing is a suitable technique for reading a large number of detector channels, using only a few connecting lines. In the HOLMESexperiment, this is based on inductively coupled rf-SQUIDs fed by TES (Transition Edge Sensors). Operation of the whole rf-SQUID chain is achieved with a single transmission line, by means of the recently introduced flux-ramp modulation technique—a sawtooth signal which allows signal reconstruction while operating the rf-SQUIDs in an open loop condition. Due to the crucial role of the sawtooth signal, it is very important that it does not suffer from ground-loop disturbances and electromagnetic interference (EMI). Introducing a transformer between the sawtooth source and the SQUID is very effective in suppressing disturbances. The sawtooth signal has both slow and fast components, and the frequency can vary between a few kHz up to a MHz, depending on the TES signal and SQUID characteristics. A transformer able to handle such a broad range of conditions must have very stringent characteristics and needs to be custom designed. Our solution exploits standard commercial and inexpensive transformers for LAN networks, stacked in a user-selectable number, to better fit the bandwidth requirements. A model that allows handling of the low- and high-frequency operating range has been developed.

Characterization of the microwave multiplexing readout and TESs for HOLMES

A powerful tool to determine the effective electron-neutrino mass is the calorimetric measurement of the energy released in a nuclear beta decay. Performing a precision measurement of the end point of the Electron Capture decay spectrum of 163Ho, HOLMES aims at pushing down the sensitivity on the neutrino mass below 1 eV. In its final configuration HOLMES will deploy an array of 1000 microcalorimeters based on Transition Edge Sensors with gold absorbers in which the 163Ho will be ion implanted. The best technique to easily read out such a number of detector with a common readout line is the microwave frequency domain multiplexing. Therefore, the TESs are coupled to multiplexed rf-SQUIDS operated in flux ramp modulation for linearization purposes. The rf-SQUIDS are then coupled to superconducting quarter wavelength resonators in the GHz range, from which the modulating signal is finally recovering using software defined radio techniques. In the last two years an extensive R&D activity has been carried out in order to maximize the multiplexing factor while preserving the performances of each detector which fulfil the HOLMES requirements ( i.e. an energy resolution of few eV and a time-resolution of a few microseconds). We report here the progress made towards the characterization of the multiplexing system together with the results of the characterization of the HOLMES detectors.

Toward Large Field-of-View High-Resolution X-ray Imaging Spectrometers: Microwave Multiplexed Readout of 28 TES Microcalorimeters

We performed small-scale demonstrations at GSFC of high-resolution X-ray TES microcalorimeters read out using a microwave SQUID multiplexer. This work is part of our effort to develop detector and readout technologies for future space-based X-ray instruments such as the microcalorimeter spectrometer envisaged for Lynx, a large mission concept under development for the Astro 2020 Decadal Survey. In this paper we describe our experiment, including details of a recently designed, microwave-optimized low-temperature setup that is thermally anchored to the 55 mK stage of our laboratory ADR. Using a ROACH2 FPGA at room temperature, we read out pixels of a GSFC-built detector array via a NIST-built multiplexer chip with Nb coplanar waveguide resonators coupled to rf-SQUIDs. The resonators are spaced 6 MHz apart (at $$\sim $$ 5.9 GHz) and have quality factors of $$\sim $$ 15,000. In our initial demonstration, we used flux-ramp modulation frequencies of 125 kHz to read out 5 pixels simultaneously and achieved spectral resolutions of 2.8–3.1 eV FWHM at 5.9 keV. Our subsequent work is ongoing: to-date we have achieved a median spectral resolution of 3.4 eV FWHM at 5.9 keV while reading out 28 pixels simultaneously with flux-ramp frequencies of 160 kHz. We present the measured system-level noise and maximum slew rates and briefly describe our future development work.

Microwave SQUID Multiplexing of Metallic Magnetic Calorimeters: Status of Multiplexer Performance and Room-Temperature Readout Electronics Development

To our present best knowledge, microwave SQUID multiplexing ( $$\mu $$ MUXing) is the most suitable technique for reading out large-scale low-temperature microcalorimeter arrays that consist of hundreds or thousands of individual pixels which require a large readout bandwidth per pixel. For this reason, the present readout strategy for metallic magnetic calorimeter (MMC) arrays combining an intrinsic fast signal rise time, an excellent energy resolution, a large energy dynamic range, a quantum efficiency close to $$100\%$$ as well as a highly linear detector response is based on $$\mu $$ MUXing. Within this paper, we summarize the state of the art in MMC $$\mu $$ MUXing and discuss the most recent results. This particularly includes the discussion of the performance of a 64-pixel detector array with integrated, on-chip microwave SQUID multiplexer, the progress in flux ramp modulation of MMCs as well as the status of the development of a software-defined radio-based room-temperature electronics which is specifically optimized for MMC readout.

