Axion search with a quantum-limited ferromagnetic haloscope
N. Crescini, D. Alesini, C. Braggio, G. Carugno, D. D Agostino, D. Di Gioacchino, P. Falferi, U. Gambardella, C. Gatti, G. Iannone, C. Ligi, A. Lombardi, A. Ortolan, R. Pengo, G. Ruoso, L. Taffarello
AAxion search with a quantum-limited ferromagnetic haloscope
N. Crescini,
1, 2, ∗ D. Alesini, C. Braggio,
2, 4
G. Carugno,
2, 4
D. D’Agostino, D. Di Gioacchino, P. Falferi, U. Gambardella, C. Gatti, G. Iannone, C. Ligi, A. Lombardi, A. Ortolan, R. Pengo, G. Ruoso, † and L. Taffarello (QUAX Collaboration) INFN-Laboratori Nazionali di Legnaro, Viale dell’Universit`a 2, 35020 Legnaro (PD), Italy Dipartimento di Fisica e Astronomia, Via Marzolo 8, 35131 Padova, Italy INFN-Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Roma, Italy INFN-Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy INFN-Sezione di Napoli, Via Cinthia, 80126 Napoli, Italy and Dipartimento di Fisica,Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy IFN-CNR, Fondazione Bruno Kessler, and INFN-TIFPA, Via alla Cascata 56, 38123 Povo (TN), Italy INFN-Sezione di Padova, Via Marzolo 8, , 35131 Padova, Italy (Dated: January 27, 2020)A ferromagnetic axion haloscope searches for Dark Matter in the form of axions by exploitingtheir interaction with electronic spins. It is composed of an axion-to-electromagnetic field transducercoupled to a sensitive rf detector. The former is a photon-magnon hybrid system, and the latteris based on a quantum-limited Josephson parametric amplifier. The hybrid system consists of ten2.1 mm diameter YIG spheres coupled to a single microwave cavity mode by means of a staticmagnetic field. Our setup is the most sensitive rf spin-magnetometer ever realized. The minimumdetectable field is 5 . × − T with 9 h integration time, corresponding to a limit on the axion-electron coupling constant g aee ≤ . × − at 95% CL. The scientific run of our haloscope resultedin the best limit on DM-axions to electron coupling constant in a frequency span of about 120 MHz,corresponding to the axion mass range 42 . . µ eV. This is also the first apparatus to perform anaxion mass scanning by changing the static magnetic field. The axion is a beyond the Standard Model (BSM) hy-pothetical particle, first introduced in the seventies as aconsequence of the strong CP problem of quantum chro-modynamics (QCD) [1–3]. Present experimental effortsare directed towards “invisible” axions, described by theKSVZ [4, 5] and DFSZ [6, 7] models, which are extremelylight and weakly coupled to the Standard Model parti-cles. Axions can be produced in the early Universe bydifferent mechanisms [8–11], and may be the main con-stituents of galactic Dark Matter (DM) halos. Astro-physical and cosmological constraints [12, 13], as well aslattice QCD calculations of the DM density [14, 15], pro-vide a preferred axion mass window around tens of µ eV.Non-baryonic DM is where cosmology meets particlephysics, and axions are among the most interesting andchallenging BSM particles to detect. Their experimentalsearch can be carried out with Earth-based instrumentsimmersed in the Milky Way’s halo, which are thereforecalled “haloscopes” [16]. Nowadays, haloscopes rely onthe inverse Primakoff effect to detect axion-induced ex-cess photons inside a microwave cavity in a static mag-netic field. Primakoff haloscopes allowed to exclude ax-ions with masses m a between 1.91 and 3.69 µ eV [17–19],and, together with helioscopes [20], are the only exper-iments which reached the QCD-axion parameter space.The last years saw a flourishing of new ideas to search foraxions and axion-like-particles (ALPs) [21–33]. Amongthese, the QUAX experiment [34, 35] searches for DM ax-ions through their coupling with the spin of the electron. This experiment aims to implement the idea of Ref. [36]as follows.The axion-electron interaction is described by the La-grangian L ae = g aee m e ∂ µ a (cid:0) ¯ ψ e γ µ γ ψ e (cid:1) , (1)where g aee is the axion-electron interaction constant, a isthe axion field, ψ e and m e are the electron wavefunctionand mass, and γ µ and γ are Dirac matrices. This vertexdescribes an axion-induced flip of an electron spin, whichthen decays back to the ground state emitting a photon.Since v a , the relative speed between Earth and the DMhalo, is small, we may use the non-relativistic limit ofEuler-Lagrange equations and recast the interaction term L ae (cid:39) − µ B σ · (cid:16) g aee e (cid:17) ∇ a ≡ − µ B σ · B a . (2)Here − µ B σ and e are the spin and charge of the elec-tron, µ B is the Bohr magneton, and B a is defined asthe axion effective magnetic field. As ∇ a ∝ v a [36], thenon-zero value of v a results in