Flux ramp modulation based MHz frequency-division dc-SQUID multiplexer
Daniel Richter, Ludwig Hoibl, Thomas Wolber, Nick Karcher, Andreas Fleischmann, Christian Enss, Marc Weber, Oliver Sander, Sebastian Kempf
FFlux ramp modulation based MHz frequency-division dc-SQUID multiplexer
Daniel Richter, Ludwig Hoibl, Thomas Wolber, Nick Karcher, Andreas Fleischmann, Christian Enss, Marc Weber, Oliver Sander, and Sebastian Kempf
1, 3, a) Kirchhoff-Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120 Heidelberg,Germany. Institute for Data Processing and Electronics, Karlsruher Institute of Technology, Hermann-von-Helmholtz-Platz 1,76344 Eggenstein-Leopoldshafen, Germany. Institute for Micro- and Nanoelectronic Systems, Karlsruher Institute of Technology, Hertzstraße 16,76187 Karlsruhe, Germany. (Dated: 5 March 2021)
We present a MHz frequency-division dc-SQUID multiplexer that is based on flux ramp modulation and aseries 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 coupledto 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 modeof operation, an input signal injected in the input coil of one of the SQUIDs and being quasi-static withina 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 thesampled array output voltage. Using a prototype multiplexer as well as a custom readout electronics, wedemonstrate the simultaneous readout of four signal sources with MHz bandwidth per channel.Direct-current superconducting quantum interferencedevices (dc-SQUIDs) are presently one of the most sensi-tive wideband devices for measuring any physical quan-tity that can be naturally converted into magnetic flux.For this reason, dc-SQUIDs are nowadays routinely usedfor applications ranging from investigations of magneticnanoparticles to diagnostics in health care or the explo-ration of mineral deposits . The intrinsic compatibilitywith mK operation temperatures as well as the excellentnoise performance make SQUIDs also key componentsfor the readout of cryogenic particle detectors .The maturity of fabrication technology allows buildingSQUID systems with hundreds or thousands of identicalsensors. Moreover, the size of present-day SQUID sys-tems is not limited by fabrication technology but othersystem constraints such as cooling power or system com-plexity. This particularly applies to SQUID systems op-erating at mK-temperatures as used, for example, to readout cryogenic particle detectors. For this reason, multi-plexing techniques are required to realize multi-channelSQUID systems providing ultra-low power dissipation atcryogenic temperatures, a readout bandwidth of several10 kHz up to some MHz, a large dynamic range as wellas a linear relation between the input and output signal.Existing SQUID-based multiplexing techniques in-clude time-division multiplexing , frequency-divisionmultiplexing using MHz and GHz carriers, code-division multiplexing as well as hybrid multiplexingschemes . But despite of the great success and theirnumerous advantages, they suffer from minor draw-backs that practically challenge their application: MHzfrequency-division multiplexers, for example, employ a) [email protected] large on-chip passive filter circuits limiting the overallchannel count per given chip area. In addition, para-sitic impedances within the readout circuit as well as acbiasing of the sensors leads to severe effects that com-plicate the sensor readout . The frame rate of time-division SQUID multiplexers is too low to acquire wide-band signals without signal deterioration. Though GHzfrequency multiplexing can easily resolve these issues,it comes at the expense of an elaborated cryogenic mi-crowave setup as well as a complex readout electronics.In view of this, we present a MHz frequency-divisionSQUID multiplexing technique. It is based on flux rampmodulation, a modulation technique that had been orig-inally developed for linearizing the output signal of amicrowave SQUID multiplexer . It relies on injectinga periodic, sawtooth-shaped modulation current signal I ramp ( t ) into the modulation coil of a current-sensingSQUID to induce a linearly rising flux ramp with anamplitude of several flux quanta inside the SQUID loopcausing the SQUID output voltage to vary according toits flux-to-voltage characteristic. The flux ramp repeti-tion rate sets the effective sampling rate and hence thesignal bandwidth. It is chosen such that the input sig-nal appears to be quasi-static within a time frame of theflux ramp. In this configuration, the input signal leads toa constant magnetic flux offset causing a phase-shift ofthe flux-to-voltage characteristics that depends linearlyon the actual amplitude of the input signal. Determiningthis phase shift, e.g. using Software-defined radio (SDR)based readout electronics, provides an intrinsically lin-earized measure of the input signal. A phase-shift of 2 π corresponds to a magnetic flux change of one magneticflux quantum.Fig. 1a shows a schematic circuit diagram of a four-channel multiplexer that is based on our multiplexingapproach. Four SQUIDs (one SQUID for each readout a r X i v : . [ phy s i c s . i n s - d e t ] M a r time t / a.u.020020 S Q U I D v o l t age V S Q , i / (cid:541) V
