Design and Operational Experience of a Microwave Cavity Axion Detector for the20− 100 µeV Range

S. Al Kenanya, M.A. Anilb, K.M. Backesa, B.M. Brubakerc, S.B. Cahnc, G. Carosid, Y.V. Gurevichc, W.F. Kindelb,S.K. Lamoreauxc, K.W. Lehnertb, S.M. Lewisa, M. Malnoub, D.A. Palkenb, N.M. Rapidisa, J.R. Roota, M.

Simanovskaiaa,∗, T.M. Shokaira, I. Urdinarana, K.A. van Bibbera, L. Zhongc

aDepartment of Nuclear Engineering, University of California Berkeley, Berkeley CA, 94720 USAbJILA and the Department of Physics, University of Colorado and National Institute of Standards and Technology, Boulder CO, 80309

USAcDepartment of Physics, Yale University, New Haven CT, 06511 USA

dPhysical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore CA, 94551 USA

Abstract

We describe a dark matter axion detector designed, constructed, and operated both as an innovation platform for newcavity and amplifier technologies and as a data pathfinder in the 5−25 GHz range (∼ 20−100µeV). The platform is smallbut flexible to facilitate the development of new microwave cavity and amplifier concepts in an operational environment.The experiment has recently completed its first data production; it is the first microwave cavity axion search to deploya Josephson parametric amplifier and a dilution refrigerator to achieve near-quantum limited performance.

Keywords: axion, dark matter, Josephson Parametric Amplifier, microwave cavity, standard quantum

limit, superconducting magnet

1. Introduction

The axion is a hypothetical pseudoscalar arising fromthe Peccei-Quinn mechanism to protect the strong inter-action from CP-violating effects. Also, an axion in the1− 100 µeV mass range is a compelling dark matter can-didate. A comprehensive review of the particle physics ofthe axion, its cosmological and astrophysical significance,and experimental searches for it can be found in Ref. [1].

The axion, like the π0, can couple to two photons, oneof which may be virtual. Sikivie thus proposed a prac-tical detection strategy based on the resonant conversionof the dark matter axion to a single microwave photoncarrying its full energy (mass + kinetic) in a high-Q cav-ity permeated by a strong magnetic field [2, 3? ]. Theresonant conversion condition is that the axion mass ma

is close to the resonant frequency νc of a cavity modewith an appropriate spatial profile; more precisely, |δν| =∣∣νc −mac

2/h∣∣ . ∆νc, where ∆νc is the linewidth of the

mode. The axion kinetic energy distribution is generallyassumed to be Maxwellian, parametrized by the virial ve-

locity⟨v2⟩1/2 ∼ 10−3 c. The signal is thus monochromatic

to a part in 106, with linewidth ∆νa = ma

⟨v2⟩/h ∆νc;

see Fig. 1.The axion conversion power in such a microwave cavity

∗Corresponding authorEmail address: simanovskaia@berkeley.edu (M.

Simanovskaia)

detector is

Psig =

(g2γα2

π2

~3c3 ρaΛ4

)×(

β

1 + βωc

1

µ0B2

0V Cmn`QL1

1 + (2δν/∆νc)2

).

(1)

Eq. (1) is valid in any self-consistent set of units; thetwo sets of parentheses contain theory and detector pa-rameters, respectively. On the theoretical side, α is thefine-structure constant, Λ = 77.6 MeV encodes the depen-dence of the axion mass on hadronic physics, and the localaxion dark matter density ρa and coupling constant gγare the parameters that experiment can constrain.1 It isconventional to fix ρa = 0.45 GeV/cm3 [4] and quote lim-its on gγ , a model-dependent dimensionless coupling thatis related to the physical coupling gaγγ appearing in theaxion-photon Lagrangian by gaγγ =

(gγα/πΛ2

)ma. In

the KSVZ (DFSZ) benchmark axion model, gγ = −0.97(0.36), independent of the axion mass.

The experimental parameters in Eq. (1) include themagnetic field strength B0, the cavity volume V , and sev-eral factors characterizing the cavity mode, with ωc =

1The value of Λ used in our analysis was obtained from chiralperturbation theory [3]. Note also that Λ4 = χ(T = 0), where χ isthe QCD topological susceptibility which may be calculated on thelattice. The most recent lattice calculation, in Ref. [? ], obtainedΛ = 75.6 MeV, which would result in an 11% enhancement of thesignal power.

Preprint submitted to Elsevier February 24, 2017

arX

iv:1

611.

0712

3v2

[ph

ysic

s.in

s-de

t] 2

3 Fe

b 20

17

2πνc. The coupling between the cavity mode and the re-ceiver used to detect the signal, parametrized by β, reducesthe quality factor from Q0 to QL = Q0/ (1 + β). The formfactor Cmn` parametrizes the overlap between the cavitymode and the external magnetic field. For the cylindricalgeometry commonly used in cavity axion detectors, Cmn`may be written

Cmn` =

(∫d3x z · e∗mn`(x)

)2V∫

d3x ε (x) |emn`(x)|2, (2)

where emn`(x) is the normalized electric field profile of themode, ε(x) = 1 is the dielectric constant inside the cavity,and B0 is axial and homogeneous. Nodes in the electricfield profile lead to cancellations in the form factor, andthus it is only appreciable for low-order TM0n0 modes.

Inserting typical values for the detector described inthis work, which are close to the limits of present technol-ogy, the peak signal power is Psig ∼ 5×10−24 W at KSVZcoupling, a factor of 109 below room-temperature thermalnoise power in a typical cavity bandwidth. Thus cryo-genic operation and a low-noise receiver are necessary forany practical realization of a cavity axion detector. Theintrinsic spectral resolution of the linear receivers used incavity axion searches to date implies that the relevant noisebandwidth is ∆νa rather than ∆νc, and moreover that ameasurement at any given cavity frequency simultaneouslyprobes ∼ ∆νc/∆νa independent values of the axion mass.Further improvement in the signal-to-noise ratio (SNR)may then be obtained by averaging the cavity noise for atime τ . The preceding discussion is formalized in the Dickeradiometer equation [5], in which the SNR is defined as

Σ =Psig

kBTsys

√τ

∆νa. (3)

For any phase-insensitive linear receiver the systemnoise temperature Tsys may be written

kBTsys = hνNsys = hν

(1

ehν/kBT − 1+

1

2+NA

), (4)

where the three additive contributions correspond respec-tively to a blackbody gas in equilibrium with the cavityat temperature T , the zero-point fluctuations of the black-body gas, and the input-referred added noise of the re-ceiver. The price we pay for spectral resolution is thequantum limit NA ≥ 1/2 on the added noise of any phase-insensitive linear receiver [6], which together with the sec-ond term in Eq. (4) implies a “standard quantum limit”Nsys ≥ 1 for microwave cavity axion detection. Theselimits imply that units of quanta, used throughout thiswork, are more appropriate than temperature units forsufficiently low-noise receivers.

The axion mass is a priori unknown, so the cavity mustbe tuned in small discrete steps after each measurementinterval τ ; the SNR for any given value of the axion mass

is then given by a quadrature sum of terms with the formof Eq. (3). An average scan rate is obtained by solvingfor 1/τ and multiplying by the frequency step size. Withthe simplifying assumption that the detector parametersremain approximately constant over its tuning range, thescan rate is

dν

dt≈ 4

5

QLQaΣ2

(g2γα2

π2

~3c3ρaΛ4

)2

×(1

~µ0

β

1 + βB2

0V Cmn`1

Nsys

)2

,

(5)

where Qa =(⟨v2⟩/c2)−1

is the “quality factor” of the ax-ion signal, and the factor of 4/5 comes from a sum over thesquared Lorentzian factors characterizing the effect of theaxion’s changing detuning from the cavity mode. This is agood approximation for any frequency step size . ∆νc/2;qualitatively, a smaller step size implies that the same sen-sitivity can be achieved with smaller τ , and the two effectscancel out in the scan rate. Note also that, while Eq. (1)is maximized at critical coupling (β = 1) for a given Q0,the scan rate is maximized for an overcoupled cavity withβ = 2. Eq. (5) is the most useful figure of merit for thecavity axion search.

