Characterization of a flux-driven Josephson parametric amplifier with near quantum-limited added noise for axion search experiments
?a?lar Kutlu, Arjan F. van Loo, Sergey V. Uchaikin, Andrei N. Matlashov, Doyu Lee, Seonjeong Oh, Jinsu Kim, Woohyun Chung, Yasunobu Nakamura, Yannis K. Semertzidis
CCharacterization of a flux-driven Josephson parametric amplifier with nearquantum-limited added noise for axion search experiments
C¸a˘glar Kutlu,
1, 2, a) Arjan F. van Loo, Sergey V. Uchaikin, Andrei N. Matlashov, Doyu Lee, b) Seonjeong Oh,
1, 2
Jinsu Kim,
1, 2
Woohyun Chung, Yasunobu Nakamura,
3, 4 and Yannis K. Semertzidis
1, 2 Korea Advanced Institute of Science and Technology, Daejeon 34051, Republic of Korea Center for Axion and Precision Physics Research, Institute for Basic Science, Daejeon 34051,Republic of Korea Center for Emergent Matter Science (CEMS), RIKEN, Wako, Saitama 351–0198,Japan Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Meguro–ku,Tokyo 153–8904, Japan (Dated: 22 January 2021)
The axion, a hypothetical elementary pseudoscalar, is expected to solve the strong CP problem of QCD and isalso a promising candidate for dark matter. The most sensitive axion search experiments operate at millikelvintemperatures and hence rely on instrumentation that carries signals from a system at cryogenic temperaturesto room temperature instrumentation. One of the biggest limiting factors affecting the parameter scanningspeed of these detectors is the noise added by the components in the signal detection chain. Since the firstamplifier in the chain limits the minimum noise, low-noise amplification is of paramount importance. Thispaper reports on the operation of a flux-driven Josephson parametric amplifier (JPA) operating at around2 . I. INTRODUCTION
Axions are spin-0 particles that emerge as a result ofthe Peccei-Quinn mechanism which was originally pro-posed as a solution to the strong CP problem of quan-tum chromodynamics . They were also identified asviable candidates for all or a fraction of the cold darkmatter in our universe . It is possible to detect axionsupon their conversion to microwave photons, using res-onant cavities immersed in high magnetic fields . Sincethe axion mass is unknown, these detectors employ amechanism to scan different frequencies correspondingto different axion masses. The scanning rate of suchdetectors scales with 1 /T , where T sys is the systemnoise background characterized in units of temperature.It can be decomposed as T sys = T cav + T add , where thefirst term denotes the noise temperature accompanyingthe signal itself and the second one denotes the noiseadded by the signal detection chain. Throughout thiswork, noise temperature refers to the added noise unlessotherwise stated. In order to reduce T cav , the cavity iscooled to millikelvin temperatures. If the first amplifierhas sufficiently high gain ( G ), its noise temperature ( T )will be the dominant contribution to T add as given bythe well-known relation : T add = T + T rest G where T rest is the noise temperature of the whole chain except thefirst amplifier. Amplifiers based on Josephson junctions a) [email protected] b) Present address: Samsung Electronics, Gyeonggi–do 16677, Re-public of Korea including microstrip superconducting quantum interfer-ence device amplifiers (MSA) and JPA have already beenshown to be capable of gains higher than 30 dB, and noisetemperatures approaching the quantum limit . Whilean MSA has an internal shunt resistor used for biasingwhich hinders noise performance , by design the JPArequires no resistive element to operate. Several exper-iments presently searching for dark matter axions havealready adopted the JPA as the first amplifier . Inthis work, the frequency coverage, gain and noise proper-ties of a flux-driven JPA for use in an axion dark matterexperiment operating around 2 . : S n ( f, T ) = hf (cid:16) hfk B T (cid:17) − (1)where h is Planck’s constant and k B is Boltzmann’sconstant. The first term in the brackets is the meannumber of quanta at frequency f at the bath temper-ature T and the second term is the contribution fromzero-point fluctuations. The lower limit on noise tem-perature for linear phase-insensitive amplifiers is givenby T Q = lim T → S n ( f, T ) / ( k B ) = hf / (2 k B ) which isabout 55 . . . T add ≈
