Flux-driven Josephson parametric amplifier for sub-GHz frequencies fabricated with side-wall passivated spacer junction technology
Slawomir Simbierowicz, Visa Vesterinen, Leif Grönberg, Janne Lehtinen, Mika Prunnila, Juha Hassel
FFlux-driven Josephson parametric amplifier forsub-GHz frequencies fabricated with side-wallpassivated spacer junction technology
Slawomir Simbierowicz , Visa Vesterinen , , LeifGr¨onberg , Janne Lehtinen , Mika Prunnila and JuhaHassel VTT Technical Research Centre of Finland Ltd & QTF Centre of Excellence,P.O.Box 1000, FI-02044 VTT, FINLAND QCD Labs, COMP Centre of Excellence, Department of Applied Physics,Aalto University, P.O. Box 13500, 00076 Aalto, FinlandE-mail: [email protected]
May 2018
Abstract.
We present experimental results on a Josephson parametric amplifiertailored for readout of ultra-sensitive thermal microwave detectors. In particular,we discuss the impact of fabrication details on the performance. We show that thesmall volume of deposited dielectric materials enabled by the side-wall passivatedspacer niobium junction technology leads to robust operation across a wide rangeof operating temperatures up to 1.5 K. The flux-pumped amplifier has gain inexcess of 20 dB in three-wave mixing and its center frequency is tunable between540 MHz and 640 MHz. At 600 MHz, the amplifier adds 105 mK ± Keywords : Josephson junction, parametric amplifier, SQUID array a r X i v : . [ c ond - m a t . s up r- c on ] M a y lux-driven Josephson parametric amplifier for sub-GHz frequencies
1. Introduction
In recent years, high-fidelity detection of radio-frequency (rf) and microwave signals that can consistof only a few photons has spun a lot of interest inthe development of low-noise amplifiers. Such weaksignals are encountered for instance in the search fordark-matter particles [1–3], fast readout of quantumbits (qubits) [4–7], and characterization of low-loss res-onators [8] or nano-mechanical systems [9]. A promis-ing branch of superconducting amplifiers, with nearquantum-limited noise performance, exploits paramet-ric pumping of the non-linear inductances exhibited byJosephson junctions [10–16] or those intrinsic to super-conductors [17]. The Josephson parametric amplifier(JPA) has also proven to be capable of generating andusing squeezed electromagnetic states [18–20] to go be-low the standard quantum limit of noise added by anamplifier [21].Although the most common applications for theJPA are in the frequency band of 4–8 GHz, we recentlyreported on a JPA for 600 MHz [22] to be usedin conjunction with a nano-calorimeter [23, 24] or a-bolometer [25, 26] with a matching readout frequency.Our main motivation to develop the JPA is to allowthe calorimeter to reach the accuracy of a singlemicrowave photon and set a new record for the noise-equivalent power going below 10 − W / √ Hz [27, 28] inthe bolometric mode. More recently, rf reflectometryof charge qubits has also emerged as a possible usecase for the sub-GHz JPA [29]. Aiming to servesuch applications, the realized JPA utilized the non-linearity of niobium-based superconducting quantuminterference devices (SQUIDs) in a lumped-element rfresonator. The amplifier of Ref. 22 was narrowband,but the center frequency of the gain was designed to betunable with an external magnetic flux. However, thedevice suffered from multiple issues that prohibited itsimmediate use in calorimetry.The first prominent issue discovered in Ref. 22was an ill-behaved, hysteretic response of the resonancefrequency to the applied magnetic flux. Its origin wasattributed to flux trapping in the device geometry. Thesecond issue was a high sensitivity to changes in theoperating temperature, requiring stabilization of theJPA with closed-loop temperature control. We believethat the temperature sensitivity stemmed from two-level systems (TLSs) in a deposited dielectric layer thathad a large participation ratio to the JPA resonance. This layer was made of silicon dioxide that is notoriousfor its high TLS density which significantly affectsmaterial properties at millikelvin temperatures [30, 31].Here, we seek to improve on the shortcomings ofRef. 22 while keeping the design conceptually similar.We present several important modifications to the JPA,the first of which is the fabrication of the Josephsonjunctions with the so-called side-wall passivated spacer(SWAPS) process that we introduced recently [32].This enables us to largely avoid using plasma-enhancedchemical vapour deposited (PECVD) silicon dioxidewhich is a necessity in our standard niobium tunneljunction processes [33]. Measures to control the fluxtrapping are implemented as well. The new JPA alsoemploys three-wave mixing with an rf flux pump attwice the signal frequency [34] as opposed to the four-wave mixing of Ref. 22 which utilized an rf currentpump [11, 13] in the vicinity of the signal frequency.We report on good measured performance in boththe non-degenerate and degenerate modes [35] of theJPA, warranting its later integration into the nano-calorimetry setup.
