(Dated: 6 July 2017) a) b) Contribution of a U.S. government agency, not subject to copyright.

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1 Simultaneous readout of 128 X-ray and Gamma-ray Transition-edge Microcalorimeters using Microwave SQUID Multiplexing J.A.B. Mates, 1 D.T. Becker, 1 D.A. Bennett, 2 B.J. Dober, 2 J.D. Gard, 1 J.P. Hays-Wehle, 1, 2 J.W. Fowler, 1, 2 G.C. Hilton, 2 C.D. Reintsema, 2 D.R. Schmidt, 2 D.S. Swetz, 2 L.R. Vale, 2 and J.N. Ullom 1, 2 1) University of Colorado, Boulder, CO 80309, USA. a) 2) National Institute of Standards and Technology, Boulder, CO, USA b) (Dated: 6 July 2017) The number of elements in most cryogenic sensor arrays is limited by the technology available to multiplex signals from the arrays into a smaller number of wires and readout amplifiers. The largest demonstrated arrays of transition-edge sensor (TES) microcalorimeters contain roughly 250 detectors and use time-division multiplexing with Superconducting Quantum Interference Devices (SQUIDs). The bandwidth limits of this technology constrain the number of sensors per amplifier chain, a quantity known as the multiplexing factor, to several 10s. With microwave SQUID multiplexing we can expand the readout bandwidth and enable much larger multiplexing factors. While microwave SQUID multiplexing of TES microcalorimeters has been previously demonstrated with small numbers of detectors, we now present a fully scalable demonstration in which 128 TES detectors are read out on a single pair of coaxial cables. Superconducting transition-edge sensors (TESs) 1 are exquisitely sensitive devices for the measurement of incident power and energy, due to the very low thermal fluctuations at cryogenic temperatures. However, the size of arrays of TESs and other cryogenic sensors has been limited by the technology available to multiplex the signals into a reasonable number of output channels that carry the signals to room temperature. For example, TES microcalorimeters routinely achieve record sensitivities for energy dispersive detectors at x-ray and gamma-ray wavelengths, but the largest demonstrated arrays contain only about 250 detectors multiplexed using a time-division (TDM) basis set 2,3, and are read out using approximately 50 pairs of wires. Other multiplexing techniques, such as frequency division multiplexing (FDM) 4 and code-division multiplexing (CDM) 5 have been used to demonstrate smaller arrays, but none have demonstrated multiplexing factors greater than about 30 detectors per output channel. Fundamentally, the multiplexing factors of these techniques are all limited by the available per-output-channel bandwidth of about ten megahertz. Microwave SQUID multiplexing 6 8, shown in Fig. 1a, uses rf-squids inductively coupled to cryogenic sensors (e.g. TESs) to modulate the frequency of high-q microwave resonators. By coupling these resonators to a common microwave feedline with each resonator tuned to a different frequency, we can read out all the sensors simultaneously. A microwave tone placed on one resonance measures its frequency shift and thus its detector signal. A superposition of microwave tones, one for each resonator, can measure all detectors. The SQUIDs provide the necessary gain to boost the signals and the noise of the detectors above the noise of a high-bandwidth a) John.Mates@Colorado.EDU b) Contribution of a U.S. government agency, not subject to copyright. cryogenic HEMT amplifier. The SQUID response is linearized through flux-ramp modulation 9. The large bandwidth of microwave transmission lines allows this approach to achieve significantly higher multiplexing factors than have been achieved for TES sensors in the past. Any multiplexing technique must satisfy at least five requirements: (1) readout noise below the noise of the sensors of interest, (2) sufficient dynamic range for the largest signals of interest, (3) sufficient bandwidth to measure both fast signals and signals from a usefully large number of sensors (4) sufficient isolation between sensors in the same readout chain, and (5) the existence of electronics able to perform the necessary control functions in a fashion that scales well to large numbers of sensors. In this Letter, we show that microwave SQUID multiplexing fulfills all these criteria for arrays of cryogenic microcalorimeters, and explain how the interrelated nature of these criteria determine the achievable