Experimental search for an exotic spin-spin-velocity-dependent interaction using an optically polarized vapor and a rare-earth iron garnet
EExperimental search for an exotic spin-spin-velocity-dependent interaction using anoptically polarized vapor and a rare-earth iron garnet ∗ P.-H. Chu*, † Y. J. Kim*, ‡ S. Newman, and I. M. Savukov
MPA-Quantum, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
C. D. Hughes and J. C. Long
Department of Physics, Indiana University, Bloomington IN 47405 and IUCenter for Exploration of Energy and Matter, Bloomington IN 47408, USA (Dated: October 2, 2020)We report an experimental search for an exotic spin-spin-velocity-dependent interaction betweenpolarized electrons of Rb atoms and polarized electrons of a solid-state mass, violating both the time-reversal and parity symmetries. This search targets a minute effective magnetic field induced by theinteraction. A spin-exchange relaxation-free (SERF) magnetometer based on an optically polarizedRb vapor is the key element for both a source of polarized electrons and a high-sensitivity detector. Adysprosium iron garnet (DyIG) serves as the polarized mass, with an extremely small magnetizationat the critical temperature around 240 K and a high spin density. To reduce the magnetization,one of major systematic effects, a home-built cooling system controls the mass temperature. To ourknowledge, this is the first search for an exotic spin-dependent interaction using the compensatedferrimagnet DyIG as a polarized mass. The experiment set the most stringent limit on the electron-electron coupling strength in the centimeter interaction range, in particular g eV g eV < at λ = 2 cm. Experimental searches for exotic spin-dependent in-teractions between fermions are expanding, as part ofthe growing interest in the application of quantum sens-ing in high-energy physics [1]. Early phenomenologicalwork by Moody and Wilczek [2] explored exotic spin-0 boson exchange, and was expanded by Dobrescu andMocioiu [3] to include potentials dependent on the rela-tive velocity between interacting fermions through spin-1boson exchange. These bosons provide sensitive observ-ables for testing theories beyond the Standard Model thatcan solve several outstanding mysteries in fundamentalphysics. For example, the strong charge-parity problemin quantum chromodynamics can be resolved by the ax-ion [4]. Cold dark matter can be composed of axions [5]or spin-1 dark photons [6–8]. Theoretical solutions to thephysics questions including the unification of gravity andthe Standard Model, the hierarchy problem, and darkenergy also predict the existence of new bosons [9] whichcan mediate the exotic spin-dependent interactions.Most experiments have focused on static spin-dependent interactions, described by the potentials V , V , V and V , where we have adopted thenumbering convention in Ref. [3]. Techniques have in-cluded spectroscopy [10], spin-polarized torsion pendu-lums, magnetometry, atomic parity non-conservation,and electric dipole moment searches [9, 11–15]. Someof these [12–14] used compensated ferrimagnets with lowintrinsic magnetism as spin-polarized electron sources.A few searches for spin-velocity-dependent interactionsbetween polarized and unpolarized fermions have beenperformed using cold neutron beams [16, 17], magneticstripes [18], and polarized He relaxation [19, 20]. Wealso have conducted two such searches with a spin-exchange relaxation-free (SERF) magnetometer [21, 22]. Investigating spin-spin-velocity-dependent interactions(SSVDIs), on the other hand, is relatively challengingbecause the spin-polarized masses can generate a spu-rious magnetic signal, limiting the experimental sensi-tivity. Some experiments have been performed: Hunter et al. first applied polarized geoelectrons with a
Hg-Cs co-magnetometer [23]; Ji et al. used a K-Rb SERFco-magnetometer with SmCo spin sources [24]; and atthe atomic scale from an analysis of spin-exchange in-teractions [25]. However, while these experiments weresensitive at either large or extremely small distances, themedium interaction range is still lack of measurement.In this letter we explore a SSVDI at centimeter dis-tances with a SERF magnetometer and a spin-polarizedmass: V = − g eV g eV (cid:126) πm e c × { [ˆ σ · ( (cid:126)v × ˆ r )](ˆ σ · ˆ r ) + (ˆ σ · ˆ r )[ˆ σ · ( (cid:126)v × ˆ r )] }× (cid:18) λ r + 3 λr + 3 r (cid:19) e − r/λ , (1)where two interacting particles are electrons with spinunit vector ˆ σ inside the SERF vapor cell and ˆ σ in themass, and the electron mass ( m e ); their relative distanceand relative velocity are (cid:126)r and (cid:126)v ; (cid:126) is the reduced