Aliasing Effect on Flux Ramp Demodulation: Nonlinearity in the Microwave Squid Multiplexer
J. M. Salum, Timo Muscheid, A. Fuster, Manuel Elías García Redondo, Matías Rolf Hampel, Luciano Pablo Ferreyro, J.M. Geria, J. Bonilla-Neira, Nahuel Agustín Müller, J. Bonaparte, Alejandro Almela, Luis Eduardo Ardila-Perez, M. Platino, Oliver Sander, M. Weber
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.
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.
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.
The Microwave SQUID Multiplexer (μMUX) is the device of choice for the readout of a large number of low-temperature detectors in a wide variety of experiments within the fields of astronomy and particle physics. While it offers large multiplexing factors, the system noise performance is highly dependent on the cold- and warm-readout electronic systems used to read it out, as well as the demodulation domain and parameters chosen. In order to understand the impact of the readout systems in the overall detection system noise performance, first, we extended the available μMUX simulation frameworks, including additive and multiplicative noise sources in the probing tones (i.e., phase and amplitude noise), along with the capability of demodulating the scientific data, either in the resonator’s phase or the scattering amplitude. Then, considering the additive noise as a dominant noise source, the optimum readout parameters to achieve minimum system noise were found for both open-loop and flux-ramp demodulation schemes in the aforementioned domains. Later, we evaluated the system noise sensitivity to multiplicative noise sources under the optimum readout parameters. Finally, as a case study, we evaluated the optimal demodulation domain and the expected system noise level for a typical software-defined radio readout system. This work leads to an improved system performance prediction and noise engineering based on the available readout electronics and the selected demodulation domain.
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.
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.
Microwave SQUID multiplexers (μMUX) have become a key technology for the readout of large arrays of low-temperature detectors, particularly in cosmic microwave background experiments. A critical element of this technique is the flux-ramp modulation signal, whose noise, especially at low frequencies, directly limits the readout performance. This work proposes and experimentally demonstrates the use of a Josephson Arbitrary Waveform Synthesizer (JAWS) as a low-noise, high precision source for generating the sawtooth-shaped flux-ramp signal required in μMUX readout systems. The JAWS, based on the AC Josephson effect, provides intrinsically quantized and spectrally pure waveforms with excellent signal-to-noise ratio. The operation of a 9000-junction JAWS array is characterized and integrated with a cryogenic μMUX device and a custom SDR-based readout system. With this setup, the noise floor level around the harmonic typically used for phase demodulation of the SQUID signal to recover the detector signal was −104dBc/Hz, and the signal-to-noise ratio of this harmonic was 73dB. These results demonstrate the feasibility of using JAWS-based waveform synthesis for μMUX flux-ramp generation.
Abstract A novel approach, frequency-domain cascading microwave multiplexers (MW-Mux), has been proposed and its basic operation has been demonstrated to increase the number of pixels multiplexed in a readout line U of MW-Mux for superconducting detector arrays. This method is an alternative to the challenging development of wideband, large power, and spurious-free room-temperature (300 K) electronics. The readout system for U pixels consists of four main parts: (1) multiplexer chips connected in series those contain U superconducting resonators in total. (2) A cryogenic high-electron-mobility transistor amplifier (HEMT). (3) A 300 K microwave frequency comb generator based on N (≡ U / M ) parallel units of digital-to-analog converters (DAC). (4) N parallel units of 300 K analog-to-digital converters (ADC). Here, M is the number of tones each DAC produces and each ADC handles. The output signal of U detectors multiplexed at the cryogenic stage is transmitted through a cable to the room temperature and divided into N processors where each handles M pixels. Due to the reduction factor of 1/ N , U is not anymore dominated by the 300 K electronics but can be increased up to the potential value determined by either the bandwidth or the spurious-free power of the HEMT. Based on experimental results on the prototype system with N = 2 and M = 3, neither excess inter-pixel crosstalk nor excess noise has been observed in comparison with conventional MW-Mux. This indicates that the frequency-domain cascading MW-Mux provides the full (100%) usage of the HEMT band by assigning N 300 K bands on the frequency axis without inter-band gaps.