multiplexing factor. Having satisfied these requirements, we report the demonstration of large-scale readout of TES microcalorimeters using microwave SQUID multiplexing. The demonstration takes the form of an instrument called Spectrometer to Leverage Extensive Development of Gamma-ray TESs for Huge Arrays using Microwave Multiplexed Enabled Readout, or SLEDGEHAM- MER 10. This instrument targets precision gamma-ray spectroscopy for nuclear materials accounting. When completed, SLEDGEHAMMER will be a 512-element TES microcalorimeter array, implemented in two packages of 256 detectors each. In the current configuration, we have demonstrated simultaneous readout of 128 detectors multiplexed into one channel with 1 GHz of bandwidth. For the moment, we are limited by the available bandwidth of our room temperature electronics, but we plan to upgrade these electronics to a total bandwidth of 4 GHz which will allow us to read out all 512 TESs in the SLEDGEHAMMER instrument on two coaxial cables The microwave SQUID multiplexer exhibits noise from two primary sources: two-level-system (TLS) 11 noise and

2 2 HEMT amplifier noise. The TLS noise arises from the switching of uncorrelated two-level systems coupled to the resonator cavity. As these systems change state they change the effective electrical length of the resonator and therefore produce resonance-frequency noise. The power spectral density of this noise exhibits a characteristic 1/ f dependence on frequency (f), making it dominate signals close to the carrier. The HEMT is a broadband noise source and can be described simply by a noise temperature, typically T N 3 K. Because the TLS noise falls off with frequency, the HEMT noise dominates farther from the frequency of the microwave readout tone. We modulate the SQUIDs to ensure the signal appears in the range where the TLS noise is sub-dominant. The effective gain is determined by two factors: the fractional change in the two-port microwave transmission function, and the power of the microwave tone probing the resonance. While the full calculation 12 is beyond the scope of this paper, we can write the probe power as P in = p 2 f 0 Φ 0 I c /16η where f 0 is the resonance frequency, I c is the critical current of the Josephson junction, and Φ 0 is the magnetic flux quantum. The parameter η f/bw relates the resonance frequency shift due to the SQUID to the resonance bandwidth and is a design optimization, usually targeted for η 0.8. The parameter p describes the amplitude of the microwave excitation of the SQUID in units of Φ 0. For small p, the microwave transmission is linear and increasing p simply increases the gain of the system. However, as p approaches 1, the non-linearity of the SQUID begins to steal power from the resonator and convert it to higher harmonics. Simulation shows that the optimal gain should be achieved at p 0.6. For I c = 5 µa and f 0 = 5 GHz this implies an optimal feedline power of approximately 72 dbm per tone. At approximately this power level, we observe a readout noise level of 2 µφ 0 / Hz. With a typical input coupling of M in = 230 ph, this adds an input-referred current noise of 19 pa/ Hz, sufficient for readout of the SLEDGEHAMMER detectors whose typical sensor noise is greater than 100 pa/ Hz. While the response of rf-squids to applied flux is periodic in the flux quantum, the use of flux ramp modulation provides a dynamic range that is effectively infinite so long as a slew rate requirement is met. The flux-ramp demodulation algorithm, which must identify phase shifts of the flux-ramp response between one ramp period and the next, cannot distinguish a phase shift of more than π from a negative phase shift of less than π. For accurate flux-ramp demodulation, we therefore require input signal slew rates not to exceed Φ 0 f r /2M in, where f r is the flux ramp frequency. Specification of readout noise and signal slew rate therefore determine both the input coupling and the necessary bandwidth per resonator. A resonator bandwidth of 300 khz allows for a 2 Φ 0 flux ramp frequency of 62.5 khz which satisfies this requirement for SLEDGEHAMMER, for which signals of interest have a peak slew rate of 0.05 µa/µs. The use of coaxial cabling and a HEMT amplifier can potentially provide access to several GHz of analog bandwidth. In practice, our system bandwidth is limited to 1 GHz by the electronics that convert signals from the digital to the