FFT Pre-amp

Magnet

Cavity

!"a

!"c

Figure 1: Schematic of the microwave cavity search for dark matteraxions. The axion signal is designated by the narrow peak (red)within the bandpass of the cavity (pink).

The detector described in this work builds upon expe-rience from the Axion Dark Matter eXperiment (ADMX),a larger platform designed to operate initially in the sub-GHz range. ADMX entered into operation in 1996 with aphysical temperature of T ≈ 1.5 K [4]. The readout chain,initially led by a high electron mobility transistor amplifier(HEMT) [4], was later upgraded to include a microstrip-coupled SQUID amplifier (MSA) [7]. A dilution refriger-ator has recently been incorporated into the setup, andcommissioning is underway.

Our detector was conceived as both an innovation plat-form and a data pathfinder for the microwave cavity axionsearch in the 5 − 25 GHz range (∼ 20 − 100 µeV axion

2

masses; 1 GHz = 4.136 µeV). The next decade in fre-quency brings new challenges for both microwave cavitiesand receivers. On the cavity side, preserving the aspectratio, the volume of the cavity V ∼ ν−3, resulting in anincreasing penalty in conversion power with increasing fre-quency. This requires insightful cavity designs to maintainuseful volume at higher frequencies without sacrificing theform factor or incurring an unacceptable density of in-truder TE modes in the spectrum. The absolute machin-ing and alignment tolerances will also become tighter forsmaller structures, to avoid mode localization. Anotherchallenge is that MSAs do not work well above a gigahertz;to circumvent this problem we have introduced Josephsonparametric amplifiers (JPA) that are ideal for the 5 GHzrange. Together with a dilution refrigerator (DR), builtinto our design from the beginning, the JPA allows us topush down towards the Standard Quantum Limit and thusremain competitive with lower-frequency limits despite theloss of sensitive volume.

At the same time, this frequency range presents an op-portunity to deploy entirely novel technologies that promisedramatic new capability for the microwave cavity search.A technology that will be investigated in the near futureis a receiver based on squeezed states of the vacuum tocircumvent the Standard Quantum Limit. Innovations tobe tested in the microwave cavity domain include photonicband gap resonators, designed to eliminate the spectrumof TE modes which otherwise mix with the TM010 modeof interest as it is tuned, resulting in a loss of sensitivity atmode crossings and making it more difficult to track theTM010 mode. Other schemes to be investigated are theapplication of distributed Bragg reflector based resonatorschemes, and thin-film Type II superconducting coatingsto improve the quality factor Q of the cavity.

2. Description of Experimental Setup

Fig. 2 presents an overview of the experiment, sited atthe Wright Laboratory of Yale University, and its integra-tion. The microwave cavity and the magnetically-shieldedcanister housing the JPA are assembled on a gantry sus-pended from the dilution refrigerator. The gantry assem-bly is lowered by crane into the bore of the magnet, whichis located in a room below the floor level of the lab con-taining the electronics and computer control.

The DR precooling system and the magnet cryogenicsystem use pulse tube and Gifford-McMahon cryocoolers,respectively. This allows operation of our detector withoutexternal liquid cryogens, providing major simplification ofoperations, and a substantial reduction in operating costs.However, such a cryogen-free system relies on an uninter-rupted supply of electrical power as the consequences of amagnet quench can be severe (see section 2.2).

The individual systems are described in detail below.

2.1. Dilution Refrigerator

The DR was manufactured in 2007 by VeriCold Tech-nologies (subsequently acquired by Oxford Instruments),and was among the first commercially available external-cryogen-free DRs. The only major modification was thereplacement of the VeriCold pulse tube with a Sumit-omo RDK-415D Gifford-McMahon cryocooler (in retro-spect this was a poor choice because of excessive vibra-tion). In addition, instead of using the DR’s Lakeshoretemperature bridge to control the mixing chamber plate,we have incorporated a custom temperature PID-feedbackcontroller at the mixing chamber level, resulting in reduceddelay and improved performance.

The cooling power of the DR is about 150 µW at 127mK, which is the system operating temperature. Thisoperating temperature was chosen because we observedstrong modulation of the JPA gain by vibrational fluctua-tions at lower temperatures; the temperature-dependenceappears to originate in the circulator’s magnetic shielding,whose susceptibility and heat capacity both fall below 4K. In addition, operating at higher temperature resultsin reduced temperature excursions from mechanical mo-tions and actuation of the microwave switch, due to theincreased heat capacity of the mixing chamber plate. Thecavity, JPA, mixing chamber, and still temperatures aremonitored with calibrated ruthenium oxide sensors.

The support gantry is a tripod with copper alloy legsand copper rings at both ends, which are clamped to thebottom of the DR’s mixing chamber plate and to the upperendcap of the cavity, respectively. The equilibration timefor changes in the mixing chamber temperature to prop-agate to the cavity temperature (measured at the lowerendcap) is on the order of a few minutes. This might besurprising as the cavity is constructed of stainless steel,which has very low thermal conductivity. However, thecavity has a thick Cu plating (0.125 mm) which providesa sufficient thermal link for a short equilibration time.

The cavity and gantry are thermally shielded with anextension of the DR still shield. This extension comprisestwo demountable sections with dimensions 17.8 cm OD× 45 cm and 13.0 cm OD × 53.3 cm for the upper andlower sections, respectively. At the bottom of the stillshield extension, there is a G-10 fiberglass disk attachedvia a stainless steel rod, which centers the shield extensionand maintains the 0.5 cm gap between the still shield andmagnet bore. The still shield extension was originally con-structed from 0.16 cm sheet copper with welded seams, butthat was deformed when we experienced a magnet quench(more information in section 2.2). Subsequently, we con-structed a replacement using heavily plated stainless steel(0.125 − 0.250 mm), prompted by our experience that aheavy copper plating provides a good thermal link.

The DR and magnet share a single common insulat-ing vacuum space. Extensions of the 4 K and 77 K DRstages overlap the corresponding stages at the top of themagnet, and thermal contact is provided by finger stock

3

Microwave Cavity (copper)

3He/4He Dilu8on Refrigerator

9.4 Tesla, 10 Liter Magnet Josephson Parametric Amplifier

Figure 2: Overview of the experiment and its integration.

that presses between the extensions and the correspond-ing magnet thermal stages and also by blackbody radia-tion between the overlapping surfaces. This design allowsthe DR/cavity/still shield assembly to be easily insertedinto and removed from the magnet by use of an overheadhoist. The gas flow and electronic control lines are longenough that only a few cables must be disconnected to in-sert or remove the cryostat. The DR itself is supportedfrom above, and the magnet is on a cart equipped withjack screws. When the DR is lifted, the magnet can berolled away and the DR lowered again to its support, al-lowing easy and safe access to the assembly below the DR.To insert the DR, the magnet is rolled to the appropri-ate location, the DR and extension are lowered into themagnet, and the jack screws are used to raise the magnetuntil the corresponding DR and magnet cryostat vacuumflanges contact, after which the flanges are bolted together.

The DR operating alone has a cooldown time of about14 hours; with the gantry, cavity, and magnet, the cooldowntime to 127 mK cavity temperature is 72 hours.

2.2. Magnet

The magnet and its controller were designed and man-ufactured by Cryomagnetics, Inc., based on an existingdesign for a gyrotron system with similar field require-ments. As mentioned already, the magnet is a pulse-tube

cooled system, requiring no external cryogens or heliumgas, and operates in a persistent mode. The magneticfield is ramped up to a maximum of 9 T over 8 hours; therate is limited by heating of the magnet itself and by eddycurrent heating of the cavity/gantry/still shield assembly.An interesting feature of the heating due to the rampingis that the heat load inferred from the rise in cavity tem-perature is largest when the field is between about 4 and7 T, which we attribute to electrons being polarized in thestainless steel cavity body.