B a (cid:54) = 0.If accounting for the whole DM, the numeric axion den-sity is n a (cid:39) × (42 µ eV /m a ) cm − . For v a (cid:39) − c ,where c is the speed of light, the de Broglie wave-length and coherence time of the galactic axion field are λ ∇ a = 25 (42 µ eV /m a ) m, and τ ∇ a = 85 ( m a / µ eV) µ s[34, 35]. The effective field frequency is proportional tothe axion mass, ω a / π = 10 ( m a / µ eV) GHz, while its a r X i v : . [ h e p - e x ] J a n amplitude depends on the properties of the DM halo andof the axion model, B a = g aee e (cid:114) n a (cid:126) m a c m a v a (cid:39) × − (cid:16) m a µ eV (cid:17) T , (3)where (cid:126) is the reduced Planck constant. These featuresallows for the driving of a coherent interaction between B a and the homogeneous magnetization of a macroscopicsample. The sample is immersed in a static magneticfield B to couple the axion field to the Kittel mode ofuniform precession of the magnetization. The interactionyields a conversion rate of axions to magnons which canbe measured by searching for oscillations in the sample’smagnetization. Due to the angle between B and B a , theresulting signal undergoes a full daily modulation [37].The maximum axion-deposited power is related to Eq. (3)and to the characteristics of the receiver, namely numberof spins N s and system relaxation time τ s P a = γ e µ B N s ω a B a τ s , (4)where γ e is the electron gyromagnetic ratio.To detect this signal we devised a suitable receiver. Asit measures the magnetization of a sample, it is config-ured as a spin-magnetometer used as an axion haloscope.The device consists of an axion field transducer and ofan rf detection chain.At high frequencies and in free field, the electron spinresonance linewidth is dominated by radiation damping,which limits τ s [38–40]. To avoid this issue, the mate-rial is placed in a microwave cavity. If the frequencyof the Kittel mode ω m = γ e B is close to the cavitymode frequency ω c , the two resonances hybridize andthe single mode splits into two, following an anticrossingcurve [41, 42]. The B -dependent hybrid modes frequen-cies are ω and ω and the cavity-material coupling is g cm = min( ω − ω ). If g cm is larger than the hybridmode linewidths γ , (cid:39) ( γ c + γ m ) /
2, where γ c and γ m are the cavity and material dissipations, the system isin the strong coupling regime. To increase P a , N s and τ s must be large, so a suitable sample has a high spindensity and a narrow linewidth. The best material iden-tified so far is Yttrium Iron Garnet (YIG), with roughly2 × spins / cm and 1 MHz linewidth [43].In the apparatus that we operated at the Labora-tori Nazionali di Legnaro of INFN, the TM110 modeof a cylindrical copper cavity is coupled to ten 2.1 mm-diameter spheres of YIG. The spherical shape is neededto avoid geometrical demagnetization. We devised an on-site grinding and polishing procedure to obtain narrowlinewidth spherical samples starting from large single-crystals of YIG. The spheres are placed on the axis ofthe cavity, where the rf magnetic field is uniform.Several room temperature tests were performed to de-sign the YIG holder: a 4 mm inner diameter fused silicapipe, containing 10 stacked PTFE cups, each one large enough to host a free rotating YIG. Free rotation permitsthe spheres’ easy axis self-alignment to the external mag-netic field, while a separation of 3 mm prevents sphere-sphere interaction. The pipe is filled with 1 bar of heliumand anchored to the cavity for thermalization. The cavityand pipe are placed inside the internal vacuum chamber(IVC) of a dilution refrigerator, with a base temperaturearound 90 mK. Outside the IVC, in a liquid helium bath,a superconducting magnet provides the static field withan inhomogeneity below 7 ppm over all the spheres. FIG. 1: Measured (left) and modeled (right) transmis-sion functions of the HS. The right plot is the function f cdmn ( ω, ω m ), based on the second quantization of coupledharmonic oscillators, while the left one is a SO-to-Readout(see Fig. 2) transmission measurement with the JPA off, per-formed at 90 mK. Color scales are in arbitrary units (brightercolors corresponds to higher amplitudes). The dashed line inthe left plot identifies the hybrid mode frequencies ω , wherewe performed measurements. The resulting hybrid system (HS) has been studiedby collecting a B vs frequency transmission plot, re-ported in Fig. 1 (left). The measured plot is not a usualanticrossing curve. In our system the cavity frequency ω c / π = 10 . ω gets close and couples to ahigher order mode of the cavity. This hybrid mode fur-ther splits into others, making the two oscillators de-scription unsuitable. Other