120 mK is achieved. This corresponds toa T sys ≈
190 mK for an axion haloscope experimentrunning at a bath temperature of 50 mK. The lowerbound for T sys is given by the standard quantum limit T SQL = 2 T Q which is about 110 mK at 2 . a r X i v : . [ c ond - m a t . s up r- c on ] J a n II. FLUX-DRIVEN JPA
The equivalent circuit diagram of the tested device isshown in Figure 1. It consists of a superconducting quan-tum interference device (SQUID) attached to the end ofa coplanar waveguide λ/ C c ) to the transmission line for the signalinput and output. The SQUID acts as a variable induc-tor whose value depends on the magnetic flux passingthrough its loop. In the setup, a superconducting coil isused to provide the necessary DC flux ( φ ) through theSQUID loop in order to tune the resonance frequency( f r ). Parametric amplification is achieved by modulatingthe flux through the SQUID using a pump signal. Thepump tone is provided by a separate transmission line in-ductively coupled to the SQUID. The JPA is operated inthe three-wave mixing mode where the pump ( f p ), thesignal ( f s ), and the idler ( f i ) frequencies satisfy the rela-tion f p = f s + f i . The signal input and output share thesame port. A circulator is used to separate them. Sincethe λ/ . Figure 2 shows a schematicfor the axion search experimental setup. ϕ C c InOut
Pump λ /4 Coil FIG. 1: Equivalent circuit diagram of the JPA sample.The JPA was fabricated by photolithography of a Nblayer, deposited on a 0 . . Thesample was attached to a printed circuit board (PCB)and the transmission lines were bonded with Al wires.The PCB was fixed onto a gold plated copper structureand placed inside a superconducting coil. The wholestructure was covered tightly with a lead shield andattached to the mixing-chamber (MC) plate using agold plated copper rod. III. MEASUREMENTS
When there is no pump tone present, the JPA can bemodeled as a resonator with a well-defined quality factorand resonance frequency which are functions of flux. Theresonance frequency is estimated from the frequency do-main phase response using a parameter fit . The phaseresponse is obtained by doing a transmission S-parametermeasurement using a vector network analyzer (VNA) inthe configuration as shown in Figure 2. The resonance frequency was measured as a function of the coil current(see Figure 3). It was found that the minimum observableresonance frequency was at 2 .
18 GHz and the maximumwas 2 .
309 GHz. The lower bound is due to the frequencyband of the circulators which spans from 2 .
15 GHz to2 .
60 GHz. At the lower frequencies, the JPA becomesmuch more sensitive to flux noise due to a higher ∂f r ∂φ .This work mainly focused on operation with frequenciesabove 2 . CAV
U1U2
MC PlateStill Plate4K PlateIN1 IN2 OUT
HEATER
NoiseSource
JPA
ShortPump
PUMP
20 dB10 dB20 dB 20 dB10 dB20 dB
AttenuatorBandpass fi lterDirectional CouplerCirculatorIsolatorBias-tee50 Ω termination NbTi CoaxCuNi CoaxSplitter RT Plate
VNA SASG
40 dB
20 dB20 dB20 dB
REFPLANE (800 mK) (50 mK)
FIG. 2: The experimental setup used in all thecharacterization measurements. SG, VNA, and SAstand for the signal generator, vector network analyzer,and spectrum analyzer, respectively. During this work,the switch that selects between the cavity and the noisesource was always kept at the position shown in thefigure. The ports IN2 and OUT were used to directlymeasure the JPA characteristics, bypassing the cavity.The microwave short element shown next to the JPAwas used to bypass the JPA for calibrationmeasurements. U1 and U2 are HEMT amplifiers withnoise temperatures of 1 . ± i b ), the pumpfrequency ( f p ), and the pump power ( P p ). The mea-surements shown in this work had i b confined to the re-gion where the flux through the SQUID loop is given by − . φ < φ <
0, where φ is the magnetic flux quantum.Therefore, f r can be unambiguously converted to φ or i b .All experiments began with a transmission measurement,with the resonance frequency tuned to 2 .