2. Devices
Amplifying the readout signals of a nano-calorimeterrequires sufficiently high dynamic range and enoughbandwidth from the JPA. More specifically, theamplifier should be able to handle input signals ata maximum power of -120 dBm without going intosaturation, and it needs to respond to detector signalsin the time scales of 10–1000 µ s. These targets weremet in Ref. 22 using a JPA realized with a lumped-element LC resonator for radio frequencies. Theinductance originated largely from Josephson junctionsin a series array of 200 SQUIDs with a maximalcritical current of 35 µ A. Shunted with a capacitance of ’
30 pF, the flux-tunable resonator had a maximumresonance frequency f of 650 MHz. The capacitivecoupling to an external 50-Ω rf environment set thegain-bandwidth product to 2 πf /Q e ’ π × . Q e ’
300 is the external quality factor. In thiswork, the device parameters are similar, and a detailedlisting is provided in the Supplement [36].The devices [Fig. 1(a)] incorporate an on-chip fluxbias line (FBL) on a dedicated superconductive layer.Among many solutions for FBLs [12, 13, 37–40], ourimplementation has the advantage that the dc biascan be routed as a twisted pair through the cryostat lux-driven Josephson parametric amplifier for sub-GHz frequencies O /Nb) with thicknesses100 nm / 10 nm / 100 nm. The tri-layer is etched to astrip geometry and following the SWAPS process thesidewalls are passivated with PECVD silicon dioxide,as shown in a scanning electron micrograph in theSupplement. Crucially, the passivation step leavesno residual dielectric layer to the device area outsidethe junctions. The next step is the deposition of120 nm of niobium for the main wiring layer. TheJosephson junctions form wherever this layer crossesthe tri-layer strips. Because of the need for the on-chip FBL, we add a thin, 40-nm insulating layer ofALD Al O with wet-etched contact holes. Finally, theFBL and some superconducting cross-overs are definedfrom 120 nm of niobium deposited as the topmostlayer. The capacitors of the previous JPA design [22]were formed from parallel plates separated by a silicondioxide layer, but here we use interdigitated fingerswhere the participation ratio of the lossy dielectricsis dramatically lower. The initial maximum resonancefrequency of the devices at zero applied magnetic fluxis about 500 MHz. We fine-tune it to a higher valueby removing a part of the shunt capacitance with afocused ion beam (FIB) [Fig. 1(c)].Two nominally identical devices A and B wereprepared with the maximal resonance frequencytargeted on 650 MHz, in order to make flux pumpingfeasible at the operating frequency of 600 MHz. Thechip containing the JPA is placed on a holder andinside an aluminum-Amumetal 4K magnetic shieldboth of which are thermalized to the mixing stageof a dry dilution refrigerator. Prior to pumping, aninitial characterization of the device takes place. Itcomprises the study of the small-signal response witha vector network analyzer (VNA) while tuning theresonance frequency with a magnetic flux, generatedby a dc current applied to the FBL. A fit to therecorded reflection coefficient of the JPA allows us todetermine the resonance frequency. Device A showsexcellent reproducible tuneability between 520 MHzand 667 MHz [Fig. 1(d)] from which can be concludedthat the SQUID array has a relatively homogeneousmagnetic flux bias. Only a slight hysteresis occursbelow 640 MHz probably in part because of thegeometric inductances [41]. In contrast, the previousgeneration amplifier had very irregular frequency response and only two viable operating points [22].There are several factors that could play a role in theobserved improvement. First, a ground plane withflux-trapping holes [42] has been added to the devicelayout. Second, we have increased the size of theSQUID loops by 65 % to 2 . × . µ m so that lessdc current is needed in the FBL. Finally, we have paidspecial attention to using non-magnetic materials inclose proximity to the JPA chip.