Planckconstant; c is the speed of light; and λ is the interac-tion length. g eV is the vector electron coupling [11, 26]with the spin-1 dark photon [27]. Note that V violatesboth the time-reversal and parity symmetries. We alsonotice that some authors argued that the V vanishes ifboth polarized fermions are identical [11], but the cor-responding constraints were still published [23, 24]. Weinvestigated the V based on our recently proposed ex-perimental approach [28], where the SERF magnetome- a r X i v : . [ nu c l - e x ] S e p ter serves as both a source of spin-polarized electronsand a high-sensitivity detector. The V between ˆ σ with the gyromagnetic ratio γ and ˆ σ generates an effec-tive magnetic field (cid:126)B eff that can interact with the SERFelectron, similarly as the ordinary magnetic field [29]: V = ∆ E = γ (cid:126) ˆ σ · (cid:126)B eff , where ∆ E is the energy shiftof the SERF Rb spin-polarized electrons. The B eff isour signal to be measured with the SERF magnetome-ter. As the SERF magnetometer, we utilized a QuSpincm-scale magnetometer based on an optically polarized Rb 3 mm cubic vapor cell [30] (for more detail, seeRefs. [21, 22, 31]). The cell was heated to about ∼ ◦ Cto elevate a Rb atomic density to ∼ cm − .A rare-earth iron garnet (dysprosium iron garnet,Dy Fe Fe O , DyIG) was employed as the spin-polarized mass. DyIG is a ferrimagnet which exhibits or-bital compensation of the magnetism due to the electronspins. Three sublattices contribute to the net magnetiza-tion: Dy ions occupy dodecahedral sites in the garnetlattice, and Fe ions occupy octahedral and tetrahedralsites [32]. The magnetic moments of Dy are nominallyaligned with the octahedral ion moments but anti-alignedwith the tetrahedral ion moments. As in any ferrimag-netic material, DyIG exhibits net magnetization belowthe Curie temperature. At the critical or compensationtemperature ( T c ) below the Curie temperature, the twoopposing Dy and Fe moments equalize, resulting in azero net magnetic moment and hence zero magnetization.Part of the Dy magnetism is orbital, so there is a spinexcess at T c , calculated to be 0.6 spins per molecule [26].Based on the measured mass density of the sample used,the electron spin density of DyIG is 1 . × m − . Toour knowledge, this is the first experiment to employDyIG since it was proposed for spin-polarized masses [26],due to its T c near room temperature and relatively highspin density. A polycrystalline DyIG sample was synthe-sized at Indiana University using a metal hydroxide pre-cipitation technique [26, 33]. The resulting sample haddiameter 8 mm, thickness 1.7 mm and a mass of 0.32 g,as shown in the inset of Fig. 1. The sample was thencharacterized in a SQUID magnetometer (Quantum De-sign MPMS-XL) [34]. It was magnetized to saturation,after which the applied field was switched off and theremnant magnetization measured as a function temper-ature. The results are shown in Fig. 1, which indicates arepeatable T c of 240 K. Before installation in the exper-iment at Los Alamos National Lab (LANL), the samplewas re-magnetized to saturation along its symmetry axiswith a permanent magnet.A dominant systematic effect in our experiment is themagnetic field generated by the spin-polarized DyIG sam-ple. According to Fig. 1, this field can be strongly sup-pressed by keeping the sample at T c , which we do witha cooling system as discussed below. While previous ex-periments used ferrimagnets at room temperature to takeadvantage of the partial compensation [12–14], to our DyIG . mm FIG. 1. The measured magnetism of the DyIG sample syn-thesized at Indiana university (the inset) as a function of thetemperature. The measurement was performed by coolingand warming the sample in several cycles. knowledge this is the first experiment to attempt opera-tion at T c for maximal cancellation.Figure 2(a) shows a schematic of the experimentalsetup at LANL to probe V and photos of main el-ements. Because the SERF magnetometer operates inlow-field environments, it was located inside a magneti-cally shielded room (MSR), and also compensation coilswere added at the magnetometer head to additionallycancel the fields from magnetic sources inside the MSR.The main body of the circulating cooling system–a chiller(PolyScience IP-100) that can achieve the temperatureas low as 180 K in a liquid cryostat and an alcohol liq-uid bucket that contains a submersible pump for liq-uid circulation–was located outside the MSR in order toavoid their magnetic noise. For the design simplification,the cooling system components except the chiller werewrapped by flexible thermal insulation made of aerogeland fiberglass. In such