First Results from ABRACADABRA-10cm: A Search for Sub- eV ... · ABRACADABRA is a new experimental program to search for axion dark matter over a broad range of masses, 10 12. m a.

First Results from ABRACADABRA-10 cm: A Search for Sub-µeVAxion Dark Matter

Jonathan L. Ouellet,1, ∗ Chiara P. Salemi,1 Joshua W. Foster,2 Reyco Henning,3, 4 Zachary Bogorad,1

Janet M. Conrad,1 Joseph A. Formaggio,1 Yonatan Kahn,5, 6 Joe Minervini,7 Alexey Radovinsky,7

Nicholas L. Rodd,8, 9 Benjamin R. Safdi,2 Jesse Thaler,10 Daniel Winklehner,1 and Lindley Winslow1, †

1Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.2Leinweber Center for Theoretical Physics, Department of Physics,

University of Michigan, Ann Arbor, MI 48109, U.S.A.3University of North Carolina, Chapel Hill, NC 27599, U.S.A.

4Triangle Universities Nuclear Laboratory, Durham, NC 27708, U.S.A.5Princeton University, Princeton, NJ 08544, U.S.A.

6Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, U.S.A.7Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.

8Berkeley Center for Theoretical Physics, University of California, Berkeley, CA 94720, U.S.A.9Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.

10Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.(Dated: March 12, 2019)

The axion is a promising dark matter candidate, which was originally proposed to solve the strong-CP problem in particle physics. To date, the available parameter space for axion and axion-likeparticle dark matter is relatively unexplored, particularly at masses ma . 1µeV. ABRACADABRAis a new experimental program to search for axion dark matter over a broad range of masses,10−12 . ma . 10−6 eV. ABRACADABRA-10 cm is a small-scale prototype for a future detectorthat could be sensitive to the QCD axion. In this Letter, we present the first results from a 1 monthsearch for axions with ABRACADABRA-10 cm. We find no evidence for axion-like cosmic dark mat-ter and set 95% C.L. upper limits on the axion-photon coupling between gaγγ < 1.4 × 10−10 GeV−1

and gaγγ < 3.3 × 10−9 GeV−1 over the mass range 3.1× 10−10 eV – 8.3× 10−9 eV. These results arecompetitive with the most stringent astrophysical constraints in this mass range.

INTRODUCTION

The particle nature of dark matter (DM) in the Uni-verse remains one of the greatest mysteries of contempo-rary physics. Axions are an especially promising candi-date as they can simultaneously explain both the parti-cle nature of DM and resolve the strong-CP problem ofquantum chromodynamics (QCD) [1–6]. Axion-like par-ticles (ALP) are generically expected to have a couplingto electromagnetism of the form [7]

L ⊃ −1

4gaγγaFµνF

µν = gaγγaE ·B, (1)

where gaγγ is the axion-photon coupling. The QCD axionis predicted to have a narrow range of couplings propor-tional to the axion mass, while a general ALP may haveany gaγγ . In this work, “axion” refers to a general ALP.Axion DM (ADM) with mass ma � 1 eV behaves todayas a classical field oscillating at a frequency f = ma/(2π)[3, 4]. The Lagrangian (1) implies that a time-dependentbackground density of ADM modifies Maxwell’s equa-tions. In particular, in the presence of a static magneticfield B0, ADM generates an oscillating magnetic field,Ba, as if sourced by an effective AC current density par-allel to B0 [8],

Jeff = gaγγ√

2ρDMB0 cos(mat). (2)