3. Gain and noise in the non-degenerate mode
The JPA operating points defined by the triplet of thedc bias current, the associated flux pump frequency,and pump power are optimized and characterized byan automated procedure described in the Supplement.To study the gain and signal-to-noise ratio (SNR),we apply a weak probe tone at an offset of -10 kHzfrom the halved pump frequency where the JPA gainis maximal. The probe power is set to -146 dBm(-136 dBm) at frequencies below (above) 580 MHz, toadjust accordingly to the dynamic range. In the dataof Fig. 2(a), the SNR is optimized at each static-fluxoperating point, while constraining the maximum gainto 20.5 dB. A gain of 18.5–20.5 dB is attained andthe SNR improves by 15–18 dB, as compared to theunity-gain reference where the noise floor is set by theHEMT post-amplifier. The independently measurednoise added by the HEMT is 10–13 K. The saturationof the JPA is investigated at the discovered operatingpoints by varying the probe power [Fig. 2(b)] and itis found that the lower limit of -120 dBm, required forcalorimeter readout, is easily surpassed by about 10 dBat 600 MHz. After increasing the pump frequencyslightly to lower the gain to 15 dB, a gain-bandwidthproduct of 2 π × ±
200 kHz, or ± O coating of the JPA, thejunction critical current, and the kinetic inductance ofniobium [43]. lux-driven Josephson parametric amplifier for sub-GHz frequencies Figure 1.
Layout and measurement of JPA. (a) Mask drawing showing the whole JPA with the SQUID array in red and an on-chipflux bias line (FBL) in light blue. The wiring layer in dark blue features bonding pads, shunt and coupling capacitors, and theground plane. The holes in the ground plane trap magnetic flux. (b) Simplified measurement setup with the JPA enclosed in thedashed box. The FBL carries both a pump tone and a dc current used to bias the SQUIDs and, thus, modify the resonance frequencyof the device. The probe tone enters through a circulator and three-wave mixing within the JPA allows the pump tone to producesignal and idler photons according to f pump = f probe + f idler . A second circulator (not shown) further enhances the isolation froma subsequent cascode of post-amplifiers. (c) Scanning electron micrograph showing a part of the SQUID array and the interdigitalshunt capacitor cut with a focused ion beam to fine-tune the resonance. A close-up of the other end of the array is shown in theSupplement. (d) Tuneability of the resonance frequency of Device A. Shown are a single up sweep and a down sweep of currentmeasured with the pump off. The arrow indicates a deterministic branch selected for subsequent measurements. To better estimate the noise added by the JPA,the system noise temperature is determined with theY-factor method [44]. Essentially, the power spectraldensity at the output of the JPA is surveyed witha spectrum analyzer while the JPA is subject toan impedance-matched resistive noise source with acontrolled temperature. The source temperature isvaried between 59 mK and 852 mK independentlyof the JPA temperature that is held constant at30 mK with closed-loop control. The measurementsare carried out with the Device B and the fullsetup is shown in the Supplement. The systemnoise temperature, referenced to the JPA input, takesits minimum value of 165 mK close to the halvedpump frequency [Fig. 4(a)]. Since the noise addedby the JPA is reasonably independent of the offset [Fig. 4(b)], we may take the average with the invertedvariances as weights. This yields a noise estimate of105 mK ±
4. Degenerate gain
In a dispersive sensor, such as the nano-calorimetersof Ref. 24, it is possible to choose the excitationand readout in such a way that the rf carrierand the information-carrying signal are in differentquadratures. In this situation, it is possible to utilize lux-driven Josephson parametric amplifier for sub-GHz frequencies Figure 2.
