Resonant frequencies and SQUID inductancesLSin a microwave SQUID multiplexer are studied for the purpose of reliable design applicable for a future large-format array of transition edge sensors (TESs). The key element of the multiplexer chip is a quarter-wave-length resonator terminated by a dissipationless rf SQUID connected to TES. For the resonator, we found that a small correction to the effective length of the resonators made the designed resonant frequencies fit the experimental one over the whole readout band of 4-8 GHz covered by our cryogenic amplifier. We also found that microstrip-type SQUIDs with vertical loops are suitable for accurate design of small inductanceLS<; 10<; pH to operate the rf SQUID in dissipationless regime. Based on these well-designed resonators and SQUIDs, we have successfully demonstrated the multiplexing of three pulsed signals with 1-ms width and spacing given at the input ports of three SQUIDs. The equivalent noise current refer to the SQUID input is not dominated by SQUIDs and estimated to be 200-270 pA/ √Hz, whose improvement approach is quantitatively discussed.
Resonant frequencies and SQUID inductancesLSin a microwave SQUID multiplexer are studied for the purpose of reliable design applicable for a future large-format array of transition edge sensors (TESs). The key element of the multiplexer chip is a quarter-wave-length resonator terminated by a dissipationless rf SQUID connected to TES. For the resonator, we found that a small correction to the effective length of the resonators made the designed resonant frequencies fit the experimental one over the whole readout band of 4-8 GHz covered by our cryogenic amplifier. We also found that microstrip-type SQUIDs with vertical loops are suitable for accurate design of small inductanceLS<; 10<; pH to operate the rf SQUID in dissipationless regime. Based on these well-designed resonators and SQUIDs, we have successfully demonstrated the multiplexing of three pulsed signals with 1-ms width and spacing given at the input ports of three SQUIDs. The equivalent noise current refer to the SQUID input is not dominated by SQUIDs and estimated to be 200-270 pA/ √Hz, whose improvement approach is quantitatively discussed.
Superconducting transition-edge sensors (TESs) with high sensitivity can detect electromagnetic wave radiations from millimeter/submillimeter, optical to x/γ rays, and have been successfully used in many fields. To improve detection efficiency and sensitivity, large-scale TES arrays are required in combination with multiplexing readout electronics. Compared to other multiplexing schemes, microwave SQUID multiplexing (μMUX), consisting of high-quality microwave superconducting resonators and RF SQUIDs, is most suitable since it provides a wider bandwidth (GHz) and consequently higher multiplexing factor. We designed two types of circuits with different mutual inductances (MT) between the resonator and the RF SQUID: 2.3 pH for the weak-coupling channel and 6.5 pH for the strong- coupling channel. The resonator and RF SQUID washers made of 150 nm Nb are first fabricated by magnetron-sputtering and reactive ion etching (RIE), followed by deposition of Nb/Al-AlOx/Nb trilayer and definition of the Josephson junctions of the RF SQUIDs. This work presents a μMUX demonstration chip with five channels with Q1values of 787 and 3626, and the measured frequency shifts (Δfpp) of ∼500 kHz and 4 MHz for the weak- and strong-coupling channels, respectively. The open-loop equivalent noise current, obtained from the measured phase noise and resonator responsivity, is ∼80 pA/ √Hz with the strong-coupling channel.
Dissipationless microwave radio frequency superconducting interference device (RF-SQUID) multiplexers are attractive for readouts of large format arrays of transition edge sensors (TES). This multiplexer has the potential for readout bandwidth of several GHz and power consumption of ≈0.1 pW per pixel, which are ≈103 and ≈10-4 times as large as those of DC-SQUID-based conventional multiplexers. To evaluate their readout performance for TES photon counters ranging from near infrared to gamma ray, white noise of this multiplexer was experimentally studied at 4 K. The reason for this was, firstly, to avoid the low-frequency fluctuation obvious at around 0.1 K but trivial for the energy resolution of photon counters, and secondly for a feasibility study of readout operation at 4 K for extended applications. To increase resonant Q at 4 K and maintain low-noise SQUID operation, multiplexer chips consisting of niobium nitride (NbN)-based coplanar-waveguide resonators and niobium (Nb)-based RF-SQUIDs have been developed. This hybrid multiplexer exhibited 1×104≤QI≤2×104 and the square root of spectral density of current noise referred to the SQUID input √SI =31 pA/√Hz, where QI is the internal Q of resonators. The former and the latter are factor-of-five and seven improvements from our previous results on Nb-based resonators, respectively. Systematic noise measurement with various microwave readout power PMR and two-directional readout on the complex plane of transmission component of scattering matrix S21 makes the contribution of each noise source obvious. By decreasing these noises to the degree achievable by current technology, we predicted the microwave RF-SQUID multiplexer would exhibit √SI ≤5 pA/√Hz; i.e., close to √SI of state-of-the-art DC-SQUID-based multiplexers.