Our design specification was that the field needs to behomogenous at a level such that the perpendicular (radial)field at the inner surface of the cylindrical cavity barrel isless than 50 G. For future versions of this axion detector,we are interested in coating this inner surface with su-perconducting thin films to improve Q0. The mentioneddesign specification is a requirement for a thin film super-conducting layer to remain effective in the presence of astrong magnetic field. The idea is that the vortices formedby the perpendicular component of the field would be ofsufficiently low density and mobility to not contribute sig-nificantly to radiofrequency power loss in the film [8]. Themodification of the gyrotron design includes a set of su-perconducting coils in series with the main magnet thatcancel the axial field over a 15.2 cm region to less than50 G. This is the location of the JPA and its shield.

4

The magnet bore diameter is 14 cm inside the mainsolenoid and steps up to 18.4 cm further up, where thebucking coils are supported. The effective and homoge-neous region in the field maximum extends axially over atleast 25 cm.

An unfortunate disadvantage of a cryogen free sys-tem is that it relies on an uninterrupted source of power.The time to quench after a power loss is about 4 minutesfor our system. In principle, Yale has fast acting emer-gency backup power, but due to system upgrades andother issues, this emergency power was not available inearly March 2016, when an unscheduled power outage re-sulted in a magnet quench, causing significant mechani-cal/structural damage to the DR and coaxial microwavelines. The repairs of this damage took two months, andfortunately none of the DR’s 3He was lost; in spite ofthe mechanical damage, the gas flow lines were in no waycompromised. Most of the forces due to this quench werecaused by the large copper rings at the lower part of thegantry, and by the copper still shield extension. As notedabove, we have replaced the copper still shield extensionwith another made from copper-plated stainless steel. Infuture designs, most of the gantry components will be con-structed from copper-plated stainless steel, which shouldlead to more than a 100-fold reduction in forces during aquench.

2.3. Microwave cavity

The initial microwave cavity for the experiment con-sists of a right circular cylinder of stainless steel, electro-plated with oxygen-free high conductivity (OFHC) cop-per. After annealing, the cavity achieves a near-theoreticalmaximum value of the quality factor Q, as limited by theanomalous skin depth [9],

δanom =

(√3 c2me vF

8π2 ω n e2

)1/3

, (6)

where me is the mass of the electron, n the electron densityin the metal, vF the Fermi velocity, and ω the angularfrequency. For copper, n = 8.5 × 1022 cm−3 , and vF =1.57× 108 m/s.

The cavity employed for the initial data run was 25.4 cmin height and 10.2 cm in diameter. A single large diameterrod, Ø 5.1 cm, was used to tune the cavity (see Fig. 2).The rod pivoted around an off-axis ceramic axle, such thatits radial position could be adjusted from touching thewall to centered within the cavity. This produced a dy-namic range of the TM010-like mode of 3.6− 5.8 GHz. Tomake finer frequency steps, we used a tuning vernier, a3.2 mm diameter alumina rod, of variable insertion depthinto the cavity. With the tuning rod centered, the cav-ity is more properly described as an annular cavity, whichhas the largest volume for a TM010-like mode at a givenfrequency. The upper endcap had ports for two antennas,one with weak coupling used to measure the cavity’s re-sponse in transmission and one whose insertion depth (and

14 cm

56 cm

Field compensation coil

JPA magnetic shielding

Main magnet coil

Mixing chamber plate

Still plate

Cavity

Figure 3: Layout of the experiment. The red volume is the DR vac-uum shield, the blue volume is the magnet body, and the orangeshaded region is the volume bounded by the still shield and its ex-tensions. The magnet’s 70 K and 4 K shields are not shown belowtheir interface with the fridge shields.

thus coupling β) was variable. The penetrations and ser-vices of the cavity are shown in Fig. 4. Around 5.8 GHz,typical values were C010 ∼ 0.5 for the form factor andQ0 ∼ 30, 000 for the unloaded cavity Q.

Our cavity development program has involved preci-sion metrology and modeling in simulation environmentssuch as CST Microwave Studio. Fig. 5 displays a sim-ulation of the TM010-like mode and a mode map of thecavity. Another innovation of this axion search is the useof the bead perturbation method to measure field profilesin a microwave cavity. To date, these have been longitu-dinal profiles along the full length of the cavity at a singletransverse position, derived by translating a small dielec-tric bead (alumina, ε ∼ 10) on a Kevlar line controlled bya stepper motor and some pulleys. For a dielectric bead,the shift in mode frequency in perturbation theory is givenby:

∆ω

ω=− (ε− 1)

2

VbeadVcav

E(r)2

〈E(r)2〉cav(7)

where Vbead and Vcav indicate the volume of the dielec-

5

Cavity Barrel

Tuning Rod

Antenna

Tuning Vernier

Weak Port

(a)

(a)

(b)

(b) (c)

(c)

Compression Springs

Kevlar Lines

Coax

Dielectric Stem

Figure 4: Top and side view of the cavity upper endcap, detailing thepositions and design of the main tuning rod, tuning vernier, signalinjection port, and the variable-coupling antenna.

tric bead and cavity, respectively [10]. For the TM010-likemode, the electric field should be longitudinally invariant,and thus the shift in frequency as a function of longitudi-nal distance should be constant. In the microwave cavityaxion search, the bead perturbation technique is usefulin the design and testing of new resonators, to determinethe symmetry of a mode, to confirm or correct alignmentand machining tolerances to eliminate mode localization,and to identify mode-crossings regions where the modeshave become substantially admixed, and thus the formfactor Cmnl of the TM010-like mode has begun to dimin-ish (Fig. 6). A detailed study of microwave cavities for thedark matter axion experiment bringing together metrol-ogy, simulation, and EM characterization will be the sub-ject of a future publication. For the present, a few obser-vations in relation to experiments an order of magnitudelower in frequency [4, 7] may be useful.

First, for cavities of characteristic dimension O(10 cm),machining and alignment tolerances to avoid significantmode localization [11] are approaching the limit of goodmachine shop standards and readily available components.Even the transverse play of the inner race of the bearingfor the axle of the tuning rod, of order 50 − 75µm, cancause a tilt in the TM010 axial electric field profile of sev-eral percent. Second, modeling revealed that for the largetuning rod used in this experiment (r/R = 0.5), the formfactor C010 only approached the value associated with theidealized case (i.e. the rod electrically joined to the topand bottom endcaps) for gaps G < 250µm. Third, itis becoming clear that engineered features necessary forpractical cavities (e.g. penetrations for the antenna cou-pling, diagnostic ports, etc.) have a significant effect onthe mode, and are likely to be more important at higherfrequencies given the larger relative size of mechanical andelectrical components penetrating the cavity.

3.75%

4.25%

4.75%

5.25%

5.75%

f%(GH

z)%

θ%(degrees)%180%135%90%45%0%

θ

n%=%0%%

1%2%

3%

4%

TM01n%

TE%

(a)

(b)

Figure 5: (a) CST Microwave Studio simulation of the TM010-likemode with the tuning rod in the middle of the cavity. (b) Measuredmode map of the cavity, as a function of the pivot angle of thetuning rod within the cavity. The frequencies of the TM01n modesdecrease steeply with increasing radial distance of the tuning rodfrom cavity center. TE modes (indicated by yellow arrows) becomeapparent approaching mode crossings with TM modes; the TE modefrequencies are largely insensitive to the position of the tuning rod.

2.4. Mechanical Controls

The experiment has three mechanical systems: the ro-tary cavity tuning, the adjustment of the vernier, and theadjustment of the antenna. All mechanical controls arebased on Applied Motion Products HT-23-595D NEMA23, high-torque, double-shaft stepping motors, driven bymodel 5000-235 STR2 microstepping controllers. One sideof each stepping motor double shaft is coupled to a tenturn potentiometer that encodes the net rotation angle.The vernier and antenna stepping motors are coupled tothe experiment using 10:1 worm gear reductions, while thecavity tuning motor is coupled directly. The rotary mo-tions are coupled into the vacuum using three K.J. LeskerFMH-25A Dynamic O-Ring Shaft Seal feedthroughs.