Systematic characterization of Device A at 10 mK.At each operating point determined by a static flux bias current,the pump power is optimized first and the gain is then adjustedwith the pump frequency. (a) The best signal-to-noise ratioimprovement and corresponding gain while limiting to gainsunder 20.5 dB. The quantities are in respect to a reference thatis measured with the JPA detuned and the pump switched off.(b) 1-dB compression points of gain at a probe offset of -10 kHzfrom the halved pump frequency where the gain is maximal. Ataround 590 MHz the pumping was unsuccessful. (c) Lorentziangain profiles as a function of the signal frequency at 24 selectedoperating points. The target gain of each measurement was15 dB.
551 552 553 554 555 556
Frequency (MHz) A pp r o x i m a t e ga i n ( d B )
40 mK80 mK150 mK220 mK290 mK360 mK430 mK500 mK600 mK720 mK800 mK920 mK1450 mKT =
40 100 1000
Temperature (mK) -505 G ( d B ) Figure 3.
Approximate gain profiles for Device A at 553 MHzat varying temperatures of the sample stage starting from a gainof 20 dB at 40 mK. In the absence of reference data, the recordedsignal is normalized to the edges of the peak. The pump poweror frequency are not re-optimized during heating proving thetemperature robustness of the amplifier. Inset: change in gainfrom 40 mK, as a function of temperature. squeezing to de-amplify the carrier and to amplifythe signal. This may be used to effectively increasethe dynamic range of the later stages of the readout.Ideally, the amplification does not add any noise if aJPA is used to perform the squeezing.To observe squeezing in the degenerate mode ofthe JPA, where the pump is exactly at twice theprobe frequency, a brief experiment is carried outwith the Device B. Using a single rf source, thepump is synthesized with a frequency doubler and therelative phase θ of the probe is controlled as shown inFig. 5(a). The JPA gain as a function of θ is π -periodicas expected, and amplification and de-amplificationalternate. The JPA is thus capable of squeezing [45].However, here we do not attempt a proper investigationof the quadratures to determine how much vacuumsqueezing is attainable. lux-driven Josephson parametric amplifier for sub-GHz frequencies Figure 4.
Noise temperature of Device B at 600 MHzdetermined with the Y-factor method using a calibrated noisesource. Data from Ref. 22 are added for comparison. (a) Systemnoise temperature T sys as a function of the probe offset fromthe halved pump frequency. The separated contribution of theHEMT amplifier to T sys is the smallest at zero offset where theJPA gain is maximal. (b) The noise added by the JPA is thedifference between the system noise temperature and the partadded by HEMT as well as the input noise: 30 mK in recentexperiments and 40 mK in Ref. 22. Figure 5.