an open environment, the chillercould cool the liquid in the bucket as low as 230 K.The liquid circulates through 2 m-long transport hosemade of 1 cm-diameter PVC clear tubing that was con-nected to a plastic fitting placed inside the MSR througha hole with 6.35 cm radius on the MSR wall. The fit-ting contains a cold finger of a sapphire rod with 1 cmdiameter and 5 cm length provided by Egorov Scientific.For the mass cooling, the DyIG mass was attached atthe end of the sapphire rod with a high thermal con-ductivity (34.6 W/m/K) and a low magnetic suscepti-bility ( − . × − ; thus, no systematic magnetic sig-nal is generated). The mass was concentrically alignedwith the SERF Rb vapor cell. For the mass motion,a motor (Haydonkerk EC042B-2PM0-804-SP), locatedoutside the MSR and enclosed by an one-layer µ -metalbox, was connected to the fitting through a G-10 rod.The cold finger/mass assembly was enclosed by a plastic M S R T r a n s po r t ho se C h i l l e r Liquid bucket C o o li n g s y s t e m Motor (not shown)Transport hoseSERF module & cold finger Cold fingerSERF module S E R F C o l d f i n g e r & D y I G Ferrite 𝝁 -metal SERF sensor headCompensation coils Cold finger T r a n s p o r t h o s e DyIGlocation (a) !" ! yz x ! DyIG !" " d r = 7.5 cm S E R F s e n s o r h e a d R b c e ll (b) Fitting B eff Liquid bucketMotor
FIG. 2. (a) A schematic of the experimental setup comprised of a home-built cooling system and a SERF magnetometermodule (scaled) and photos of main elements. The main elements of the cooling system, the chiller and the liquid bucket, arelocated outside the MSR. The cooled liquid in the bucket circulates through the transport hose connected to the plastic fittingcontaining the sapphire cold finger inside the MSR. The DyIG mass is attached at the end of the cold finger (not shown). Thecold finger/mass assembly is wrapped by aerogel thermal insulation inside the plastic tube. The motor outside the MSR isconnected to the assembly to rotate the mass. The SERF magnetometer with compensation coils is inside the MSR and its Rbvapor cell is concentrically aligned with the DyIG mass. The open ferrite box and one-layer µ -metal box are located betweenthe magnetometer and the mass. (b) A schematic of the configuration of the Rb vapor and the DyIG mass. The mass is rotatedaround the z -axis and the magnetometer sensitive to the field component along the z -axis measures B eff . cylindrical box filled with 5 mm-thick aerogel sheet.A temperature sensor (Lake Shore DT-670-SD) wasmounted on the transport hose near the liquid bucket tomonitor the liquid temperature. It was observed that thetemperature was around 235 K with the drift of 4 K forone day due to the ambient temperature variation. Weobserved that the mass temperature was a few degreeshigher than the liquid temperature, thus close to the T c of 240 K. Although the mass was cooled down to aroundthe critical temperature, the residual field from the masswas measured to be ∼ µ T and the field drift caused bythe temperature drift deteriorated the performance of theSERF magnetometer. To this end, the cold finger/massassembly was surrounded by an open thin one-layer µ -metal box and an open ferrite box additionally enclosedthe SERF magnetometer, as shown in Fig. 2(a). Thisconfiguration resulted in the increase of the distance be-tween the nearest surfaces of the Rb vapor cell and theDyIG mass, δr , up to 7.5 cm.Figure 2(b) illustrates a schematic of the configurationof the SERF Rb vapor with spins oriented along the x -axis and the DyIG mass with spins oriented along the z -axis. In order to generate the relative velocity termin V , the mass was rotated by the motor with a con-stant angular velocity ω , leading to the B eff along the z -axis that can be precisely measured by the SERF mag- netometer, sensitive to the z field component with theintrinsic field sensitivity of 15 fT/ √ Hz at low frequencybelow 100 Hz.The suppression of the systematic effects (SERF dcoffset on the order of pT; mass residual field on the or-der of µ T) was achieved by continuously alternating themass rotation between clockwise and counterclockwiseto subtract the magnetometer signals because the signof B eff is reversed for the opposite rotations, unlike thesystematic effects. The motor outputed a trigger sig-nal indicating the rotation direction, enabling to distin-guish the direction in the magnetometer signals. Fig-ure 3(a) shows standard magnetometer signals in thetime domain together with motor trigger signals, bothof which simultaneously recorded, that represent two fullcycles of the mass rotation reversal. In one cycle, themass was rotated with ω = 0 .