Within the cryostat, the antenna and vernier are con-trolled by 0.36 mm Kevlar thread lines that are wound

6

Z [Step]

5.104 5.108 5.112 5.116 5.100 5.104 5.108 5.112 5.116

S12 S12

f [GHz]

-40

-80

-60

-100

-120

TM010 TE

(a) (b) -40

-80

-60

-100

-120

0 20 40 60

5.1048

f [GHz] 5.1047

5.1046

0 20 40 60 5.1124

5.1126

5.1128

5.1130

5.1132

0 20 40 60 5.1111

5.1112

5.1113

5.1114

0 20 40 60

5.1136

5.1134

5.1132

5.1130

Figure 6: Cavity spectra for two different rod positions, as theTM010-like mode approaches a crossing with a high-order TE mode.For each rod position, the plots above the main panels show the shiftsin frequency of the two modes, as a small dielectric bead is translatedaxially through the cavity. The frequency shift at each axial positionZ is proportional to the square of the local electric field according toperturbation theory (see Eq. 7), thus elucidating the nature of themode. (The spectra in the main panels are with the bead removedfrom the cavity.) (a) At a separation of 8 MHz, the purity of theTM010-like mode is confirmed by the flat axial field profile shownon the top left. (b) At a separation of 2 MHz, the lower-frequencymode now clearly reflects a strong admixture of both a high-orderTE mode along with the TM010-like mode.

directly onto the rotary feedthrough shaft that extendsinto the vacuum. At each stage of the DR, the lines passthrough 3.2 mm ID, 2.5 cm long tubes that are thermallylinked to the DR stage and serve as radiation shields. Thelines are routed to the cavity by use of nylon pulleys withball bearings (McMaster-Carr 3434T13) that have beenultrasonically cleaned to remove all lubricants that wouldfreeze at low temperatures. It should be noted that Kevlarexpands on cooling, and the spring tensioning of the linesmust absorb the length change lest the lines loosen andpossibly fall out of the pulley grooves.

The antenna and vernier are mounted on fixtures thatallow motion along the cavity axis only. A spring is com-pressed when the antenna or vernier is pulled out of thecavity by the Kevlar thread, ensuring smooth and reversiblemotion.

Rotary motion for the tuning rod system is deliveredto the mixing chamber level by use of a cryogenic G-10tube (6.4 mm diameter, 0.79 mm wall). The ends of theG-10 tube are fitted with glued-in brass extensions whichallow the use of set screws to couple to the feedthrough atthe top, and to the mechanics at the mixing chamber end.At each DR stage, a 2.5 cm section of brass tubing (6.4mm ID, 0.4 mm wall) is glued to the G-10, and a loose-fitting brass tube (1.9 cm long, 0.4 cm ID) is slipped overeach 2.5 cm section and coupled to the stage using copperbraid. At the 4 K stage, the G-10 tube inside has a brassblackbody radiation block.

Just below the mixing chamber, a pulley and torsion

spring system is used to transfer rotary motion from theupper G-10 tube to a cryogenic G-10 tube (also 6.4 mm)along the DR and magnet axis, supported at the mixingchamber end by a ceramic bearing. A kevlar line connectsthe brass extension of the upper shaft to the 10.2 cm di-ameter pulley, and the torsion spring ensures that the lineis always pulled taut. The lower G-10 shaft runs throughthe JPA magnetic shield and down to the cavity, where a1.4:1 anti-backlash gear reduction provides the final radialdisplacement required to couple to the tuning rod axle.

These mechanical systems have generally provided thelevels of control needed for the antenna and vernier; allthree required appropriate selection of the microsteppingresolution and had negligible heat loads at the operat-ing temperature. The cavity bearings had some stictiondue to alignment issues, and this resulted in sometimeserratic positioning, and a slow drift to final equilibriumafter stepping. In operation of the experiment, the finefrequency control was done using the vernier, with less fre-quent larger rotations of the tuning rod which required upto 15 minutes of waiting for the rod to come to its equi-librium position. We plan to eliminate this problem byimproving the cavity mechanics and replacing the room-temperature tuning rod drive system with an AttoCubepiezoelectric rotator at base temperature.

2.5. Josephson Parametric Amplifier

A JPA is a nonlinear LC resonator capacitively coupledto a transmission line with an array of SQUIDs playing therole of the nonlinear inductance (see Fig. 7). By applying aDC flux through the SQUID loops, the resonant frequencycan be tuned over several gigahertz. Driving the systemnear its resonance with a strong pump tone enables am-plification of a weak signal nearby in frequency. The gainof this amplification can be traded off with the bandwidthover which it occurs by adjusting the pump power andfrequency.

When the signal of interest is centered about the pumptone, the amplification process is noiseless (insofar as theJPA’s internal loss is negligible) but phase-sensitive. Inthis mode of operation, the signal quadrature in phasewith the pump is amplified by

√G, while the one 90 de-

grees out of phase is squeezed by 1/√G, where G is the

single-quadrature power gain. When detuned completelyto one side of the pump, the signal is amplified independentof its phase, but the JPA’s intermodulation gain impliesthat an extra noise term enters from the image frequency,symmetric with the signal about the pump. In this con-figuration the added noise of a lossless JPA is equal to thethermal noise at the image frequency, giving rise to thequantum limit NA = 1/2 at zero temperature.

It is important to note that operating in the phase-sensitive mode by itself does not eliminate the half-photonof noise associated with the zero-point motion of the black-body gas in the cavity (i.e., the second additive term inEq. (4)). Moreover, the factor of two improvement innoise temperature for a lossless JPA in the phase-sensitive

7

Figure 7: Microphotograph of JPA circuit. The SQUID array (ap-proximately 150 µm long) is highlighted in red on the left; the cir-cuit’s resonance is determined by the SQUID inductance and thegeometric capacitance (blue). The circuit is coupled to a 50 Ω trans-mission line through a smaller capacitance (green). The surroundingsuperconducting ground plane is waffled in order to pin magneticflux vortices in place and keep them from the SQUID array.

mode is exactly canceled by the loss of information in onequadrature. Thus, phase-sensitive operation offers no im-provement in axion search sensitivity unless we can alsoeliminate the zero-point motion of the input noise, e.g.,by initializing the cavity in a squeezed state [12]. R&Dwith this aim is ongoing within the collaboration; for thepresent, we operate the JPA in the phase-insensitive mode.

The JPA currently installed in the experiment has amaximum resonant frequency of 6.5 GHz and a gain band-width product

√GB = 26 MHz. Half a flux quantum

threaded through the area of a single SQUID loop in thearray tunes the circuit through its full 2 GHz range; thisextreme flux sensitivity necessitates specialized magneticshielding, detailed in section 2.6. The circuit was fabri-cated using a Nb/Al-Ox/Nb trilayer process; the nonlinearinductance comes from 20 SQUIDs in series, where eachSQUID comprises two Josephson junctions of critical cur-rent 6 µA in parallel. The flux bias is delivered througha coil comprising about 20 turns of superconducting wirewound around the copper box housing the JPA chip.

The JPA can be turned into a passive mirror very sim-ply by tuning off the pump tone and tuning the resonantfrequency ∼10 linewidths from the frequency of interestvia the flux bias; we use this process to calibrate the ab-solute JPA gain. We set a gain target of ' 21 dB, belowthe onset of bifurcation inferred from deviations from agaussian distribution in the JPA’s quadrature noise spec-tra, but large enough to overwhelm the ∼ 20 quanta addednoise of the HEMT amplifier which follows the JPA in thereceiver chain. At this operating point the JPA bandwidthis about 2.3 MHz.