Device B in the degenerate mode at an operatingtemperature of 30 mK. The probe frequency reads f probe = f pump = f idler = 601.85 MHz. (a) A frequency doublergenerates the phase-locked pump tone. The probe is directed toa voltage-controlled electronic line stretcher (ELS) to adjust thephase difference between the probe and the pump. Afterwards,the VNA is used to calibrate the phase versus the control voltage.(b) Gain (circles) and SNR improvement (triangles) as a functionof the calibrated phase. The latter is determined by comparing toa measurement where the JPA is detuned with applied magneticflux. The observed difference of 3 dB between the gain maxima islikely caused by varying pump power, due to voltage dependencein the reflection coefficient of the ELS: a signal leaking backwardsto the input of the doubler interferes with the signal followingthe direct path. lux-driven Josephson parametric amplifier for sub-GHz frequencies
5. Conclusion
We have overcome all the major issues discoveredwith the previous-generation JPA [22], and we haveattained robust performance over a wide frequencyrange without sacrificing bandwidth, gain, or dynamicrange. Additionally, we have minimized the amountof TLS-hosting dielectrics and their participation ratiowith the SWAPS [32] fabrication process. Thisrenders the JPA relatively insensitive to temperature,facilitating its use at variable mK-temperatures as onlyminor corrections to the JPA operating parameters areneeded. Furthermore, the JPA is now flux-pumped attwice the readout frequency of the nano-calorimeter,easing the filtering required to avoid back-action suchas residual heating by the pump. As an important steptowards sub-GHz sensor readout at a fidelity beyondthe standard quantum limit [46], squeezing has beenobserved in the degenerate mode of the JPA.The noise added by the JPA has decreased to105 mK at 600 MHz. This can largely be attributedto better isolation from the HEMT post-amplifier bymeans of an additional circulator. However, the addednoise remains at an elevated level with respect tothe lower bound set by the input thermal noise at30 mK, likely due to poorly thermalized attenuators[47] or a fundamental limit of the amplifier itself.The noise performance also remains inferior to thatof a microstrip SQUID amplifier with a reported noisetemperature of 48 mK at 612 MHz [44]. Yet, we havedemonstrated a sub-GHz JPA that is well suited forintegration into a nano-calorimetry [24] or -bolometry[26] apparatus and we will pursue the latter goal in afuture experiment.
Acknowledgments
We thank Paula Holmlund for sample preparation,Harri Pohjonen for help with lithographic masks,and Mikko Kiviranta for operating the FIB. Weacknowledge the fruitful discussions with Olli-PenttiSaira, Roope Kokkoniemi, Mikko M¨ott¨onen, and JukkaPekola. This work was performed as part of theAcademy of Finland Centre of Excellence program(projects 284594, 312059, 251748, and 284621). Thework also received funding from Academy of Finlandproject QuMOS (project numbers 288907 and 287768),Future Makers Funding Program by TechnologyIndustries of Finland Centennial Foundation and Janeand Aatos Erkko Foundation. eferences [1] Bradley R, Clarke J, Kinion D, Rosenberg L J,van Bibber K, Matsuki S, M¨uck M and Sikivie P2003
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Slawomir Simbierowicz , Visa Vesterinen , , Leif Gr¨onberg ,Janne Lehtinen , Mika Prunnila and Juha Hassel VTT Technical Research Centre of Finland Ltd & QTF Centre of Excellence,P.O.Box 1000, FI-02044 VTT, FINLAND QCD Labs, COMP Centre of Excellence, Department of Applied Physics, AaltoUniversity, P.O. Box 13500, 00076 Aalto, FinlandE-mail: [email protected]
May 2018 a r X i v : . [ c ond - m a t . s up r- c on ] M a y Dynamic range
The limitation of dynamical range at low frequency is circumvented by adding 200SQUIDs in series, enabled by the expression for the bifurcation power of a parametriccurrent pump [1]: P bf = N χ Qφ ω √ ηQ e Z LC , (1)where N is the number of Josephson elements in series, ω / (2 π ) is the drive frequencyof the device, Q and Q e are the total and external quality factors, and χ = √ Q − η − .The quantity η = 1 / (1 + L (1)geom /L (1)J ) is controlled with the geometric and Josephsoninductances. Finally, φ = ~ / (2 e ) is the reduced flux quantum. Our devices weredesigned using a ratio of L (1)geom /L (1)J = 0 .
30 and a characteristic impedance of Z LC = p L/C = 8 . L = L (1)geom + L (1)J and C is the total capacitance of the resonator.Determining quality factors from experiments performed on Device A, we get Q e = 230and Q i = 1771 at 601 MHz. Then, χ = 0 .
06 and P bf = -92.9 dBm which is 1 dB higherthan in Ref. 1 and sufficient for amplifying nano-calorimeter signals. Junction structure
Figure 1.