020 0.00 0.50 1.00time t / a.u.020 -1000100-1000100 m odu l a t i on c u rr en t I r a m p / (cid:541) A -1000100-1000100 SQ3SQ2SQ1SQ4 G M in M in M mod,1 M in M in M mod,2 M mod,3 M mod,4 I b I ramp SQ1SQ2SQ3SQ4 V SQ (cid:541) FFT a) I s i g , I s i g , I s i g , I s i g , time t time t time t time t b) c)d) I r a m p time t FIG. 1. (Color online) (a) Schematic circuit diagram of a four-channel dc-SQUID multiplexer. It is based on a series array offour current-biased dc-SQUIDs, each being equipped with a tightly coupled input and modulation coil. A periodic, sawtooth-shaped current signal I ramp ( t ) is driven through the common modulation coil and the voltage V SQ across the SQUID seriesarray is measured. The currents I sig ,i ( t ) represent exemplary input signals as used for demonstration purposes. (b) Modulationcurrent I ramp ( t ) (blue) and resulting output voltage V SQ ,i ( t ) (red) of the individual SQUIDs. For better visibility, we used arather low amplitude of the flux ramp. In actual experiments, the flux ramp amplitude is much higher and several tenth ofperiods are induced. (c) Output signal V SQ ( t ) of the SQUID array. (d) Fast Fourier transform F [ V SQ ( t )] of the voltage signal V SQ ( t ) as acquired during one cycle of the flux ramp. channel) are connected in series and dc-current biasedsuch that the voltage V SQ across the array is the sumof the output voltages V SQ ,i of the individual SQUIDs.Each SQUID is equipped with a tightly coupled inputcoil with mutual inductance M in that is connected to theactual signal source, e.g. a superconducting pick-up coilor a cryogenic detector. Furthermore, the SQUIDs areequipped with modulation coils, each having a differentmutual inductance M mod ,i (the choice of values is dis-cussed below), that are serially connected. By injectinga sawtooth-shaped current signal I ramp ( t ) into these coils,a linearly rising flux ramp is induced inside each SQUIDloop. The actual amplitude of the flux ramp (magneticflux signal inside the SQUID loop in units of Φ ) dependson the mutual inductance M mod ,i and the amplitude ofthe modulation current, the latter being adjusted suchthat multiple flux quanta are induced inside each SQUIDloop. For this reason, the flux ramp causes the out-put voltage V SQ ,i of the i -th SQUID to vary accordingto its flux-to-voltage characteristics, where the numberof periods depends on the height of the flux ramp (seeFig. 1b). The periodic oscillation of the output voltage V SQ ,i ( t ) of the i -th SQUID hence acts as a carrier sig-nal which is phase-modulated by the signal source con-nected to the SQUID input. In case that the mutualinductances M mod ,i are properly chosen, the carrier fre-quencies f c ,i = I ramp , pp M mod ,i f ramp / Φ are unique andcan be set by the amplitude I ramp , pp and repetition rate f ramp of the modulation signal. Since each time frame ofthe flux ramp is used to acquire exactly one sample of theinput signal, the flux ramp repetition ramp f ramp simul-taneously defines the effective sampling rate of the signaland is hence adjusted to the requirements of the specificapplication. For this reason, the carrier frequencies are in practice mainly set by the amplitude I ramp , pp of themodulation signal. The series connection of the individ-ual SQUIDs allows to sum the carriers into the outputvoltage V SQ across the entire array (see Fig. 1c and d).By channelizing this overall output voltage signal V SQ ( t )for each cycle of the flux ramp using, for example, digi-tal down converters combined with subsequent low-passfilters, the phase of the individual carriers can be con-tinuously monitored and acquired in real-time. In thissense, N signals can be simultaneously read out usingonly two bias lines as well as two lines connected to thecommon modulation coil. However, the number