Here ρDM is the local DM density, whichwe take to be 0.4 GeV/cm3 [9, 10]. The ABroadband/Resonant Approach to Cosmic AxionDetection with an Amplifying B-field RingApparatus (ABRACADABRA) experiment, as firstproposed in [11], is designed to search for the axion-induced field, Ba, generated by a toroidal magnetic field(see also [12] for a proposal using a solenoidal field).ABRACADABRA searches for an AC magnetic fluxthrough a superconducting pickup loop in the center ofa toroidal magnet, which should host no AC flux in theabsence of ADM. The time-averaged magnitude of theflux through the pickup loop due to Ba can be writtenas

|Φa|2 = g2aγγρDMV

2G2B2max ≡ A, (3)

where V is the volume of the toroid, G is a geometric fac-tor calculated for our toroid to be 0.027 [13], and Bmax

is the maximum B-field in the toroid. The pickup loopis read out using a SQUID current sensor, where an ax-ion signal would appear as a small-amplitude, narrow(∆f/f ∼ 10−6) peak in the power spectral density (PSD)of the SQUID output at a frequency given by the axionmass. The present design uses a simplified broadbandreadout, but the same approach can be significantly en-hanced using resonant amplification and recent develop-ments in powerful quantum sensors [14, 15], which is thesubject of future work.

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In this Letter, we present first results fromABRACADABRA-10 cm, probing the axion-photoncoupling gaγγ for ADM in the frequency rangef ∈ [75 kHz, 2 MHz], corresponding to axion massesma ∈ [3.1× 10−10, 8.3× 10−9] eV. This mass range ishighly motivated for QCD axions, where the axion decayconstant lies near the GUT scale and is easily compati-ble with pre-inflationary Peccei-Quinn (PQ) breaking ina variety of models, including grand unified theories [16]or string compactifications [17, 18], and such low-massaxions may be favored anthropically [19]. Additionally,such light ALPs may explain the previously-observedtransparency anomaly of the Universe to TeV gamma-rays [20–23], though in this case the ALP is not requiredto be DM. Recently, this mass range has gathered sig-nificant experimental interest [11, 12, 24–28] to name afew, or see [29] for a comprehensive review. Furthermore,this mass range is highly complementary to that probedby the ADMX experiment [30–32], HAYSTAC [33], andother microwave cavity experiments [34–36], which probema ∼ 10−6−10−5 eV. Our result represents the most sen-sitive laboratory search for ADM below 1µeV, is compet-itive with leading astrophysical constraints from CAST[37], and probes a region where low-mass ALPs whichcan accommodate all the DM of the universe withoutoverclosure [38–42], as well as particular models of QCDaxions with enhanced photon couplings [43, 44]. Asidefrom the ALP models currently being probed, this resultis a crucial first step towards a larger-scale version ofABRACADABRA sensitive to the smaller values of gaγγrelevant for the typical QCD axion models in the massrange where axions can probe GUT-scale physics.

MAGNET AND CRYOGENIC SETUP

ABRACADABRA-10 cm consists of a superconductingpersistent toroidal magnet produced by SuperconductingSystems Inc. [45] with a minimum inner radius of 3 cm, amaximum outer radius of 6 cm, and a maximum height of12 cm. The toroidal magnet is counter-wound to cancelazimuthal currents; see [13] for details. We operate themagnet in a persistent field mode with a current of 121 A,producing a maximum field of 1 T at the inner radius. Weconfirmed this field with a Hall sensor to a precision of∼ 1 %. Due to the toroidal geometry of the magnet, thefield in the center should be close to zero (in the absenceof an axion signal).

To reduce AC magnetic field noise, we use both mag-netic shielding and vibrational isolation. The toroid ismounted in a G10 support inside a tin-coated copper shellwhich acts as a magnetic shield below 3.7 K, when the tincoating becomes superconducting. The toroid/shield as-sembly is thermalized to the coldest stage of an OxfordInstruments Triton 400 dilution refrigerator and cooledto an operating temperature of ∼ 1.2 K. The weight of

FIG. 1. Left: Rendering of the ABRACADABRA-10 cmsetup. The primary magnetic field is driven by 1,280 super-conducting windings around a POM support frame (green).The axion-induced field is measured by a superconductingpickup loop mounted on a PTFE support (white). A secondsuperconducting loop runs through the volume of the magnetto produce a calibration signal. All of this is mounted inside asuperconducting shield. Right: Picture of the exposed toroidduring assembly.

the shield and magnet is supported by a Kevlar stringwhich runs ∼2 m to a spring attached to the top of thecryostat. This reduces the mechanical coupling and vi-bration between the detector and cryostat.