18 GHz. Thisbecomes the baseline measurement to be used for theduration of the experiment. When the result was com-pared to a separate measurement, in which a microwaveshort was put in place of the JPA, it was found that thebaseline obtained via such an off-resonance measurementwas at most 0 . G J ) was estimated by dividing the transmis-sion magnitude response with the baseline’s magnituderesponse.To investigate the gain behavior, a sweep over the pa-rameters i b , f p , P p was made and the maximum gain wasmeasured at each point. After each i b tuning step, theresonance frequency is estimated by performing a phasemeasurement and applying a parameter fit. With the de-tuning defined as δ = f p / − f r , the equigain contourshad a minimum in necessary pump power around δ = 0,as shown in Figure 4a. It was observed that for resonancefrequencies above 2 .
299 GHz the minimum starts to shiftto lower detunings which is attributed to pump-inducedshifts in resonance frequency . Figure 4b shows that theslice of δ = 0 can be used to achieve peak gains of up to30 dB along the frequency range of the device.FIG. 3: Resonance frequency versus flux obtained bysweeping the coil current and measuring the phaseresponse at each step. One period corresponds to acurrent of 324 . µ A. The inset shows the fit performedto estimate the resonance frequency for each appliedflux.To investigate noise temperature, a methodology sim-ilar to the well-known Y-factor method was used. A50 Ω cryogenic microwave terminator was used as thenoise source. A bias-tee was attached in front for im-proved thermalization of its inner conductor. These twocomponents were fixed onto a gold-plated copper platealong with a ruthenium oxide temperature sensor anda 100 Ω resistor functioning as a heater. This platewas then fixed onto the MC plate so that the dominantthermalization was through a thin copper wire attachedto the MC plate. The noise source was connected tothe switch input using a superconducting coaxial cable,which provides thermal isolation while minimizing losses.Using a PID controller, the terminator temperature couldbe adjusted from 50 mK to 1 K without affecting the MCplate temperature. The noise power generated by thenoise source was measured using a spectrum analyzer (a) P p ( d B m ) f r = 2.290 GHz G J ( d B ) (b) f r (GHz)80757065605550 P p ( d B m ) = 0 5811141720232629 G J ( d B ) FIG. 4: (a) Maximum gain measured as a function ofdetuning and pump power for a flux bias correspondingto f r = 2 .
29 GHz. (b) Maximum gain as a function offrequency and pump power with f p = 2 f r .(SA) with 1 kHz resolution bandwidth after being ampli-fied by the JPA and the rest of the signal detection chain.The power spectra were recorded at noise source temper-atures ( T s ) of 60, 120 and 180 mK. The power values wereconverted into power spectral densities (PSD) by dividingthem with the noise bandwidth corresponding to the SAsettings used. Before each PSD measurement, the JPAgain and passive resonance were measured. From thesemeasurements, it was concluded that there were neithergain changes nor resonance shifts. From the obtainedPSD values S ( T s ), a fit was done to a function of thefollowing form independently for each frequency bin (seeFigure 5) : S ( T s ) = (2 G J − G L G tot G J ( S n ( T s ) + rk B T n + γ ) (2) P S D ( W / H z ) × T s =0.060 K T s =0.120 K T s =0.180 K200 100 0 100 200 (kHz)0.00.10.20.30.40.50.6 T n ( K ) T s (K)01234 P S D ( W / H z ) × =10 kHz=30 kHz=50 kHz FIG. 5: The upper plot shows the set of power spectraobtained during a noise temperature measurementperformed for a tuning at f r = 2 .
305 GHz with f p = 2 f r . The offset ν is defined as ν = f − f r where f is the center of the frequency bin at which the powerwas measured using the spectrum analyzer. T s is thetemperature of the noise source. The inset shows threevertical slices which were fit with Equation (2). Thelower plot shows the estimated noise temperature of thewhole chain as a function of ν .where S n ( T s ) is the noise PSD of the source, G tot isthe total gain seen from the reference plane, G L is theloss factor between the 50 Ω terminator and the refer-ence plane and T n is the noise temperature. The ref-erence plane is at the end of the superconducting cableconnected to the noise source (see Figure 2). Here, r and γ are factors that are explained in Appendix A.Since the amplifier needs to be tuned along with thecavity during the axion experiment, the noise temper-ature was investigated at different frequencies. Themeasurements were done in 5 MHz steps from 2 .
28 to2 .