disturbances are related toresidual sphere-sphere interaction and to non-identicalspheres. To model the HS, we write an hamiltonian basedon two cavity modes, c and d , and two magnetic modes, m and n H cdmn = ω c − iγ c g cm g cn ω d − iγ d g dm g dn g cm g dm ω m − iγ m g mn g cn g dn g mn ω n − iγ n , (5)where g , ω and γ indicate their couplings, resonant fre-quencies and dissipations, respectively. Fig. 1 (right)shows the function f cdmn ( ω, ω m ) = det (cid:0) ω I − H cdmn (cid:1) ,whose maxima identify the resonance frequencies of theHS. By comparing the two plots of Fig. 1, one can see thatthe model appropriately describes the system, allowingus to extract the linewidths, frequencies and couplings ofthe modes through a fit. The typical measured values are γ (cid:39) . g cm (cid:39)
638 MHz, yielding τ s (cid:39)
84 nsand N s (cid:39) . × spins, respectively. Remarkably, themode ω is not altered by other modes, thus we will useit to search for axion-induced signals. For a fixed B thelinewidth of the hybrid mode is the haloscope sensitiveband. By changing B , we can perform a frequency scanalong the dashed line of Fig. 1. M ag n e t m w - c a v i t y YIGD1D2 - SO - - - AuxA1A2Readout - - Pump JPAsp i 90 mK4 K TT Calibration
FIG. 2: Schematics of the apparatus. The cavity is reportedin orange, the ten YIG spheres are in black, and the blueshaded region is permeated by a uniform magnetic field. Thecryogenic and room temperature HEMT amplifiers are A1 andA2, respectively, and the JPA ports are the signal (s), idler (i)and pump (p). Superconducting cables are brown, the red-circled T s are the thermometers, SO is a source oscillator, andattenuators are shown with their reduction factor in dB. Asinset, we show the calibration of the system gain and noisetemperature, obtained by injecting signals in the SO line. Thepower injected in the HS is given in terms of an effectivetemperature proportional to A cal . The errors are within thesymbol dimension. See text for further details. The electronic schematics, shown in Fig. 2, consists infour rf lines used to characterize, calibrate and operatethe haloscope. The HS output power is collected by adipole antenna (D1), connected to a manipulator by athin steel wire and a system of pulleys to change its cou-pling. The source oscillator (SO) line is connected to a weakly coupled antenna (D2) and used to inject signalsinto the HS, the Pump line goes to a Josephson paramet-ric amplifier (JPA), the Readout line amplifies the powercollected by D1, and Aux is an auxiliary line. The Read-out line is connected to an heterodyne as described in[35], where an ADC samples the down-converted powerwhich is then stored for analysis. The JPA is a quan-tum limited amplifier, with resonance frequency of about10 GHz resulting in a noise temperature of 0.5 K. Its gainis close to 20 dB in a band of order 10 MHz, and its work-ing frequency can be tuned thanks to a small supercon-ducting coil [44]. Excluding some mode crossings, hybridmode and JPA frequencies overlap between 10.2 GHz and10.4 GHz, and allow us to scan the corresponding axionmass range.The procedure to calibrate all the lines of the setup is:( i ) the transmittivity of the Aux-Readout path K AR ismeasured by decoupling D1 or by detuning ω ; ( ii ) forthe Aux-SO and SO-Readout paths, K AS and K SR areobtained by critically coupling D1 to the mode ω . Thetransmittivity of the SO line is K SO (cid:39) (cid:112) K SR K AS /K AR .If a signal of power A in is injected in the SO line,the fraction of this power getting into the HS results A cal = A in K SO . Since A cal is a calibrated signal, it canbe used to measure gain and noise temperature of theReadout line. From this measurement we obtain a sys-tem noise temperature T n = 1 . Source EstimatedQuantum noise 0.50 KThermal noise 0.12 KHEMTs noise 0.25 KExpected total 0.87 KMeasured total T n To double check the accuracy of the result, we measurethe thermal noise of the HS. The noise difference for ω on and off the JPA resonance (dark blue and light blue)gives the noise added by the hybrid mode (orange curve),as shown in Fig. 3. The excess noise is compatible witha temperature of the HS ∼