We measure AC magnetic flux in the center of thetoroid with a solid NbTi superconducting pickup loop ofradius 2.0 cm and wire diameter 1 mm. The induced cur-rent on this pickup loop is carried away from the magnetthrough ∼ 50 cm of 75µm solid NbTi twisted pair read-out wire up to a Magnicon two-stage SQUID current sen-sor. The 75µm wire is shielded by superconducting leadproduced according to [46]. The majority of the 1 mmwire is inside the superconducting shielding of the mag-net, but about 15 cm is only shielded by stainless steelmesh sleeve outside the shield.

The two-stage Magnicon SQUID current sensor is op-timized for operation at < 1 K; we operate it at 870 mK.The input inductance of the SQUID is Lin ≈ 150 nH andthe inductance of the pickup loop is Lp ≈ 100 nH. TheSQUID is operated with a flux-lock feedback loop (FLL)to linearize the output, which limits the signal band-width to ≈ 6 MHz. We read out the signal with anAlazarTech ATS9870 8-bit digitizer, covering a voltagerange of ±40 mV. The digitizer is clocked to a StanfordResearch Systems FS725 Rb frequency standard. In or-der to fit the signal into the range of our digitizer, wefilter the signal through a 10 kHz high-pass filter and a1.9 MHz anti-aliasing filter before sending it to the digi-tizer.

To calibrate the detector, we run a superconductingwire through the volume of the toroid at a radius of4.5 cm into which we can inject an AC current to gen-erate a field in the pickup loop, similar to what we ex-

3

pect from an axion signal. The coupling between thecalibration and pickup loop can be calculated from ge-ometry to be ≈50 nH. We perform a calibration scan tocalculate the end-to-end gain of our readout system. Ourcalibration measurements indicate that our pickup-loopflux-to-current gain is lower than expected by a factor of∼ 6. We determined this to be likely due to parasiticimpedances in the circuit, and we will address this issuein future designs.

DATA COLLECTION

We collected data from July 16, 2018 to August 14,2018, for a total integration time of Tint = 2.45 × 106 s.The data stream was continuously sampled at a samplingfrequency of 10 MS/s for the duration of the data-takingperiod. After completing the magnet-on data run, wecollected two weeks of data with the magnet off, but oth-erwise in the same configuration.

During data taking, the data follow two paths. First,we take the discrete Fourier transform (DFT) of indi-vidual sequential 10 s buffers of 108 samples each toproduce a series of PSDs. These are accumulated to-gether to produce an average PSD, called F10M, witha Nyquist frequency of 5 MHz and a frequency resolu-tion of ∆f = (10 s)−1 = 100 mHz. In the second path,the streamed data are decimated by a factor of 10, toa sampling frequency of 1 MS/s, collected into a 100 sbuffer of 108 samples, then transformed and compiledinto a similar running average PSD, F1M, with Nyquistfrequency of 500 kHz and ∆f = (100 s)−1 = 10 mHz. The1 MS/s data stream is further decimated in real time toa 100 kS/s stream and written directly to disk. This canbe transformed offline to produce F100k, with a Nyquistfrequency of 50 kHz and ∆f = 1/Tint ≈ 408 nHz. We donot use F100k for the present search. All DFT transformsare taken with the FFTW3 library [47].

The F10M spectra are written to disk and reset afterevery 80 averages; each stored spectrum thus covers a pe-riod of 800 s. This allows us to separate time-dependentnoise signals from a constant axion signal. Similarly, theF1M spectra are written to disk and reset every 16 aver-ages, and cover a period of 1600 s. Figure 2 shows the fullF10M spectrum as well as close-ups of the F1M spectra,converted to pickup loop flux spectral density using thecalibration measurements.