Figure 8: Schematic representation of the parameter space for JPAbiasing. All features are intended for illustrative purposes only; theydo not represent real measurements or calculations. The pump poweris on the vertical axis and the detuning ∆ between the pump fre-quency and the 0-power LC resonance of the JPA circuit is on thehorizontal axis. The black curves are contours of constant gain, andthe black arrows represent the path taken by the bias procedure out-lined in the text, intersecting each gain curve at the minimum-powerpoint. Beyond the critical point (∆c, Pc), the system begins to oscil-late and can be bistable or multistable. We operate at lower power(red dot) to avoid this region of parameter space.

The procedure used to bias the JPA to this target gainis illustrated schematically in Fig. 8. The detuning ∆ be-tween the LC resonance and the pump frequency is ad-justed by varying the flux bias. The gain is optimizedwith respect to detuning at constant pump power, andthe pump power is increased if the gain remains too lowafter this optimization; the pump frequency remains fixedthroughout the biasing process. With this procedure wealways obtain within 0.2 dB of the target gain, and alwaysoperate at the point of lowest pump power for a given gain,where the JPA is most stable. The biasing procedure isfully automated and incorporated into the LabVIEW codethat controls the data acquisition (see section 2.8). It typ-ically takes ∼ 6 s to adjust the bias parameters after eachcavity tuning step.

Maintaining high gain throughout the tuning rangerequires the pump power and flux bias to be controlledto 0.01 dB and 2 parts in 105, respectively. The lattercondition corresponds to 300 nA current resolution withour present bias coil, which we easily obtain using a 20-bit ADC with 10 µV resolution and a homemade currentsource with 1 mA/V transconductance.

2.6. Magnetic Shielding

Shielding of the sensitive receiver components, in par-ticular the JPA, from the stray field of the 9 T magnetpresents a complicated engineering problem. Also of con-cern are magnetic gradients at the location of the JPA thatlead to excess amplifier noise due to gain fluctuations inthe presence of mechanical vibrations. We have success-fully attained the degree of magnetic shielding required forstable JPA operation, as shown in Fig. 9(b).

8

−2 −1.5 −1 −0.5 0 0.5 1 1.5 24

4.5

5

5.5

6

6.5

Bias Current (mA)

Bare

JPA

Res

onan

ce (G

Hz)

5/2015 measurements of JPA tuning range

no field9 T in main magnet

6.5$

6.0$

5.5$

5.0$

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4.0$'2$$$$$$$$$$$$$$$$$$'1$$$$$$$$$$$$$$$$$$$0$$$$$$$$$$$$$$$$$$$1$$$$$$$$$$$$$$$$$$$$2$$$$$$$$$$$$$$$$$$$$$$$$$$Bias$Current$(mA)$$$$$$$$$$$$

JPA$Freq

uency$(GHz

)$• $B$=$0$T$• $B$=$9$T$

(a) (b)

Persistent coils

Figure 9: (a) Magnetic shielding of the JPA, including three superconducting persistent coils and (b) JPA frequency vs. flux bias current,showing no change in frequency as the main magnetic field is ramped from 0 − 9 T. The residual flux through the JPA is inferred to be∆Φ ' 0.001 flux quantum.

The outer elements of the JPA shield can be seen inFig. 9(a). The first level of shielding is from the buckingcoils described in section 2.2. The next level of shield-ing comprises three persistent superconducting coils thatprovide a quasi-active shield against flux changes; giventhat they become superconducting before the 9 T field isramped up, the flux inside will be maintained at the orig-inal ambient level. The axial spacing of the coils is notuniform because the bucked field gradient is asymmetric,with slightly higher flux at the lower end of the shieldcompared to the upper. The axial center of the shield islocated at the field minimum.

The superconducting shield coils each comprise 100turns of Supercon Inc. SC-T48B-M-0.7mm Cu-clad NbTiSC wire, with 0.43 mm diameter NbTi core (nominal),0.70 mm diameter Cu cladding, and 0.75 mm diameterHML (Polyimide) insulation. The windings are on 9.3 cmID brass hoop forms and potted with Stycast 2850 FT.After winding, the coil wire ends are trimmed to about15 cm, and the last 5 cm of wire are annealed by heatingto red heat using a MAPP gas torch; this also burns offthe Polyimide insulation. The heated regions are cleanedand smoothed using 400 grit alumina emery paper. Thewire ends were bonded [13] to make a persistent super-conducting connection by use of a Koldweld KBM-9 wirecoldwelding machine; the dies we had available were toolarge, so the outer copper cladding was built up throughacid copper electroplating. After electroplating, the endswere trimmed back 1.6 mm, and the wire ends bonded. Amicrograph analysis of an axially mechanically sectionedbond shows that the NbTi material flowed together at the

center and pushed the copper uniformly in a radial direc-tion from the center.

A similarly wound coil, with 24 cm OD, is clamped tothe bottom of the DR mixing chamber plate. The fringefield of the 9 T magnet is about 300 G in this region;without the coil this is large enough to affect operation ofthe shielded cryogenic circulators (see section 2.7).

The ferromagnetic shield comprises a nested pair ofcylinders made of 1.5 mm thick Amumetal 4 K, annealedper Amuneal’s proprietary process. The bottoms of thecan have welded-on disks, while the tops are closed withtight-fitting lids that overlap 1.25 cm of the cylinder walls.The outer shield (FS1) has length 15.2 cm and OD 8.9 cm,while the inner shield (FS2) has length 13.3 cm and OD7.6 cm. Both top lids have holes for the tuning rod (1.25cm) and also for the JPA thermal link and transmissionline. There are also three small holes, placed at 120 inboth the top and bottom, that allow Kevlar tuning linesto pass through both shields.

Between the two ferromagnetic shields is a Pb super-conducting shield, fabricated from 1.6 mm Pb sheet, whichfits closely on the outside of FS2 and has a removable close-fitting lid. The Pb shield can is about 12.0 cm long, andcovers FS2 to just below the lid. The Pb lid is about 3.8cm long, giving an overlap with the cylinder of 2.5 cm. Theinside of the Pb can is coated with clear acrylic paint toavoid electrical contact and thermal currents, and is gluedto FS2 using Loctite 680.

The final passive shield component is a 0.13 mm thickNb sheet (99.8 % purity, Alfa-Aesar) that lines the innersurface of FS2. This sheet forms an “open cylinder” in

9

that it has no endcaps, and there is an effective axial slitalong its length which allows flux that would otherwise betrapped to escape. The sheet is long enough so that theends overlap by about 1.25 cm, and the sheet is coatedwith acrylic paint, again to prevent the formation of elec-trical contacts. The sheet is glued to the inner surfaceusing Loctite. This sheet enforces a boundary conditionthat the magnetic field must be axially homogeneous alongits surface. The ferromagnetic boundary condition at thebottom and at the lid of FS2 is that the magnetic fieldis perpendicular to the surface, which matches perfectlythe boundary condition imposed by the Nb sheet. Thecombined effect of the superconducting and ferromagneticboundary conditions is to substantially reduce field gradi-ents at the JPA.

A G-10 disk and nylon standoffs are used to supportthe JPA at the axial center of the shield, with a radialoffset to allow the tuning rod to pass. The standoffs arescrewed to 8-32 studs that extend from OFHC Cu spacersbetween the two ferromagnetic shields; the cooling of theshield assembly is through these studs and spacers whichclamp the shields to each other and to a Cu plate affixedto the gantry. The JPA itself is thermally linked to thegantry via a Cu braid that exits through the top of theFS2/Pb shield assembly.

A final active layer of magnetic shielding is provided byfeedback to the JPA flux bias coil, discussed in section 2.7.

2.7. Receiver and microwave measurements

The cryogenic microwave layout and room-temperaturemicrowave/IF layout are depicted schematically in Fig. 10and Fig. A.14 in the appendix, respectively. The receiversignal path is shown in blue in both diagrams. This sectionwill describe the microwave portion of the receiver, the RFinput lines, and other detector functionality which is bestunderstood in reference to Fig. 10 and Fig. A.14. The IFpart of the receiver chain is discussed in section 2.8 below.