305 GHz. At each step, the pump power and resonancefrequency were tuned such that the JPA gain was about 20 dB. From these measurements (Figure 6) a minimumnoise temperature of 120 mK was observed at 2 .
28 GHz. G t o t ( d B )
550 kHz T n ( K ) Frequency (GHz)
FIG. 6: Total gain and the noise temperature of thewhole chain for 6 tuning points with 19 . ± . P ).The P was measured at δ = 0 for different frequen-cies and different pump powers corresponding to differentgains. It is evident from the results (see Figure 7) thatan axion-like signal with an expected power of −
180 dBmis far from saturating the device. While saturation fromnarrowband signals is avoidable to a certain extent, it wasobserved that thermal noise at the input can also saturateand alter the behavior of the device. For frequencies be-low 2 .
28 GHz with gains above 23 dB, the device startedshowing saturated behavior with thermal noise when thenoise source temperature was raised above 120 mK, whichwas done to measure noise temperature. While this doesnot necessarily mean that the device is unusable belowthese frequencies, it renders the direct measurement ofthe noise temperature using a noise source unreliable forthese frequency and gain regions.
IV. CONCLUSION
In conclusion, a flux-driven JPA, tunable in the range2 . .
305 GHz was demonstrated and determined tobe operational for use in axion search experiments. Theadded noise temperatures of the receiver chain were mea-sured using a noise source at a location as close as pos-
18 19 20 21 22 23 24 G J (dB)154152150148146144142 P d B ( d B m ) f r =2.28 GHz f r =2.29 GHz f r =2.30 GHz FIG. 7: Saturation measurements for three different f r .Each measurement was done by sweeping the signalpowers from the VNA and observing at which inputpower the gain reduces by 1 dB. The horizontal axiscorresponds to the unsaturated gain measured with thelowest signal power available from VNA.sible to the origin of the axion signal. With an addednoise temperature of 120 mK the system was shown toreach T sys ≈ . T SQL . This is the first record of T sys be-low 2 T SQL for an axion haloscope setup operating below10 GHz. The saturation input power for the JPA wasobserved to be more than adequate for an axion-like sig-nal. Currently, the tested JPA is being used as part of aKSVZ sensitive axion search experiment at the Cen-ter for Axion and Precision Physics Research (CAPP).The system is taking physics data with a scanning speedthat has been improved more than an order of magnitude.We expect that further optimization of the JPA designcould result in improved instantaneous bandwidth andtuning range.This work was supported by the Institute for Basic Sci-ence (IBS-R017–D1–2021–a00) and JST ERATO (GrantNo. JPMJER1601). A. F. van Loo is supported by aJSPS postdoctoral fellowship.
Appendix A: Noise Temperature Estimation
The output PSD from a component with its input con-nected to a matched source can be written as : S O = GS in + S added (A1)where S in is the source PSD, G is the power gain ofthe component, and S added is the noise added by it.The noise temperature ( T n ) is a measure of the addednoise at the output of a component. By convention, itis defined as if it is for noise entering the device itself: T n = S added / ( k B G ). The entire detection chain (see Fig-ure 8), from the reference plane to the spectrum analyzer, JPA SA
D EB C F O G L G R ,T nR G c G c REFPLANE NS A G J ,G I FIG. 8: The simplified model used for the noisetemperature estimations conducted in this work. Boldletters denote the power gains of components. Thereference plane marks the input of the detector chain.Arrows denote the flow of power entering the nodesshown with a small circle. G L is a composite gain factorfor everything between the noise source and thereference plane. G c is the circulator gain factor. G J isthe signal and G I is the idler gain for the JPA. Theamplifier gain G R and noise temperature T nR containthe effects of all elements after the last circulator,including SA noise. For simplicity, circulators areassumed to have complete rotational symmetry withrespect to their ports and to be completely identical toeach other.can be described as a single composite component with G = G tot and noise temperature T n .The noise temperature can be defined for a situationsimilar to the experimental one where a narrowband ax-ion signal with power A is present. This signal entersthe chain from a source connected to the reference