of read-out channels that can be simultaneously multiplexed isultimately limited by wideband SQUID noise which addson the different carrier signals and whose amplitude in-creases as √ N .To demonstrate our multiplexing approach, we de-signed, fabricated and characterized a four-channel pro-totype multiplexer. We used our well-established fab-rication process for Nb/Al-AlOx/Nb-Josephson tunneljunctions as well as a SQUID design that we had pre-viously developed. The SQUID layout is hence not op-timized with respect to this multiplexing application.More precisely, the SQUID impedance is not matchedto the line impedance, the flux-to-voltage transfer coef-ficient is not maximized and the on-chip wiring is notoptimized for transmitting high-frequency signals. Wetherefore had to expect a reduced signal to noise ratio.Fig. 2a shows an optical microscope photograph of oneof our fabricated multiplexers. The common modulationcoil and the bias lines are colored in blue and orange,whereas the input coils are colored in red. Besides theelectrical contact pads that are required for multiplexeroperation and that are marked with colored dots, addi- to detectorJJ shuntsJosephson junctions (JJ)cooling fin a) b) c)d) SQUID loopshuntSQUIDloop 50 μ m SQUID loop modulation coil input coil bias lines μ m 50 μ mSQ1SQ4 50 μ m FIG. 2. (Color online) Optical microscope pictures of the prototype four-channel dc-SQUID multiplexer device presented withinthis paper. For clarity, the SQUID bias lines, the modulation coil as well as the input coils are colored (compare Fig. 1) (a)Overview of the entire chip. (b) Magnification of the dc-SQUID “SQ1”. (c), (d) Magnification of the part of the SQUID loopof the SQUIDs “SQ1” and “SQ4” to which the modulation coil is inductively coupled. tional pads for initial diagnostics are placed on the leftside of the chip. The latter allows, for example, to tapthe individual SQUID voltages V SQ ,i or to modulate theflux of only a subset of the entire SQUID array. TheSQUIDs are parallel gradiometers consisting of four pla-nar, single-turn coils that are connected in parallel (seeFig. 2b). Each coil is built by two superconducting loopsof different size that are connected in series. The biggerloop is used to tightly couple the input coil, while thesmaller loop is used to couple the modulation coil. Thisarrangement allows spatially and thus inductively sepa-rating the input and modulation coil to avoid parasiticcoupling of the flux ramp into a potential superconduct-ing input circuit as formed, for example, when connect-ing a superconducting pickup coil to the SQUID input.The Josephson tunnel junctions are located in the lowerpart of the SQUID and are resistively shunted to ensurea non-hysteretic behavior of the SQUID. The SQUID isequipped with SQUID loop shunts to damp the funda-mental SQUID resonance.For our prototype device, we aimed to equally spacethe mutual inductances M mod ,i in the range M mod , min ≤ M mod ,i < M mod , min with i = 1 , . . . , M mod , min being the mutual inductance of the weakest coupledSQUID. This prevents higher harmonics of the carrier sig-nals to appear in the target carrier frequency range andensures that an integer number of flux quanta is inducedin each SQUID loop when injecting a proper modulationsignal into the common modulation coil. The latter is es-sential to avoid the occurrence of voltage transients in theflux-to-voltage characteristics that potentially emerge incase that the magnetic flux threading the SQUID loop isdifferent before and after the ramp reset. We set the mu-tual inductance M mod ,i by adjusting the overlap of themodulation coil and the underlying SQUID loop. For the tightest coupled SQUID, i.e. the SQUID with the largestmutual inductance M mod ,i , the modulation coil runs di-rectly on top of the SQUID loop (see Fig. 2c) to yield thehighest possible magnetic coupling factor. For the otherSQUIDs supposed to be weaker coupled, the diameterof the modulation coil is reduced (see, for example, Fig.2d for the weakest coupled SQUID). We performed nu-merical inductance calculations of our SQUID design bymeans of InductEx and managed to adjust the overlapto yield almost equally spaced mutual inductance valuesin the range 29 . ≤ M mod ,i < . . In particular, we are goingto build two-dimensional M × N multiplexers for whichthe N modulation coils within a row and the M SQUIDswithin a column are serially connected to each other. As-suming that the mutual inductance values within a roware virtually