242 rad/s for 1 s and thenwith ω = − .
242 rad/s for 1 s. Due to the acceler-ation/deceleration times and the delay time after eachmass rotation in the motor, one cycle elapsed 2.3 s.To obtain the magnitude of B eff from the magnetome-ter signals, only data points within the yellow shaded re-gions (the last 25% of data without the regions of the mo-tor deceleration and delay, marked as the gray shaded re-gions) in each half cycle were used [see Fig. 3(a)] in orderto diminish the effects originating from motor accelera- Time (s) S E R F s i g n a l ( p T ) Time (s) -2-10 M o t o r o u t pu t ( m V ) + w - w + w - w
75% 75% 75% 75% +1 -3 +3 -1 (a)(b)
FIG. 3. (a) SERF magnetometer signals (top) and motortrigger signals (bottom) in the time domain. (b) Histogramof the B eff extracted with the drift-correction algorithm fromthe data collected for 29.4 h; the blue curve represents a fitto a Gaussian distribution. tion such as mass vibration and also to ensure stable massrotation with the constant angular velocity. The magne-tometer signals between the opposite mass rotations wereeffectively subtracted using the drift-correction algorithm(for more detail see Refs. [21, 22]). The algorithm re-moves drifts mainly due to the mass field drift (2 nT perone day) up to second-order time-dependent terms in thesignals by applying a [+1 − −
1] weighting to themean value of the data within the yellow shaded regionsfrom each half cycle within two cycles [see Fig. 3(a)].We collected data for 29.4 hours. Figure 3(b) showsa histogram of the magnitude of B eff obtained with thedrift-correction algorithm from the magnetometer signalsrecorded for 29.4 h, which was fit with a Gaussian dis-tribution, giving B eff = ( − . ± . × − T. Thedominant systematic effects have been mitigated belowthe statistical sensitivity of 1 . × − T correspondingto the experimental sensitivity ∆ E of 2 . × − eV.The limit to g eV g eV of the interaction V was derivedusing the Monte Carlo method to average the interactionpotential in Eq. 1 at different interaction ranges (for more - - -
10 1 10 (m) l - - ) e V g e V L og ( g - - - - (eV) b m dark photon This workJi, 2018Leslie, 2014(theory)
FIG. 4. Experimental limits on the electron-electron coupling g eV g eV of V as a function of the interaction range and thedark photon mass m b of our experiment (red solid curve) andthe K-Rb SERF experiment [24] (blue solid curve). The limitderived from the Hg-Cs experiment [23] is not shown. Themagenta dashed curve shows an estimated limit of anotherproposal using DyIG [26]. detail, see Refs. [21, 22, 28]), plotted in Fig. 4 (red solidcurve). The other experimental constraints on g eV g eV havebeen derived from the experiments based on the Hg-Cs co-magnetometer with polarized geoelectrons [23, 35](not shown) and the K-Rb SERF magnetometer withSmCo spins [24] (blue solid curve) for the long interac-tion range > V in the interaction range from 10 − to 10 − m.In conclusion, we probed the exotic parity- and time-reversal-odd SSVDI V