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.
Abstract The Microwave SQUID Multiplexer (
μMUX) is a critical readout technology for large-scale Superconducting Transition-Edge Sensor (TES) array. It is considered as a promising readout system for both bolometer and calorimeter applications of large-scale TES array. It has been employed in several Cosmic Microwave Background (CMB) experiments, in which the TESes are used as bolometers. However, in the field of calorimeter applications of TESes, such as X-ray detection, the
μMUX system has not been widely used. The main reason is the slew rate of calorimeter pulse signal is much faster than that of bolometer, which will increase the difficulties of data processing in
μMUX electronics. In a typical microwave SQUID Multiplexed readout scheme, the sampling rate is determined by the frequency of the flux-ramp modulation. For CMB experiment, the frequency of the flux-ramp is usually set to about
O(10~kHz). However, for X-ray detection, it is necessary to improve the frequency of flux-ramp to about 1~MHz. It is a challenge to implement the high speed data processing with current
μMUX electronics.%The
μMux readout algorithm is a crucial component.Currently, the implementation of the
μMux readout algorithm is complex, and the sampling rate for each TES is low, only reaching kHz.We propose a recursive algorithm to reconstruct the fast TES signals with high sampling rate in case of no hardware changes. This algorithm is simple enough to implement in real time data collection. %In this paper, we describe and demonstrate this technique with a reasonable simulation model of
μMUX. The simulation results shows that the recovered sampling rate can break through the frequency limitation of the flux ramp, reaching up to analog-to-digital converter (ADC) sampling rate. The non-linearity is lower to 0.25\% in full dynamic range.
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.
We report very-low-noise, fast-response, middle-scale multiplexing in a microwave superconducting quantum interference device multiplexer (MW-Mux) as a transition-edge sensor (TES) readout. Our MW-Mux is able to read 40 channels with 500 kHz sampling and has a low readout noise of 0.9 μΦ0/Hz (where Φ0 is the magnetic flux quantum), equivalent to 9 pA/Hz. By contrast, a multiplexer of less than 10 pixels with 500 kHz sampling and ∼2 μΦ0/Hz readout noise has so far been reported in the literature. Owing to the 500 kHz sampling, our MW-Mux exhibits a fast response to detect a TES pulse with a rise time around 12 μs. We demonstrated simultaneous readout of 38 pixels from an array of x-ray TES microcalorimeters. The measured full-width values at half-maximum spectral resolution ranged from 2.79 to 4.56 eV, with a median value of 3.30 eV at 5.9 keV, including a ∼10% contribution of readout noise, i.e., 0.9–1.7 eV.
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 × 10-3with increasing resonance frequency separation to ≈100 MHz. Crosstalk between SQUID channels neighboring in resonance frequency also decreases to 4 × 10-3with 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 mΦ0peak-to-peak and nonlinear errors of less than 2 mΦ0peak-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.
Abstract A novel system formed by a Microwave Superconducting Quantum Interference Device (SQUID) Multiplexer (uMUX) and a room temperature electronics employs frequency division multiplexing (FDM) technique to read out multiple cryogenic detectors. Since the detector signal is embedded in the phase of the SQUID signal, a Digital Quadrature Demodulator (DQD) is widely implemented to recover it. However, the DQD also generates a signal that aliases into the first Nyquist zone affecting the demodulated detector signal. In this work, we demonstrate how this spurious signal is generated and a mathematical model of it is derived and validated. In addition, we discuss different proposals to improve the attenuation of this undesired signal. Lastly, we implement one of the proposals in our readout system. Our measurements show an enhancement in the spurious signal attenuation of more than 35 dB. As a result, this work contributes to attenuate the spurious below the system noise.
This thesis describes a multiplexer of Superconducting Quantum Interference Devices (SQUIDs) with low-noise, ultra-low power dissipation, and great scalability. The multiplexer circuit measures the magnetic flux in a large number of unshunted rf SQUIDs by coupling each SQUID to a superconducting microwave resonator tuned to a unique resonance frequency and driving the resonators from a common feedline. A superposition of microwave tones measures each SQUID simultaneously using only two coaxial cables between the cryogenic device and room temperature. This multiplexer will enable the instrumentation of arrays with hundreds of thousands of low-temperature detectors for new applications in cosmology, materials analysis, and nuclear non-proliferation.\nThe driving application of the Microwave SQUID Multiplexer is the readout of large arrays of superconducting transition-edge sensors, by some figures of merit the most sensitive detectors of electromagnetic signals over a span of more than nine orders of magnitude in energy, from 40 GHz microwaves to 200 keV gamma rays. Modern transition-edge sensors have noise-equivalent power as low as 10-20 W / [square root] Hz and energy resolution as good as 2 eV at 6 keV. These per-pixel sensitivities approach theoretical limits set by the underlying signals, motivating a rapid increase in pixel count to access new science. Compelling applications, like the non-destructive assay of nuclear material for treaty verification or the search for primordial gravity waves from inflation use arrays of these detectors to increase collection area or tile a focal plane.\nWe developed three generations of SQUID multiplexers, optimizing the first for flux noise (0.17 mu Phi0 / [square root] Hz) the second for input current noise (19 pA / [square root] Hz) and the last for practical multiplexing of large arrays of cosmic microwave background polarimeters based on transition-edge sensors. Using the last design we demonstrated multiplexed readout of prototype polarimeters with the performance required for the future development of a large-scale astronomical instrument.