analog domain for tone generation and from the analog to the digital domain for measurement and signal extraction. Even 1 GHz of bandwidth per output channel is a 100-fold improvement over traditional TDM, FDM, and CDM readout schemes. The large analog bandwidth allows wide resonances that facilitate meeting the slew rate requirement, multiple resonances so that signals from many sensors can be combined in one output channel, and sufficient frequency spacing between resonators to minimize cross-talk. Due to the Lorentzian tails of each resonator s two-port scattering parameter for transmission (S 21 ), a change in frequency of one resonator leads to a change in measured S 21 for other resonators as well. It can be shown 12 that a fractional change in source resonator frequency ω 16n 2 BW, ω leads to a change in target resonator S 21 of where BW is the resonator bandwidth and n is number of bandwidths between resonators. Spacing resonators by 10 times their bandwidth thus leads to crosstalk below 1 part in Using the bandwidth set by input signal slew rate, this determines the number of resonances that fit in a unit of readout bandwidth. Fabrication constraints, since overcome, on resonator frequency placement have limited the frequency spacing for this demonstration to 6 MHz so that 128 resonators fit in the 1 GHz available from our current readout electronics. Having described how our multiplexing architecture fulfills the first four requirements described earlier, we now discuss its specific implementation, including the design of the rf-squid circuitry and the warm electronics that fulfill the fifth and final requirement. A photograph of a 33-resonator microwave SQUID multiplexing chip is shown in Fig. 1b-c. The trombone-like features spaced evenly across the chip are quarter-wave coplanarwaveguide resonators, each of slightly different length. They couple capacitively to the feedline that runs along the top of the chip, and inductively to their rf-squids, whose second-order gradiometers are visible along the bottom edge of the chip near the input bond pads. Between the input bond pads and the rf-squid, there are inductors (7 nh) and a shunt resistor (0.5 Ω), whose primary purpose is to maintain a suitably high Q for the resonators, independent of the details of the sensor circuit. They also act in conjunction with the TES bias circuit to protect the TESs from the microwave power stored in the resonator that could potentially couple into the TES bias circuit. In this design each resonator has a bandwidth of roughly 300 khz and the resonances are spaced 6 MHz apart. Variations to the design have produced resonators in four 250 MHz bands between 5 GHz and 6 GHz. A photograph of the fully assembled 256-TES sample box is shown in Fig. 2. Two 25-pin micro-d connectors extend from the blue circuit boards through the bottom of the box on either side. These boards route the flux-

3 3 FIG. 1. (Color online) a) A schematic representation showing just three channels of a microwave SQUID multiplexing circuit with TESs. b) A photograph of a 33-channel microwave SQUID MUX chip. c) A close-up photograph showing quarter-wave microwave resonators capacitively coupled to a feedline. The resonators are terminated by an inductively-coupled rf-squid (left). FIG. 2. (Color online) Photograph of the sample box containing the 8 TES microcalorimeter detector chips (center), 8 microwave multiplexer chips (outer vertical columns) and chips for detector bias, Nyquist filtering, and signal routing. ramp signals and the detector bias currents to the appropriate chips; in the current configuration, these signals could occupy as few as four of the available twisted pairs, saving the remaining ones for diagnostics. The microwave signals enter and exit the box through the SMA connectors in the four corners, with coax to microstrip to coplanar waveguide adapters to connect to the feedline on the multiplexing chips. The microwave signals pass through four 33-resonator multiplexing chips on either side of the box. From the outside of the box moving towards the middle, the 8 multiplexer chips connect to inductor chips (1.6 µh), resistive shunt chips (275 µω), wiring fan-out chips, and finally TES detector chips. With 256 detectors each with a square 1.45 mm tin absorber, the active area of the array is 5.38 cm 2. We mount the sample box in an adiabatic demagnetization refrigerator that provides