Each of the F10M, F1M and F100k spectra have a usablerange limited by the Nyquist frequency on the high end,and the frequency resolution required to resolve a poten-tial axion signal on the low end. With our sampling fre-quency and integration times, we could perform a searchover the range from 440 mHz – 5 MHz with enough reso-lution that a potential signal would span 5 – 50 frequencybins (assuming a typical ADM velocity of ∼ 220 km/s),though in practice our search range is limited by the sig-

nal filters.

We observed large 1/f -type behavior below ∼20 kHz,with broad noise peaks extending up to ∼100 kHz. Thisnoise is strongly correlated with vibration on the topplate of the cryostat up to the highest frequency mea-sured by our accelerometer, ∼ 10 kHz [13]. We believethat the tail of this noise continues up to higher frequen-cies before becoming sub-dominant to the flux noise ofthe SQUID above 100 kHz. This noise degrades our sen-sitivity at lower frequencies and we restrict our searchrange to 75 kHz < f < 2 MHz.

For ∼1 week after starting the data collection, we ob-served very narrow and variable noise peaks in the PSDabove ∼ 1.2 MHz. We are investigating the source ofthese peaks. After about a week, these peaks died awayslowly and did not return until we re-entered the lab torefill an LN2 dewar, then died away again after a fewdays. The affected time periods were removed and ac-count for a ∼30% decrease in our exposure. We hopethat in the future, a more detailed analysis will allow usto recover a significant fraction of this lost exposure.

DATA ANALYSIS APPROACH

Our data analysis procedure closely follows the methodintroduced in [48]. Our expected signal is a narrow peakin the pickup loop PSD, with a width ∆f/f ∼ 10−6

arising from the DM velocity dispersion. When averagedover Navg independent PSDs, the signal in each frequencybin k (fk) will follow an Erlang distribution with shapeparameter Navg and mean

sk =

A πf(v)mav

∣∣∣v=√

4πfk/ma−2fk > ma/2π ,

0 fk ≤ ma/2π ,(4)

where A is defined in Eq. (3). We assume f(v) is givenby the Standard Halo Model, with velocity dispersionv0 = 220 km/s/c, and vobs = 232 km/s/c the DM velocityin the Earth frame [49], with c the speed of light. Withthe DM density and velocity distribution specified, theonly free parameter in the predicted signal rate is gaγγ .

We expect our background noise sources to be normallydistributed in the time domain, such that when combinedwith an axion spectrum, the resulting PSD data is stillErlang-distributed. Accordingly, our combined signal-plus-background model prediction in each frequency binis an Erlang distribution P (Fk;Navg, µk) with shape pa-rameter Navg and mean µk = sk + b (see [48] for de-tails). Although the background PSD varies slowly withfrequency, the axion signal for a given mass is narrowenough that we restrict to a small frequency range andparameterize the background as a constant b across thewindow. We verified that the results of our analysis werenot sensitive to the size of the window chosen.

4

FIG. 2. Flux spectrum averaged over the the data used in this analysis. (a) The spectrum over the frequency range11 kHz < f < 3 MHz, corrected for the pre-digitizer filters (blue). For comparison, we also show the digitizer noise floor,corrected for pre-digitizer filters (gray) and the characteristic SQUID flux floor (green dashed). The axion search range isbetween the dotted black lines. (b) A zoomed view of the 10 MS/s spectrum (blue) with ∆f = 100 mHz and and an exampleaxion signal at the 95% upper limit (red dashed). (c) A zoomed view of the 1 MS/s spectrum with ∆f = 10 mHz. Note thatthe digitizer data was collected at a different time from the SQUID data, and shows a few transient peaks that are not presentin the SQUID data.

We performed our analysis on the F10M and F1M spec-tra over frequency ranges 500 kHz to 2 MHz and 75 kHz to500 kHz, respectively. We chose the frequency at whichwe transition from one set of spectra to the other so thatthe axion signal window is sufficiently resolved every-where, though we have seen that the exact choice haslittle effect on the final result. We rebin the F10M (F1M)spectra in time into 53 (24) spectra that cover 32,000 s(64,000 s) each. This was done to speed up processingtime, though it is not necessary for our analysis approach.