Development of transition edge sensors with rf-SQUID based multiplexing system for the HOLMES experiment

Measuring the neutrino mass is one the most compelling issue in particle physics. HOLMES is an experiment funded by the European Research Council for a direct measurement of neutrino mass. HOLMES will perform a precise measurement of the end point of the Electron Capture decay spectrum of 163Ho in order to extract information on neutrino mass with a sensitivity as low as 1 eV. HOLMES, in its final configuration will deploy a 1000 pixel array of low temperature microcalorimeters: each calorimeter consists of an absorber, where the Ho atoms will be implanted, coupled to a Transition Edge Sensor thermometer. The detectors will be kept at the working temperature of ∼70 mK using a dilution refrigerator. In order to gather the required 3 × 1013 events in a three year long data taking with a pile up fraction as low as 10−4, detectors must fulfill rather high speed and resolution requirements, i.e. 10 µs rise time and 4 eV resolution. To ensure such performances with an efficient read out technique for very large detectors array kept at low temperature inside a cryostat is no trivial matter: at the moment, the most appealing read out technique applicable to large arrays of Transition Edge Sensors is rf-SQUID multiplexing. It is based on the use of rf-SQUIDs as input devices with flux ramp modulation for linearisation purposes; the rf-SQUID is then coupled to a super-conductive λ/4-wave resonator in the GHz range, and the modulated signal is finally read out using the homodyne technique.

Interchannel Crosstalk and Nonlinearity of Microwave SQUID Multiplexers

In order to read out current signals from large-scale arrays of transition edge sensors (TES), microwave SQUID multiplexers (MW-MUX) have been developed by several groups. Reduction of crosstalk induced in the multiplexer is important in order to maintain the energy resolution or the noise equivalent power of detector arrays. In the present study, crosstalk between channels in MW-MUX with five different designs is experimentally evaluated. The resonance frequency separation is ten times as large as the resonator bandwidth. Without flux-ramp modulation, crosstalk between two adjacent channels neighboring in position decreases to ≍1 × 10–3 with increasing resonance frequency separation to ≍100 MHz. Crosstalk between SQUID channels neighboring in resonance frequency also decreases to 4 × 10–3 with increasing the distance to 2.5 mm. We show that nonlinear error can occur due to the crosstalk with flux-ramp modulation. Flux readings from a well-designed multiplexer exhibit crosstalk of less than 1 mΦ0 peak-to-peak and nonlinear errors of less than 2 mΦ0 peak-to-peak, which is sufficient for the readout of the gamma-ray TES arrays being developed. These results can provide guidelines for suppressing both the crosstalk and the nonlinear error to less than the criterion of TES spectrometers with typical energy-resolving ability.

Development of microwave-multiplexed superconductive detectors for the HOLMES experiment

In recent years, the progress on low temperature detector technologies has allowed design of large scale experiments aiming at pushing down the sensitivity on the neutrino mass below 1 eV. Even with outstanding performances in both energy (~eV on keV) and time resolution (~ 1 μs) on the single channel, a large number of detectors working in parallel is required to reach a sub-eV sensitivity. HOLMES is a new experiment to directly measure the neutrino mass with a sensitivity as low as 2eV. HOLMES will perform a calorimetric measurement of the energy released in the electron capture (EC) decay of 163 Ho. In its final configuration, HOLMES will deploy 1000 detectors of low temperature microcalorimeters with implanted 163 Ho nuclei. The baseline sensors for HOLMES are Mo/Cu TESs (Transition Edge Sensors) on SiNx membrane with gold absorbers. The readout is based on the use of rf-SQUIDs as input devices with flux ramp modulation for linearization purposes; the rf-SQUID is then coupled to a superconducting lambda/4-wave resonator in the GHz range, and the modulated signal is finally read out using the homodyne technique. The TES detectors have been designed with the aim of achieving an energy resolution of a few eV at the spectrum endpoint and a time resolution of a few micro-seconds, in order to minimize pile-up artifacts.

High-resolution gamma-ray spectroscopy with a microwave-multiplexed transition-edge sensor array

We demonstrate very high resolution photon spectroscopy with a microwave-multiplexed two-pixel transition-edge sensor (TES) array. We measured a $^{153}$Gd photon source and achieved an energy resolution of 63 eV full-width-at-half-maximum at 97 keV and an equivalent readout system noise of 86 pA/$\sqrt{\text{Hz}}$ at the TES. The readout circuit consists of superconducting microwave resonators coupled to radio-frequency superconducting-quantum-interference-devices (SQUID) and transduces changes in input current to changes in phase of a microwave signal. We use flux-ramp modulation to linearize the response and evade low-frequency noise. This demonstration establishes one path for the readout of cryogenic X-ray and gamma-ray sensor arrays with more than $10^3$ elements and spectral resolving powers $R=\lambda/\Delta\lambda > 10^3$.

Flux-Ramp Modulation for SQUID Multiplexing

SQUIDs are typically operated in a flux-locked loop to linearize their response to input flux. However, a flux-locked loop is not possible with a microwave SQUID multiplexer. We describe an alternative technique called flux-ramp modulation and report its successful implementation.