The input of the receiver is the cryogenic microwaveswitch S1, which may be toggled to connect the receiverto either the cavity or a termination thermally anchoredto the DR still plate at TH = 775 mK. This switch al-lows us to calibrate the receiver’s added noise in situ viaa procedure described in detail in section 2.9.

The JPA, playing the role of the preamplifier, com-prises the magnetically shielded JPA circuit described insection 2.5, a directional coupler for the pump tone in-put, and a commercial ferrite circulator to separate inputand output signals. Two other circulators are required toisolate the JPA from both the backaction of the second-stage amplifier and its own backaction in reflection fromthe cavity. Signals exiting the JPA are amplified further bya HEMT amplifier at 4 K and another low-noise transistoramplifier at room temperature, and then routed both to acommercial vector network analyzer (VNA) and to an IQmixer (M2) serving as the input of a homemade spectrumanalyzer. The former path is used for cavity and receivercharacterization, the latter for periodic noise calibrations

Figure 10: The cryogenic microwave layout. Blue arrows indicatethe receiver signal path from the cavity to room temperature; blackarrows indicate other paths used for network analysis, noise calibra-tion, and JPA biasing. Component part numbers and manufacturersare listed in Table A.1, in the Appendix.

and the cavity noise measurements constituting the axionsearch dataset.

Swept tones produced by the VNA may be directed viasoftware-controlled switches S2 to any of three fridge in-put lines, through which they are transmitted through thecavity, reflected off the cavity, or sent directly to the JPA,bypassing the cavity. The first two lines are used to mea-sure the cavity parameters νc, QL, and β; the third line isused for JPA biasing and gain measurements, as discussedin section 2.5. Room-temperature attenuators were cho-sen to equalize sweep power incident on the JPA througheach path. Attenuators at 4 K and base temperature re-duce room-temperature thermal noise and the phase noiseof the JPA pump generator to ∼ mK contributions we cansafely ignore.

0.085′′ NbTi/NbTi coaxial cables are used in the re-ceiver signal path between base temperature and 4 K; thesecables (marked SC in Fig. 10) remain superconducting inthe 9 T field due to flux pinning. Stainless 0.085′′ coax isused between room temperature and 4 K in all four linesand down to base temperature in the input lines. All fourcoaxial lines are thermalized at each stage of the fridgewith gold-plated copper clamps; the output line inner con-nectors are thermalized via a bias tee at 4 K with its DCinput shorted to ground. NiCr resistors are used in allcryogenic attenuators and terminations.

10

The room-temperature microwave chain includes threesignal generators from Keysight in addition to the VNA.An 8340B serves as the local oscillator (LO) for both thespectrum analyzer system and the flux feedback systemdiscussed below. An E8257D with an ultra-low phasenoise option (−120 dBc/Hz at 100 kHz detuning from thecarrier) provides the pump tone for the JPA. Finally anN5183B is used to inject synthetic axion-like signals intothe cavity transmission line. All three generators, alongwith the VNA and the digitizer board used in the spectrumanalyzer, lock to a common 10 MHz reference providedby a Stanford Research Systems (SRS) FS725m rubidiumsource (not pictured).

Figure 11: (a) 100 Hz-resolution power spectra from individual 15-minute integrations around a frequency at which a synthetic axionsignal was injected. (b) The optimally weighted combined spectrum,still at 100 Hz resolution. (c) The combined spectrum after rebinningto 5 kHz with weighting that takes into account the axion lineshape;the synthetic axion is clearly visible. See [14] for an overview of theanalysis procedure, which will also be described more thoroughly ina forthcoming publication.

To generate synthetic axion signals with the expectedlinewidth (∼5 kHz for a 25 µeV axion), we inject band-limited white noise into the FM port of the N5183B; thelinewidth is then controlled by the modulation depth. Thesynthetic axion power in the cavity is only known to ±3 dBdue to unknown cryogenic insertion losses of individualcomponents. This uncertainty prevents us from using thesynthetic axion system to precisely calibrate our sensitiv-ity, but it is still useful as a way to validate both the dataacquisition and analysis procedures. Our data acquisitionsoftware includes functionality for blind injection of ax-ion signals at random frequencies throughout a data run;Fig. 11 illustrates one such injection in our first run, witha nominal intracavity power level of −190 dBm.

The room-temperature signal paths used exclusively bythe JPA flux feedback system mentioned at the end of sec-tion 2.6 are shown in pink in Fig. A.14. The JPA flux

bias is modulated at 26 Hz by adding an oscillating cur-rent (controlled by an Agilent 33220A function generator)to the DC bias current set in software. The modulationfrequency is limited by eddy current shielding in the CuJPA enclosure; the amplitude is set to yield a modulationdepth of ∼ 0.1 JPA linewidth. When the DC flux bias isoffset from the value that maximizes the JPA gain at fixedpump power and frequency, the JPA gain is modulatedat the same frequency as the flux with phase determinedby the sign of the offset. When the bias modulation iscentered on the optimal value, only higher harmonics arepresent in the gain variation. Thus the JPA gain varia-tion at the modulation frequency may be used as an errorsignal in an analog feedback system to stabilize the fluxbias.

During noise measurements we use the VNA to injecta weak CW probe tone through the pump line at 30 kHzdetuning from the pump. The function of the feedbackcircuitry in the upper left corner of Fig. A.14 is to providean LO at the appropriate IF frequency to bring the probetone to DC on the IF side of the mixers M3. Both quadra-ture outputs are amplified and squared using AD633 ana-log multipliers; the sum of squared signals is a measure ofthe received power in the probe tone and thus of the JPAgain. A Stanford Research Systems SR510 lock-in ampli-fier measures the variation of the probe tone power at themodulation frequency. By adding the SR510 output tothe bias current we obtain a simple proportional feedbackloop; the SR510 gain, phase, and filtering are chosen toprovide a stable feedback signal. During JPA biasing andsweep measurements the probe tone is not present becausethe VNA is otherwise occupied, so both modulation andfeedback are interrupted by switching off the signal andreference outputs of the 33220A in software.

2.8. Data acquisition and operations

The spectrum analyzer comprises the discrete compo-nents between M2 and ADC in Fig. A.14, along with Lab-VIEW code that computes FFTs, implements image rejec-tion, and averages power spectra in parallel with timestreamdata acquisition. During all noise measurements the LOfor M2 is set 780 kHz above the TM010 mode frequency,the JPA pump is set 820 kHz below the mode, and both IFchannels are sampled by the GaGe Oscar CSE4344 PCIedigitizer board at 25 MS/s.

Each IF channel is sensitive not only to the RF fre-quencies of interest in the lower sideband of the LO butalso to unwanted image frequencies in the upper sideband.The 90 relative phase shift between the two otherwiseidentical IF outputs of an IQ mixer may be exploited forimage rejection: adding the Q output to the I output witha +(−)90 phase shift suppresses the upper (lower) LOsideband. This is the operating principle of commercialimage reject mixers, which only work at particular IF fre-quencies because they implement the required 90 phaseshift in hardware.

11

We implement image rejection in the frequency do-main in software: this scheme works at any IF frequency,with the only possible drawback being that amplitude andphase mismatches in the discrete IF components in thetwo channels can limit the degree of image rejection. Bytaking FFTs of both the I and Q channels and definingX(ω) = (Re[I(ω)]− Im[Q(ω)]) + i (Im[I(ω)] + Re[Q(ω)])we obtain rejection of the upper sideband better than 20dB at all IF frequencies of interest in the power spectrum|X(ω)|2.