False colored scanning electron micrograph showing a cross-section of a testjunction sharing the layer composition of the JPAs. A high-resistivity silicon substratecarries the structure with the following elements: 1. the niobium cross-overs and theflux bias line; 2. the insulating ALD aluminium oxide layer; 3. the niobium groundplane and wiring layer; 4. a silicon dioxide spacer used for the passivation of junctionside-walls; 5. the Nb-Al/AlO x -Nb trilayer containing the tunnel junctions. SQUID close-up
Figure 2.
Scanning electron micrograph showing one end of the niobium SQUIDarray. The flux bias line (black) can be seen crossing over the center conductor.
Full cryogenic setup
Figure 3.
Detailed wiring schematic. The JPA lies inside an aluminum-Amumetal4K magnetic shield (gray line) thermalized to the mixing plate (MP) of a dilutionrefrigerator (BlueFors Cryogenics LD-250). A twisted pair of wires carries DC currentto the on-chip coil biasing the SQUID chain on the device. The DC bias is combinedwith the RF pump using two bias-tees: the second one terminates the pump line.Both probe and pump RF tones are heavily attenuated in steps. Two back-to-backcirculators protect the JPA from HEMT ( T N = 10–13 K) back-action. Gain andnoise measurements are performed using the VNA and the spectrum analyzer. Theredundant RF line was previously used for cancellation of the pump tone duringcurrent pumping. All RF instruments are synchronized with a rubidium frequencystandard (SRS FS725, not shown). (a) Measurement of Device A happens at 10 mK.The combination of the directional coupler and the bias-tee thermalizes the JPA tothe MP. (b) Measurements for Device B are performed at 30 mK and the signal isrerouted through a noise source: a heated 30 dB attenuator (XMA Corp.) inside acopper enclosure (small dashed box) weakly thermalized to the MP. Automated pump procedure
Before executing the automated pumping procedure, some parameters need to beselected: the range of dc coil currents, the probe power, the probe offset from the pump,and the power window during the probe power sweep that measures the 1-dB saturationpoint of the amplifier. Except in the saturation measurement, the probe power shouldbe low enough that a small change in power does not affect the gain and high enoughfor an adequate signal-to-noise ratio, especially when the pump has been turned off. Weuse a spectrum analyzer to determine SNR and gain accurately. Additionally, in orderto benefit from the higher dynamic range at high signal frequencies, the probe power isboosted by 10 dB there. Choosing the parameters may require manual operation of theamplifier.The automated script is executed at each dc coil current. It starts by fitting toS-parameter data procured by the VNA and sets the pump frequency to -3 MHz fromtwice the obtained resonance frequency. For an expected gain-bandwidth product of3 MHz, this puts the halved pump at a frequency offset reasonably detuned from theJPA resonance. Next, the pump power is increased until the JPA goes into the modeof parametric oscillation [2] which manifests itself as a strong peak measured with thespectrum analyzer at the halved pump frequency. The power is then lowered in stepsof 0.1 dBm until the oscillation disappears. We call this point the bifurcation powerbecause of the hysteresis of the parametric oscillation. We further decrease the pumppower by 0.15 dBm, arriving right below the so-called line of maximum gain [3]. Afterthis, the pump frequency is increased in steps of 100 kHz to find the range of availablegain while the probe trails the halved pump frequency by the predefined offset of -10 kHz.The spectrum analyzer is used to measure the probe power and the noise in a 20 kHzwindow centered at the probe frequency.Whenever reaching a gain threshold of 20 dB, the user-defined sweep of the probepower is performed with the VNA. Similarly, at a gain threshold of 15 dB the VNAmeasures the gain-bandwidth product using a 5 MHz window centered at the gainmaximum. To calibrate the gain, the JPA is momentarily detuned and the pump isturned off to measure the reference without changing the settings of the VNA. Finally,the script re-visits all the frequency windows on the spectrum analyzer but with theJPA detuned and the pump turned off. This establishes the references for the probepower and the noise. eferences [1] Vesterinen V, Saira O P, R¨ais¨anen I, M¨ott¨onen M, Gr¨onberg L, Pekola J and JuhaHassel 2017
Superconductor Science and Technology New Journal of Physics Physical Review B76