plane.Assuming the source is thermalized to the MC plate withthe temperature T f , then the defining relation for T n canbe written as : S O = G tot ( Aδ ( f − f s ) + S n ( T f ) (cid:124) (cid:123)(cid:122) (cid:125) S in + k B T n ) (A2)where S O is the PSD at the output, G tot is the totalpower gain for the signal from the reference plane, S n is the noise coming from the source itself. The mainidea here is that if one has a reliable estimate of T n ,and understands the source environment well ( S n ( T f )),it is straightforward to estimate A without the preciseknowledge of G tot . This is possible since S O can be easilymeasured at two frequencies f s and f (cid:48) s using a spectrumanalyzer. Provided that | f s − f (cid:48) s | is small enough so that T n is approximately the same for both frequencies, A can be estimated from these two measurements. Thisapproach forms the basis of the analysis methods appliedin axion dark matter search experiments .The detection chain consists of passive components,the JPA and the HEMT amplifiers. Each one of theseadds noise in a different way. A passive component atphysical temperature T f has S added = (1 − G ) S n ( T f ).The HEMT amplifier noise is usually estimated frommeasurements. The JPA adds noise by two main mech-anisms. The first one is by amplifying the input noiseat the idler mode onto the signal mode. The second oneis via the losses or other dissipation mechanisms insideor before the sample. Ideally, the latter can be madezero, whereas the former will approach to the half-photonadded noise in the limit of a 0 K bath temperature.Using the model shown in Figure 8, it is straightfor-ward to write a relation for the output PSD. For clarity,the explicit frequency dependence of the thermal noise S n and of the gains will be omitted. Also, the approxi-mation S n ( f, T ) ≈ S n ( f p − f, T ) will be denoted with theshorthand S nf = S n ( f, T f ). This approximation has lessthan 30 ppm error given that | f − f p | <
100 kHz. Notethat 100 kHz is the typical bandwidth for the JPA testedin this work. Furthermore, the transmission characteris-tics of the microwave components will be assumed to notvary on a scale of 100 kHz. Using the gain symbols forcomponents as shown in Figure 8, the power flow at eachnode in terms of their PSD is written as : S B = G L S A + (1 − G L ) S nf S C = G c S B + (1 − G c ) S nf S D = G c S C + (1 − G c ) S nf S E = G J S D + G I S D + G J S j S F = G c S E + (1 − G c ) S nf S O = G R ( S F + k B T nR ) (A3)The idler gain is denoted by G I , and is substitutedusing G I = G J − in the following derivations. Asshown in Equation (A3), the idler contribution to thenoise appears as G I S D . The symbol S j denotes an un-known noise density added at the JPA stage which doesnot contribute to the quantum limit but rather containslosses or other mechanisms of stationary noise. Note thatthe noise propagating back from the later stages is alsoincluded in S j . The output S O can be written for twocases. In the first case, the noise source is operational attemperature T s , and in the second case, a signal sourceat temperature T f is connected to the reference plane.The former case describes the measurement situation,whereas the latter case is only used to define T n in termsof the parameters in the model. For the first case, i.e. S A = S n ( T s ), the output PSD can be written as : S (1) O = G R G c G L (2 G J − (cid:124) (cid:123)(cid:122) (cid:125) G noise [ S n ( T s ) + S α ] (A4) S α = λ (1) S nf + G J S j (2 G J − G c G L + k B T nR G c G L (2 G J − λ (1) = β l + β c G L + β c G c G L + β c G c G L (A6) β • ≡ G • − S B = Aδ ( f − f s ) + S nf , is written as : S (2) O = G J G c G R (cid:124) (cid:123)(cid:122) (cid:125) G tot [ S B + k B T n ] (A8) k B T n = λ (2) S nf + S j G c + k B T nR G c G J (A9) λ (2) = (cid:20) G J − G J + (cid:18) β c + β c G c (cid:19) G J − G J + β c G c (cid:21) (A10)Here, the unknowns are S j , T nR and G R . It is clearfrom Equations (A9) and (A10) that T n approaches T Q as expected in the limits of G J (cid:29) G c →
0, and G L →
0. Using Equations (A4), (A5) and (A9) , S (1) O can berewritten as : S (1) O = G tot r ( S n ( T s ) + rk B T n + γ ) r = G J G L (2 G J − γ = (cid:16) λ (1) − rλ (2) (cid:17) S nf (A11)This relation is used to perform a fit with G tot and T n as the fit parameters. For the estimations, the param-eters G L and G c were taken as − .
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