More specifically, 14-bit ADCs on the GaGe board dig-itize both channels simultaneously in 5 s segments, thentransfer each segment to PC RAM. The total data in eachsegment across both IF channels is 437.5 MB, and the timerequired to transfer this data to RAM is 1.2 s, which capsthe data acquisition efficiency at 80%. The in situ process-ing code divides each segment into 500 non-overlapping10 ms records in each channel, computes the FFT of eachrecord with no windowing, combines the I and Q FFTscorresponding to the same 10 ms time slice to implementimage rejection, constructs a power spectrum from eachsample of X(ω), and averages all 500 power spectra cor-responding to each segment. All processing for each 5 ssegment occurs in RAM in parallel with the acquisition ofthe next segment. At the end of the data acquisition pe-riod (typically 15 minutes), the power spectra from all seg-ments are averaged together to obtain a single spectrumobtained from 100 Hz × 15 minutes = 9 × 104 averages,which is written to disk.

Thus the output at each tuning step is a heavily av-eraged power spectrum with 100 Hz resolution extendingfrom DC to the 12.5 MHz Nyquist frequency. The usableIF bandwidth extends to ∼ 2.5 MHz, limited by the band-width of the low-pass filters F2. The sampling rate is setso far above this to eliminate the need for a high-orderfilter with significant passband ripple on the output of theIF amps A2. The function of the F1 filters is to attenuateRF leakage into the IF chain.

The 100 Hz spectral resolution is much smaller thanthe ∼ 5 kHz expected linewidth of a virialized axion sig-nal – thus data from this detector can be used to set morestringent limits on the abundance of non-virialized axionswith Qa . 107 without any additional hardware. A tech-nical advantage of the narrow resolution is that it enablesus to better identify and eliminate individual IF bins con-taminated by narrowband interference. Empirically someof these “IF spikes” are associated with ground loops andothers are due to room-temperature electronics. The DCblocks and baluns in Fig. A.14 were added in commis-sioning to eliminate as many of the IF spikes as possible;remaining spikes are flagged and removed as part of theanalysis procedure.

Fig. 12 is a simplified diagram of the IF setup show-ing the most relevant features discussed above, and illus-trating that we further limit our analysis to 1.302 MHzcentered on the cavity. The width of this analysis band isroughly twice the maximum cavity linewidth; axion con-

Figure 12: Diagram illustrating the IF setup for the experiment.Note that the IF frequency axis is reversed relative to the RF frequen-cies of these features. The JPA gain profile and TM010 Lorentzianprofile are plotted using real data and a fit to real data, respectively.Both plots have logarithmic y axes; the absolute scale of the sensitiv-ity plot is arbitrary. The red dot-dashed arrow indicates the probetone created on the opposite side of the pump by the JPA’s inter-modulation gain. Images of the axion-sensitive Fourier componentsaround the cavity, created on the other side of the pump by the sameprocess, are omitted in the diagram for clarity.

version at larger detunings from the cavity mode frequencycontributes negligibly to the SNR. The LO frequency mustlie outside the analysis band to avoid superimposing dif-ferent analysis band Fourier components, and the pumpfrequency must lie outside the analysis band for the JPAto operate in the desired phase-insensitive mode (see sec-tion 2.5). The LO and pump frequencies also cannot beequal, or else the I and Q channels will pick out (not nec-essarily equal) linear combinations of the JPA’s amplifiedand squeezed quadratures, and image rejection will fail.

These constraints indicate that the analysis band shouldbe centered roughly halfway between the LO and pump ineach spectrum. If the analysis band were too close to thepump, the spectrum would be contaminated by both thefeedback probe tone and the pump tone’s phase noise. Ifthe analysis band were too close to DC, 1/f noise woulddominate, and the relative contribution of the 4 K HEMTamplifier to the receiver’s added noise would grow with de-tuning from the pump frequency. The precise positioningof the analysis band was tweaked to exclude bins in whichIF interference was most persistent.

Data acquisition for the experiment is fully automatedand controlled by a LabVIEW program. At the begin-ning of each iteration, the DAQ program tunes the TM010

mode, measures νc and QL with a VNA sweep throughthe cavity transmission line, then sets the LO and pumpfrequencies based on the new value of νc. It optimizesthe JPA gain as described in section 2.5, measures thegain profile over 5 MHz centered on the pump, turns onthe flux feedback system, and makes the 15-minute powerspectrum measurement described above. At the end ofthe power spectrum measurement, the JPA gain and cav-ity transmission are each measured again, to identify driftsof the cavity mode associated with mechanical relaxation(see section 2.3) and unusually large bias flux jumps thatthe feedback system was unable to correct for; roughly0.6% of spectra were cut from our initial analysis due to

12

anomalous flux or frequency drifts. Finally, β is measuredwith a reflection sweep. Noise calibrations (see section 2.9)are also performed intermittently to constrain variation ofTS throughout the run. The average live time efficiencyduring the run is 72%.

All sweep data is saved to disk along with the 100 Hzaveraged power spectrum and critical parameter valuessuch as the LO frequency; this amounts to about 3 MBper iteration. Data is stored locally at Yale and also trans-ferred to a remote server at Berkeley for back-up and longterm storage. The offline analysis procedure is outside ofthe scope of this paper, and will be the subject of a forth-coming publication.

2.9. Noise calibration

A simple way to measure the added noise of any mi-crowave receiver is via a Y-factor measurement, in whichwe connect the receiver input to two 50 Ω loads at knowntemperatures TC and TH , and measure the hot/cold noisepower ratio

Y =PHPC

=NH +NANC +NA

, (8)

where NC(NH) is the thermal noise from the cold (hot)load including the zero-point contribution, and NA is thereceiver’s added noise. We can then solve Eq. (8) for NAto obtain

NA =NH − Y NCY − 1

. (9)

In our experiment, NH comes from a 775 mK termina-tion, and NC comes from the cavity (on resonance) or froma terminated port on the directional coupler in the reflec-tion input line, reflected off the cavity (off resonance; seeFig. 10). NA includes the added noise of the JPA pream-plifier and also the added noise of subsequent amplifiersreferred to the JPA input; of those, in practice only the4 K HEMT contribution is non-negligible.

Eq. (3) indicates that the effect of imperfect powertransmission efficiency η between the cavity and the JPA isto rescale the total noise by 1/η. It is convenient to defineη = η0η1, with η0 between the cavity and S1 and η1 be-tween S1 and the JPA input. Then NA measured by theY-factor method will also include an additional additiveterm

Nη =1− η1η1

(NC +N ′A) , (10)

where N ′A indicates the sum of amplifier contributions.This term arises because the lossy elements that contributeto η1 are at temperature TC (see Fig. 10), and thus atten-uate both the hot load noise and the axion signal but notthe cold load noise. To derive Eq. (10) more formally itis important to note that the lossy elements also generatethermal noise given by (1−η1)NC . Thus our measurementof NA yields only the net effect of the JPA added noise,

HEMT noise, and η1, not any of these components indi-vidually. The effect of η0 on the SNR cannot be measuredin situ; we estimate 0.6 dB from the long superconductingcable and connector losses, and take this loss into accountin calculating our exclusion limits.

The general expression in Eq. (9) also must be modi-fied to account for several specific features of our receiver.First, as noted in section 2.5, in our present configurationthe JPA’s added noise is simply the thermal noise on theopposite side of the pump from the cavity, coupled intothe analysis band via image gain. Thus, the JPA contri-bution to the added noise differs by a known amount inthe two switch configurations: if we define NA to be theadded noise in cold load measurements, the added noisewith the switch pointed at the hot load is NA+NH −NC ,since the loss and HEMT contributions do not change withtemperature. Second, both sides of Eq. (9) are in principlefunctions of IF frequency within any given measurement;in particular the lower JPA gain at the low-IF-frequencyend of the analysis band (see Fig. 12) implies less sup-pression of the HEMT noise and thus larger NA. Third,actuating the switch affects the standing wave pattern dueto slight impedance mismatches on the cryogenic transmis-sion lines, resulting in a small change in the pump powerdelivered to the JPA. We rebias the JPA every time weactuate the switch, but small changes in the JPA gain andbandwidth between switch configurations are still possible.We take all three of these effects into account by general-izing Eq. (9) to

NA(ν) =2 [A(ν)NH − Y (ν)NC ]

Y (ν)−A(ν)+NC , (11)

where A(ν) = GH(ν)/GC(ν) is obtained from the mea-sured hot/cold JPA gain profiles.