White noise of dissipationless microwave radio frequency superconducting quantum interference device (RF-SQUID) multiplexers has been experimentally studied to evaluate their readout performance for transition edge sensor (TES) photon counters ranging from near infrared to gamma ray. The characterization has been carried out at 4 K, first to avoid the low-frequency fluctuations present at around 0.1 K, and second, for a feasibility study of readout operation at 4 K for extended applications. To increase the resonant Q at 4 K and maintain low noise SQUID operation, multiplexer chips consisting of niobium nitride (NbN)-based coplanar-waveguide resonators and niobium (Nb)-based RF-SQUIDs have been developed. This hybrid multiplexer exhibited 1 × 104 ≤ Q ≤ 2 × 104 and the square root of spectral density of current noise referred to the SQUID input √SI = 31 pA/√Hz. The former and the latter are factor-of-five and seven improvements from our previous results on Nb-based resonators, respectively. Two-directional readout on the complex plane of the transmission component of scattering matrix S21 enables us to distinguish the flux noise from noise originating from other sources, such as the cryogenic high electron mobility transistor (HEMT) amplifier. Systematic noise measurements with various microwave readout powers PMR make it possible to distinguish the contribution of noise sources within the system as follows: (1) The achieved √SI is dominated by the Nyquist noise from a resistor at 4 K in parallel to the SQUID input coil which is present to prevent microwave leakage to the TES. (2) The next dominant source is either the HEMT-amplifier noise (for small values of PMR) or the quantization noise due to the resolution of 300-K electronics (for large values of PMR). By a decrease of these noise levels to a degree that is achievable by current technology, we predict that the microwave RF-SQUID multiplexer can exhibit √SI ≤ 5 pA/√Hz, i.e., close to √SI of state-of-the-art DC-SQUID-based multiplexers.
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.
Superconducting transition-edge sensors (TESs) are highly sensitive detectors and can detect electromagnetic wave radiations from millimeter/submillimeter, optical to 𝑥/γrays, suitable for cosmology, astrophysics, quantum information, and biosensing. In principle, thousands of TESs even more are required to enhance the detection efficiency for large-scale survey. Among other multiplexing schemes, microwave SQUID multiplexer (μMUX), consisting of resonators and RF SQUIDs, has a bandwidth of several GHz, thus multiplexing factor on the order of thousands, more suitable for readout of large TES arrays. We designed and fabricated superconducting coplanar waveguide (CPW) resonators with a high qualityfactor and second-order gradient RF SQUID with two inductive coupling structures respectively. Then, we optimized the critical current density of the Josephson junction and measured the mutual inductance parameters of the second-order gradient structure SQUID, which are consistent with the simulation results. Finally, we fabricated a cryogenic μMUX chip based on RF SQUID and resonator. We discussed the results of the development of μMUX in more detail.
We report on the study of a microwave superconducting quantum interference device (SQUID) multiplexer (MW-Mux) with current noise lower than that of our typical transition-edge sensor (TES) X-ray microcalorimeter. A large mutual inductance, between SQUID loop and input inductor connected to a TES X-ray microcalorimeter in series, realizes such low current noise referred to the SQUID input, but also can cause undesirable resonances which affect the SQUID performances. In this paper, we have developed the MW-Mux with mutual inductance of about 370 pH, which is six times larger than that of the previous one, by adopting a spiral input coil longer than a half wavelength at the readout microwave frequency. Its characteristics are evaluated, and the results have shown that the distortion of the SQUID characteristics and the degradation of its noise performance are not clearly observed. Finally, we have developed an MW-Mux microstrip SQUID with a low current noise of <; 20 pA/√(Hz) which is below the typical noise of our TES X-ray microcalorimeter, 30 pA/√(Hz).