We test for an axion signal at mass ma and couplingstrength A by constructing a joint likelihood of Erlangdistributions over the 53 (24) F10M (F1M) given the ob-served PSD data [13, 48]. For each axion mass, we as-sign a unique background nuisance parameter to each ofthe rebinned F10M (F1M) spectra and profile over thejoint likelihood to construct the profile likelihood for Aat that mass. This accounts for the possibility that thebackground level might change on timescales of hours todays.

To detect an axion signal, we place a 5σ threshold ona discovery test-statistic (TS). To evaluate this we firstcalculate the profile likelihood ratio λ(ma, A), at fixedma, as the ratio of the background-profiled likelihoodfunction as a function of A to the likelihood functionevaluated at the best-fit value A. From here, we defineTS(ma) = −2 log λ(ma, 0) for A > 0 and zero otherwise.This quantifies the level at which we can reject the nullhypothesis of A = 0. The 5σ condition for discovery at agiven ma is TS(ma) > TSthresh, where [48]

TSthresh =

[Φ−1

(1− 2.87× 10−7

Nma

)]2

(5)

accounts for the local significance as well as the look-elsewhere effect (LEE) for the Nma

independent massesin the analysis (here Φ is the cumulative distributionfunction for the normal distribution with zero mean andunit variance). For this analysis, Nma

≈ 8.1 × 106 be-tween 75 kHz and 2 MHz, and TSthresh = 56.1.

Where we have no detection, we set a 95% C.L. limit,A95%, again with the profile likelihood ratio. To do so, weuse the statistic t(ma, A) = −2 log λ(ma, A), with A > A,by t(ma, A95%) = 2.71. We implement one-sided power-constrained limits [50], which in practice means that wedo not allow ourselves to set a limit stronger than the 1σlower level of the expected sensitivity band. We computethe expected sensitivity bands using the null-hypothesismodel and following the procedure outlined in [48].

We had to exclude a few specific mass points fromour discovery analysis due to narrow background linesthat were also observed when the magnet was off. Toveto these mass points as potential discoveries, we ana-lyze data collected while the magnet was off (where noaxion signal is expected) using the same analysis frame-work. If in this analysis we find a mass point with LEE-corrected significance greater than 5σ, we exclude thatmass point from our axion discovery analysis. In total,this procedure ensures a signal efficiency of & 99.8%.Our axion search yielded 83(0) excesses with significance≥ 5σ in the frequency range 500 kHz to 2 MHz (75 kHz to500 kHz), however all of these points are vetoed by themagnet-off data. We do not exclude these points fromour upper-limit analysis, though the observed limits atthese isolated points are weaker (they do not appear inFig. 3 because of down-sampling for clarity).

We verified our analysis framework by injecting a sim-

5

10−95× 10−10 5× 10−9

ma [eV]

10−10

10−9

g aγγ

[1/G

eV]

105 106Frequency [Hz]

95% Upper Limit - This Work

Expected Limit

1/2σ Containment

CAST Exclusion

95% Upper Limit - This Work

Expected Limit

1/2σ Containment

CAST Exclusion

FIG. 3. The limit on the axion-photon coupling gaγγ constructed from ABRACADABRA-10cm data described in this work.We compare the observed limit, which has been down-sampled in the number of mass points by a factor of 104 for clarity ofpresentation, to the expectation for the power-constrained limit under the null hypothesis. This down-sampling excludes the87 isolated mass points vetoed in the discovery analysis; further details will be presented in [13]. Additionally, we show theastrophysical constraint on gaγγ in this mass range from the CAST helioscope experiment [37]; the region above the grey lineis excluded.

ulated software axion signal into our real data and con-firmed that the data-quality cuts and analysis frameworkdescribed above are able to correctly detect or excludethe presence of an axion signal. In the future we hopeto build this into a hardware-based option, using the cal-ibration loop to inject “blinded” signals similar to theapproach used by ADMX [32]. Further details of theanalysis and statistical tests we have performed, as wellas an extended discussion of the noise in the excluded ex-posure, will be further described in a future publication[13].