During commissioning of the experiment, we consis-tently obtained NA ' 1.35 quanta from Y-factor measure-ments far detuned from the cavity mode independent ofRF frequency. This result is consistent with the addednoise of an ideal nondegenerate JPA at TC (0.63 quanta),' 0.2 quanta input-referred HEMT noise, and an addi-tional ' 0.5 quanta which we can attribute to ' 2 dB lossbefore the JPA. This is a plausible value result for η1, if alittle on the high side.

In cold load noise measurements near the TM010 fre-quency we observe an additional Lorentzian excess Ncav(ν)centered on the IF frequency of the mode. Naively apply-ing Eq. (11) to such measurements would treat the Ncav asa contribution to the added noise (because this expressionassumes the input noise in the cold load is completely char-acterized by the single number TC), and therefore overesti-mate the effect on the total noise Nsys, since NA appears inboth the numerator and denominator of Eq. (8), whereasNC appears only in the denominator.

Therefore, we make the ansatz that the added noise isthe same on-resonance as off-resonance, which allows us toquantify the peak excess contribution Ncav(νc) ' 1 quan-

13

Figure 13: A representative noise measurement. NC (black dottedline) is obtained from thermometry, NA (red dot-dashed line) is ob-tained from the average of off-resonance Y-factor measurements, andNcav (blue dashed line) is from a single Y-factor measurement duringthe data run. Nsys (pink solid line) is the sum of these contributions.

tum. During detector commissioning we examined thedependence of Ncav on the mixing chamber plate tem-perature TC , and observed that the excess vanished forTC & 550 mK. This behavior indicates that Ncav has athermal origin as opposed to being an artifact of feedbackbetween the JPA and cavity mode. Studies of the depen-dence of Ncav on JPA gain and on β further disfavor anysort of feedback explanation, which validates the aboveansatz.

Having established that Ncav is of thermal origin, themost likely culprit is a poor thermal link between the tun-ing rod and the cavity barrel, as the only thermal connec-tion in the present design is through a thin-walled aluminashaft. An improved thermal link through the axle of thetuning rod has been designed and is being implemented; itshould bring the tuning rod into equilibrium with the mix-ing chamber and improve the linear coupling sensitivity by20% 2.

In practice, our in situ noise calibration procedure con-sists of the following steps, repeated for each switch con-figuration: we bias up the JPA to target gain, measurethe gain profile, and take 5 s of noise data, from which weconstruct a power spectrum with 10 kHz resolution, for atotal of 130 data points in the analysis band. We wait 2minutes for thermal transients to die down after actuatingthe switch in either direction; the heat due to each switchactuation is 10 mJ.

From these measurements we obtain a typical totalnoise of Nsys ' 3 quanta on resonance, falling to ' 2.2

2Subsequent to the review of this paper, this thermal link has beenimplemented and the thermal effect has indeed been substantiallymitigated.

quanta at the edges of the analysis band. The overall frac-tional error δNsys ∼ 6% is dominated by ∼ 17% uncer-tainty in Ncav; δNA is only ∼ 4%, and the change in NCis negligible even allowing for a ±20 mK calibration errorin the mixing chamber thermometry. Individual contribu-tions to Nsys are plotted in Fig. 13 for a representativemeasurement. This is the lowest noise demonstrated todate in a microwave cavity axion search.

3. Summary and Conclusions

We have demonstrated in situ near-quantum-limitednoise performance in the first operation of this experi-ment, and achieved sensitivity to cosmologically relevantQCD axion models with gγ ≥ 2.3× gKSVZ

γ [14]. That sen-sitivity this close to the KSVZ line can be reached in anexperiment of 1.5 L volume (c.f. the 200 L volume of theADMX detector [4, 7]) underscores the role of technologyin the microwave cavity experiment. This platform is nowpoised to explore innovative concepts in both amplifiersand cavities to increase sensitivity and decrease scan time.A receiver based on injecting a squeezed state of vacuuminto the cavity by one JPA and reading it out with anotherwill be the first such innovation to be explored [12]. Beat-ing the Standard Quantum Limit with such a receiver hasbeen demonstrated on the bench [15], but this will be theopportunity to validate the feasibility of such a receiver inthe rigors of an actual operating environment.

On the cavity side, a photonic band gap resonator isbeing designed to eliminate all interfering TE modes. Asthe TM mode of interest is tuned in frequency, avoidedcrossings with TE modes block a significant fraction of fre-quency coverage. This loss of coverage has been the bane ofrapid and efficient mass coverage to date. Such structureshave been thoroughly explored in accelerator physics [16,17]; their successful adaptation to the microwave cavityaxion experiment will largely pivot on an effective and re-liable means of tunability. Similarly, cavities are beingexplored adapting design principles of distributed Braggreflector structures, which attain much higher quality fac-torsQ, providing greater sensitivity, and thereby scan rate,for the experiment [18].

4. Acknowledgements

This work was supported under the auspices of the Na-tional Science Foundation, under Grants PHY-1067242,and PHY-1306729, the Heising-Simons Foundation underGrants 2014-181, 2014-182, and 2014-183, and the U.S.Department of Energy by Lawrence Livermore NationalSecurity, LLC, Lawrence Livermore National Laboratoryunder Contract DE-AC52-07NA27344. We thankfully ac-knowledge the critical contributions by Matthias Buhlerof Low Temperature Solutions UG for design of and up-grades to the cryogenic system. M.S. is supported by theNational Science Foundation Graduate Research Fellow-ship Program under Grant no. DGE-1106400.

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Appendix A. Room-Temperature Receiver Layout

Table A.1: Component part numbers.

Thermal Environment Label Type Supplier: Part #

CryogenicBT1 Bias tee Mini-Circuits: ZX85-12G+ (ferrite removed)BT2 Bias tee Anritsu: K250C Circulator Pamtech Inc.: CTH1184K18D Directional coupler Pasternack: PE2211-20HEMT HEMT amplifier Low Noise Factory: LNF-LNC4 8AS1 Switch Radiall: R577443005SC NbTi/NbTi coax Keycom: UPJ07

Room-temperatureA1 RF amplifier Miteq: AMF-4F-04001200-15-10PA2 IF amplifier Homemade: based on Fig. 2 in [19]A3 IF amplifier Mini-Circuits: ZFL-500LN-BNC+A4 IF amplifier Stanford Research: SR445AA5 IF amplifier Stanford Research: SR560AT1 Step attenuator Agilent Technologies: 8496HAT2 Step attenuator Agilent Technologies: 8494HB Balun North Hills: 0017CCDC DC block Inmet: 8039F1 Low-pass filter Mini-Circuits: VLFX-80F2 Low-pass filter Mini-Circuits: SLP-1.9+F3 Low-pass filter Mini-Circuits: BLP-2.5+F4 Low-pass filter Homemade: 3.39 kHz single pole RC filterI1 Isolator Ditom Microwave: D314080I2 Double isolator Ditom Microwave: D414080M1 Mixer Marki Microwave: M1-0408M2 IQ mixer Marki Microwave: IQ0307LXPM3 Mixer Mini-Circuits: ZAD-8+PS1 Power splitter/combiner Mini-Circuits: ZX10-2-71-s+PS2 Power splitter/combiner Mini-Circuits: ZFRSC-2050+S2 Switch Mini-Circuits: ZFSWA2-63DR+

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Figure A.14: The room-temperature microwave/IF layout. Blue arrows indicate the receiver signal path from the top of the fridge to theADCs; black arrows indicate other paths used for network analysis, JPA biasing, providing LO power, and synthetic axion signal injection.Parts of the chain used exclusively by the JPA flux feedback system are indicated in pink. Component part numbers and manufacturers arelisted in table A.1; those shown on the diagram are from Keysight or Stanford Research Systems.

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