a temperature of 70 mk. Four coaxial cables connect to the box from room temperature. In order to perform simultaneous readout of a large number of resonators, we require control electronics that generate the appropriate probe tones and then digitize the resonator responses. Having a dedicated microwave generator per resonance would be far too expensive. Instead, two high speed digital-to-analog converters (DACs) generate a comb of tones at lower frequencies (e.g. 10 to 512 MHz), which are mixed up to microwave FIG. 3. (Color online) a) The measured S 21 2 of four microwave SQUID multiplexing chips connected in series. The four resonator bands are placed between 5 and 6 GHz. 128 of the 132 resonances are of sufficient quality to read out the SLEDGEHAMMER TESs. frequencies using an IQ mixer. A similar IQ mixer is used to mix the tones coming out of the cryostat back down to baseband frequencies, where two high speed analogto-digital converters (ADCs) digitize the entire baseband signal consisting of all the tones. The readout electronics for SLEDGEHAMMER are based on those developed for the readout of microwave kinetic inductance detectors (MKIDs) for the MUSIC 13 and ARCONS 14 experiments. These readout systems are themselves based on the Reconfigurable Open Architecture Computing Hardware (ROACH) platform developed and maintained by the Collaboration for Astronomy Signal Processing for Electronics Research Consortium. Firmware programmed into an FPGA on a 2ndgeneration ROACH (ROACH-2) digitally separates the 512 MHz bandwidth measured by the ADCs into different channels corresponding to each resonator and then demodulates the flux ramp applied to all SQUIDs in the array. The ROACH transmits the resulting data over a 10 Gb/s ethernet connection to a data acquisition computer. The firmware we have developed for the SLEDGE- HAMMER instrument is capable of simultaneous readout of 128 microwave SQUID multiplexer channels without adding significant noise and will be described in a separate publication. A vector network analyzer sweep of all four bands on one side of the detector package is shown in Fig. 3a. All of the 132 resonators achieved a resonator depth of more than 10 db. The resonators were placed with a spacing of 6 ± 1 MHz. At this frequency precision, only one resonator ended up within 2.5 MHz of another resonator. The gaps between the four bands and the smaller gaps within the bands allow for wafer-scale and chip-scale shifts in phase velocity due to changes in material parameters, layer thickness, and etch uniformity. These gaps also provide convenient frequencies at which to place the local oscillators for the up-mix. Due to the bandwidth of the current ADCs and the 6 MHz resonator spacing of this demonstration, only 64 of the resonators could be read out per ROACH-2. However, we demonstrated simultaneous readout of 128 channels using two sets of the ROACH-2 electronics, with the two local oscillators placed between bands 1 and 2 and between bands 3 and 4. The power spectral density of the input-referred current-noise of 4 representative TESs read out simultaneously is shown in Fig. 4a. The noise added by the readout can be clearly distinguished from the TES noise at frequencies above the roll-off of the TES noise around 1 KHz. The readout noise is on average a factor of ten

4 4 FIG. 4. (Color online) The current noise spectrum of 4 TESs. The inset shows a histogram of the measured current noise at 10 khz of 54 resonances read out simultaneously with a single ROACH-2. Because the microwave tones are generated digitally with a finite repetition rate, any deterministic errors (e.g. signal clipping) appear in harmonics of that rate. Here, we configured the system so that those errors appear in spikes at khz and khz, well above the signal bandwidth of our detectors. SQUID multiplexing techniques will also enable expanded TES arrays for other applications including x- ray beamline and cosmic microwave background science. We our working on doubling the resonator density and expanding the bandwidth of the room-temperature electronics, which should allow readout of 1,000 TES microcalorimeters with one set of coaxial cables and readout electronics. We expect these advances to dramatically increase the scale of future arrays of low-temperature detectors. FIG. 5. (Color online) The combined spectrum from 89 TESs measured simultaneously using microwave SQUID