RESULTS AND DISCUSSION

We observe no evidence of an axion signal in the massrange 3.1 × 10−10 eV – 8.3 × 10−9 eV and place up-per limits on the axion-photon coupling gaγγ of at least3.3× 10−9 GeV−1 over the full mass range and down to1.4× 10−10 GeV−1 at the strongest point. Our full ex-clusion limits are shown in Fig. 3. This result representsthe first search for ADM with ma < 1µeV, and with onemonth of data is already competitive with the strongestpresent astrophysical limits from the much larger CASThelioscope [37] in the range of overlap.

We note that for a significant range in frequency,we achieved the SQUID noise-limit. However, con-straints on the detector configuration introduced para-sitic impedances into the readout circuit, which lead to aloss in the ultimate axion coupling sensitivity [13]. Thiswill be addressed in future efforts and could yield up toa factor of ∼6 improvement in sensitivity with a similarexposure.

As ABRACADABRA-10 cm is a prototype detector,

there are many potential directions for future improve-ment. Our focus in this work has been on demonstratingthe feasibility and power of this new approach. Futureupgrade paths for the ABRACADABRA program willinclude improvements to shielding and mechanical vi-bration isolation, reduction of parasitic inductances, im-provements to the readout configuration, expanded fre-quency range, and construction of a larger toroid.

CONCLUSION

The axion is a promising DM candidate, but its cou-plings remain largely unconstrained at low masses. Inthis Letter we have demonstrated the capabilities of thebroadband axion search ABRACADABRA-10 cm, whichcan cover many decades of axion mass with relativelyshort data-taking time and which has nonetheless setcompetitive limits on the coupling gaγγ . We have al-ready identified stray fields from the toroid, vibration,and cross-talk with the DAQ to be significant sourcesof background [13]. Understanding these sources will becritical for scaling the experiment up to the ∼ 1 − 5 mscale to search for the QCD axion.

The ABRACADABRA program is highly complemen-tary to microwave cavity experiments like ADMX andHAYSTAC, as well as proposed experiments like MAD-MAX [51], which can probe the coupling gaγγ for ax-ion masses in the range 10−6 − 10−5 eV and 10−5 −10−3 eV, respectively. By demonstrating the efficacy ofABRACADABRA-10 cm, we have set the stage for a full-scale experiment which can probe the QCD axion [13].The combination of ABRACADABRA, microwave cav-ities, and MADMAX type detectors, along with experi-

6

ments probing the axion-nucleon coupling [25] and indi-rect constraints from black hole superradiance [52, 53],will be able to probe the range of couplings expected fortypical QCD axion models in the coming decades.

The authors would like to acknowledge the useful con-versations and advice from Henry Barthelmess of Mag-nicon Inc. This research was supported by the Na-tional Science Foundation under grant numbers NSF-PHY-1658693, NSF-PHY-1806440, NSF-PHY-1505858and NSF-PHY-1122374. This work was also supportedby DOE Early Career Grant number DE-SC0019225, bythe Kavli Institute for Cosmological Physics at the Uni-versity of Chicago, by the Miller Institute for Basic Re-search in Science at the University of California, Berke-ley, by the MIT Undergraduate Research Opportunitiesin Physics program, by the Leinweber Graduate Fellow-ship Program and by the Simons Foundation through aSimons Fellowship in Theoretical Physics. This researchwas supported in part through computational resourcesand services provided by Advanced Research Computingat the University of Michigan, Ann Arbor. This materialis based upon work supported by the U.S. Department ofEnergy, Office of Science, Office of Nuclear Physics un-der Award Numbers DE-FG02-97ER41041 and DEFG02-97ER41033 and by the Office of High Energy Physicsunder grant DE-SC-0012567. We would like to thankthe University of North Carolina at Chapel Hill and theResearch Computing group for providing computationalresources and support that have contributed to these re-search results.

∗ [email protected]† [email protected]

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