identical, in particular after optimizing thefabrication process, this scheme allows to inject individ-ual flux ramp signals to each column and thus to ensurethat each SQUID is modulated with an integer numberof flux quanta.We mounted the fabricated prototype multiplexer ona custom-made sample holder, electrically connected thechip by means of ultrasonic wedge bonds, and immersedthe setup enclosed with a soft-magnetic and supercon-ducting shield into a liquid helium transport dewar.We dc-biased the multiplexer using the low-noise biascurrent source of a commercial high-speed dc-SQUIDelectronics and amplified the voltage drop across thearray by means of a capacitively coupled, low-cost am-plifier cascade . For synthesizing the modulation sig-nal, digitizing the output voltage of the multiplexer aswell as real-time channelization and phase determina-tion, we employed a prototype SDR electronics we hadpreviously developed for operating a microwave SQUIDmultiplexer . The electronics comprises a Xilinx ZynqUltraScale+ FPGA board as well as ADC and DAC evaluation boards. The latter are connected to the FPGAboard via FMC connectors and are synchronized via anexternal 10 MHz reference. To avoid a degradation ofthe linear rise of the flux ramp, we replaced the inputtransformers of the DAC board by inductive transform-ers with passband of 15 kHz and 100 MHz. This allowedsynthesizing adequate flux ramps signals. However, welater figured out that the effective ac-coupling still dis-torted the flux ramp linearity manifesting as a changeof slope of the ramp during each cycle. The resultingcarrier frequency change within each time frame signif-icantly deteriorated the phase determination and ulti-mately led to an increased white noise floor. For thisreason, we plan for dc-coupled DACs to be used in laterapplications. For channelizing and demodulation of thecontinuously sampled output voltage signal, we used dig-ital down-conversion with subsequent low-pass filteringfor phase estimation.We comprehensively characterized the multiplexervarying, for example, the flux ramp repetition rate f ramp or the amplitude I ramp , pp of the modulation current I ramp ( t ). The resulting carrier signal frequencies were inthe frequency range between 10 MHz and 50 MHz and theeffective sampling rate was ranging between 200 kHz and1 . µ s rise time. Fig. 3 shows as an example thefour output signals when connecting test signal gener-ators to the input coils of channels SQ2 to SQ4, run-ning the multiplexer with a flux ramp repetition rate of f ramp = 1 MHz and adjusting the amplitude to yield car-rier frequencies of about 26 . . . . −
40 dB. The whitenoise level of all four channels is about 25 µ Φ / √ Hzand therefore seems to be rather high. However, sev-eral sources contribute to this elevated noise level whoseinfluence be minimized for future devices by optimiz-ing the overall setup. This includes the small SQUIDflux-to-voltage transfer coefficient, the voltage noise ofthe used amplifier cascade, the noise penalty due to fluxramp modulation , the remaining non-linearity of the −0.20.00.2−0.20.00.2 δ Φ S Q / Φ −0.20.00.2 0 50 100 150 200 time t / ms −0.20.00.2 SQ1
SQ2
SQ3SQ4
FIG. 3. (Color online) Magnetic flux excitation δ Φ i injectedin SQUID “SQ i ” versus time t derived from the demodulationof the output voltage signal of the prototype MHz dc-SQUIDmultiplexer. The test signals that have been applied to theinput coils of the different SQUIDs are illustrated in Fig. 1(a).The solid lines result from averaging fifty neighboring pointsto increase visibility. flux ramp, the impedance mismatch as well as the non-optimized device design.In conclusion, we demonstrated a MHz frequency-division dc-SQUID multiplexing technique. We showedthat our approach avoids some drawbacks of other ex-isting multiplexing techniques and allows for reading outsignal sources with MHz signal bandwidth at cryogenictemperatures. In combination with the large dynamicrange that is comparable or even higher than the dy-namic range of standard setups using flux-locked loopand that results from converting the input signal into aphase shift, our multiplexing approach paves the way forrealizing various applications requiring a simple setup,large signal bandwidth and dynamic range as well as lownoise. I. DATA AVAILABILITY
The data that support the findings of this study areavailable from the corresponding author upon reasonablerequest.
ACKNOWLEDGMENTS
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