multiplexed readout. The source of the x-rays and gamma-rays was a gadolinium-153 calibration source. The inset shows a zoomed region around the 97 kev gamma-ray peak (blue) with a Gaussian fit FWHM resolution of 55 ev (red). below the TES noise and does not have a significant effect on the achieved resolution. The inset to Fig. 4b shows a histogram of readout noise levels measured at 10 khz. Measuring across four full bands, we were able to simultaneously read out 128 channels of gamma-ray TESs illuminated with a gadolinium-153 calibration source. Fig. 5 shows the combined spectrum from 89 of the 128 possible channels. Of the 39 channels that were not used for the combined spectrum, 6 were intentionally not connected to TESs to use as diagnostics, 15 did not respond to the detector bias, and 18 showed pulses but did not have spectroscopic quality data due to problems with the detectors themselves. The most prominent lines in the spectra are the 97 and 103 kev gamma-ray lines from gadolinium-153 and the x-ray complexes around 41 kev and 47 kev from the europium K-alpha and K- beta lines respectively. The other lines are a combination of escape peaks from the bright lines, other gamma-ray lines of gadolinium-153, and fluorescence from the lead source housing and from the gold plating of the detector box. The inset shows the combined spectra in the region around 97 kev along with a Gaussian fit with a full width at half maximum resolution of 55 ev. This resolution is better than was achieved with similar detectors in a previous two channel demonstration 15, and is consistent with both the energy resolutions achieved using time-division multiplexing in an 8 column by 32 row format 2 and the inherent resolution of this TES design. Using the SLEDGEHAMMER instrument, we have demonstrated low-noise simultaneous readout of 128 TES microcalorimeters using a single output channel. SLEDGEHAMMER targets precision gamma-ray spectroscopy for nuclear materials accounting, but microwave ACKNOWLEDGMENTS The authors gratefully acknowledge the support of the U.S. DOE NEUP, NIST Innovations in Measurement Science, NASA APRA, and DOE BES ADR programs. 1 J. N. Ullom and D. A. Bennett, Superconductor Science and Technology 28, (2015). 2 D. A. Bennett, R. D. Horansky, D. R. Schmidt, A. Hoover, R. Winkler, B. K. Alpert, J. A. Beall, W. B. Doriese, J. W. Fowler, C. Fitzgerald, et al., Review of Scientific Instruments 83, (2012). 3 W. Doriese, K. Morgan, D. Bennett, E. Denison, C. Fitzgerald, J. Fowler, J. Gard, J. Hays-Wehle, G. Hilton, K. Irwin, et al., Journal of low temperature physics 184, 389 (2016). 4 H. Akamatsu, L. Gottardi, C. de Vries, J. Adams, S. Bandler, M. Bruijn, J. Chervenak, M. Eckart, F. Finkbeiner, J. Gao, et al., Journal of Low Temperature Physics 184, 436 (2016). 5 K. Morgan, B. Alpert, D. Bennett, E. Denison, W. Doriese, J. Fowler, J. Gard, G. Hilton, K. Irwin, Y. Joe, et al., Applied Physics Letters 109, (2016). 6 J. Mates, G. Hilton, K. Irwin, L. Vale, and K. Lehnert, Applied Physics Letters 92, (2008). 7 S. Kohjiro, F. Hirayama, H. Yamamori, S. Nagasawa, D. Fukuda, and M. Hidaka, Journal of Applied Physics 115, (2014). 8 S. Kempf, M. Wegner, A. Fleischmann, L. Gastaldo, F. Herrmann, M. Papst, D. Richter, and C. Enss, AIP Advances 7, (2017). 9 J. Mates, K. Irwin, L. Vale, G. Hilton, J. Gao, and K. Lehnert, Journal of Low Temperature Physics 167, 707 (2012). 10 D. A. Bennett, J. A. Mates, J. D. Gard, A. S. Hoover, M. W. Rabin, C. D. Reintsema, D. R. Schmidt, L. R. Vale, and J. N. Ullom, IEEE Transactions on Applied Superconductivity 25, 1 (2015). 11 J. Gao, M. Daal, A. Vayonakis, S. Kumar, J. Zmuidzinas, B. Sadoulet, B. A. Mazin, P. K. Day, and H. G. Leduc, Applied Physics Letters 92, (2008). 12 J. A. B. Mates, The microwave SQUID multiplexer, Ph.D. thesis, University of Colorado (2011). 13 R. Duan, S. McHugh, B. Serfass, B. A. Mazin, A. Merrill, S. R. Golwala, T. P. Downes, N. G. Czakon, P. K. Day, J. Gao, et al., Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy V 7741, 77411V (2010). 14 S. McHugh, B. A. Mazin, B. Serfass, S. Meeker, K. O Brien, R. Duan, R. Raffanti, and D. Werthimer, Review of Scientific Instruments 83, (2012). 15 O. Noroozian, J. A. Mates, D. A. Bennett, J. A. Brevik, J. W. Fowler, J. Gao, G. C. Hilton, R. D. Horansky, K. D. Irwin, Z. Kang, et al., Applied Physics Letters 103, (2013).

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