10 mK higher than the oneof the nearest load, which is realistic. Similar results areobtained by changing the D1 antenna coupling for a fixed B .The axion search consisted in fifty-six runs, each one FIG. 3: Thermal noise of the HS. The blue curves are thepower measured at the Readout with ω in the JPA band-width (dark blue) and out of it (light blue). The differencebetween the two is the HS noise (reported in orange). with fixed B . For every run a transmission measurementof the hybrid system is used to set ω , to critically coupleD1 to it, and to measure γ . The frequency stability of ω resulted well below the linewidth within an intervalof several hours, allowing long integration times. Dataare stored with the ADC over a 2 MHz band around ω for subsequent analysis. We FFT the data with a 100 Hzresolution bandwidth to identify and remove biased binsand disturbances in the down-converted spectra. To esti-mate the sensitivity to the axion field, we rebin the FFTswith a resolution RBW (cid:39) ∼ σ P = 5 . × − W, for the longest in-tegration time t = 9 h, where the Dicke prediction is k B T n (cid:112) RBW /t = 4 . × − W. In terms of rf mag-netic field, this result corresponds to σ B = 5 . × − T,which, to our knowledge, is a record one for an rf spin-magnetometer. The absence of fast rf bursts in the datais verified by using a 1 ms time resolution waterfall spec-trogram.Even if the minimum field detectable by the haloscopeis much larger than B a , these measurements can still be aprobe for ALPs, which may also constitute the totality ofDM [46]. The 95% CL upper limit on the axion electron coupling constant is g aee < eπm a v a (cid:115) k ac × σ P µ B γ e n a N s τ s (cid:39) . × − . (6)The transduction coefficient of the axionic signal k ac wascalculated with a model similar to the one of Eq. (5) [47].It essentially depends on ω and, in our bandwidth, re-sults 0 . < k ac < .
0. The overall exclusion plot obtainedwith the ferromagnetic haloscope is given in Fig. 4. Allthe experimental parameters used to extract the limitsfrom Eq. (6) are measured within every run, making themeasurement highly self-consistent.These results improved the best previous limits [35]by roughly a factor 30 in g aee and 50 in bandwidth. Theimprovement over the previous prototype is due to an in-creased material volume, to an almost quantum-limitednoise temperature, and to longer integration times. Noaxion-mass scan was performed by previous experimentsof this kind, and we now demonstrate that it is feasi-ble to tune a hybrid resonance over hundreds of MHz tosearch for axion-deposited power. Our prototype scanneda range of axion masses of about 0.7 µ eV with a field vari-ation of 7 mT, drastically simplifying the tuning of thehaloscope.In conclusion, we designed and developed a quantum-limited rf spin-magnetometer used as an axion haloscope.The instrument implements an axion-to-rf transducer,i. e. an hybrid system which embeds one of the largestquantity of magnetic material to date, and a detectionelectronics based on a quantum-limited JPA. The oper-ation of this instrument led to an axion search over aspan of 0 . µ eV around 42 . µ eV, with a maximum sen-sitivity to g aee of 1 . × − . This, to our knowledge,is the best reported limit on the coupling of DM axionsto electrons, and corresponds to a 1- σ field sensitivity of5 . × − T, which is a record one. No showstoppershave been found so far, and hence a further upscale ofthe system can be foreseen. A superconducting cavitywith a higher quality factor was already developed andtested [48]. It was not employed in this work since theYIG linewidth does not match the superconducting cav-ity one, and the improvement on the setup would havebeen negligible. With this prototype we reached the rfsensitivity limit of linear amplifiers [49]. To further im-prove the present setup one needs to rely on bolometersor single photon/magnon counters [50]. Such devices arecurrently being studied by a number of groups, as theyfind important applications in the field of quantum infor-mation [51–54].We are grateful to E. Berto, A. Benato and M. Rebes-chini, who did the mechanical work, F. Calaon and M.Tessaro who helped with the electronics and cryogenics,and to F. Stivanello for the chemical treatments. Wethank G. Galet and L. Castellani for the development ofthe magnet power supply, and M. Zago who realized the
FIG. 4: Exclusion plot at 95% CL on the axion-electron coupling obtained with the present prototype (excluded region reportedin blue and error in light blue), and overview of other searches for the axion-electron interaction. The other results are from[35] (orange) and [45] (green), while the DFSZ axion line is at about g aee (cid:39) − . The inset is a detailed view of the reportedresult. technical drawings of the system. We deeply acknowledgethe Cryogenic Service of the Laboratori Nazionali di Leg-naro, for providing us large quantities of liquid helium ondemand. ∗ Electronic address: [email protected] † Electronic address: [email protected][1] R. D. Peccei and Helen R. Quinn. CP conservation in thepresence of pseudoparticles.
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