between SERF spin-polarizedelectrons and DyIG spin-polarized electrons, and set themost stringent constraint on the electron-electron cou-pling strength at the centimeter interaction range. Theresult indicates that this experiment is able to explorethe remaining SSVDIs by proper mass movements. Theinteraction range in this experiment was limited by thefield drift of the spin-polarized mass. For a shorter inter-action range, a reduction of the mass field drift shouldbe achieved by developing a vacuum cooling system witha thermal feedback loop.This work was supported by the Los Alamos Na-tional Laboratory LDRD office through Grant No.20180129ER, the National Science Foundation grantPHY-1707986, and the Indiana University Center forSpacetime Symmetries (IUCSS). We are grateful to AlexBrown, who passed away in 2018, for his work on thesynthesis of the DyIG sample. ∗ These authors have contributed equally to this work. † Email address: [email protected] ‡ Email address: [email protected] [1] Z. Ahmed et al. , “Quantum sensing for high energyphysics,” (2018), arXiv:1803.11306 [hep-ex].[2] J. E. Moody and F. Wilczek, Phys. Rev. D , 130(1984).[3] B. A. Dobrescu and I. Mocioiu, JHEP , 005 (2006).[4] R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. , 1440(1977).[5] L. D. Duffy and K. van Bibber, New J. Phys. , 105008(2009).[6] T. Appelquist, B. A. Dobrescu, and A. R. Hopper, Phys.Rev. D , 035012 (2003).[7] B. A. Dobrescu, Phys. Rev. Lett. , 151802 (2005).[8] L. Ackerman, M. R. Buckley, S. M. Carroll, andM. Kamionkowski, Phys. Rev. D , 023519 (2009).[9] M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball,A. Derevianko, and C. W. Clark, Rev. Mod. Phys. ,025008 (2018).[10] F. Ficek, D. F. J. Kimball, M. G. Kozlov, N. Leefer,S. Pustelny, and D. Budker, Physical Review A (2017), 10.1103/physreva.95.032505.[11] P. Fadeev, Y. V. Stadnik, F. Ficek, M. G. Kozlov, V. V.Flambaum, and D. Budker, Phys. Rev. A99 , 022113(2019).[12] R. C. Ritter, C. E. Goldblum, W.-T. Ni, G. T. Gillies,and C. C. Speake, Phys. Rev. D , 977 (1990).[13] T. C. P. Chui and W.-T. Ni, Phys. Rev. Lett. , 3247(1993).[14] W.-T. Ni, T. Chui, S.-S. Pan, and B.-Y. Cheng, PhysicaB: Condensed Matter , 153 (1994).[15] W. A. Terrano, E. G. Adelberger, J. G. Lee, and B. R.Heckel, Phys. Rev. Lett. , 201801 (2015).[16] F. M. Piegsa and G. Pignol, Phys. Rev. Lett. , 181801(2012).[17] C. Haddock, J. Amadio, E. Anderson, L. Barrn-Palos,B. Crawford, C. Crawford, D. Esposito, W. Fox, I. Fran-cis, J. Fry, and et al., Physics Letters B , 227233 (2018).[18] J. Ding et al. , Phys. Rev. Lett. , 161801 (2020).[19] H. Yan and W. M. Snow, Phys. Rev. Lett. , 082003(2013), arXiv:1211.6523 [nucl-ex].[20] H. Yan, G. A. Sun, S. M. Peng, Y. Zhang, C. Fu, H. Guo,and B. Q. Liu, Phys. Rev. Lett. , 182001 (2015).[21] Y. J. Kim, P.-H. Chu, and I. Savukov, Phys. Rev. Lett. , 091802 (2018).[22] Y. J. Kim, P.-H. Chu, I. Savukov, and S. Newman, Na-ture Commun. , 2245 (2019).[23] L. R. Hunter and D. G. Ang, Phys. Rev. Lett. ,091803 (2014).[24] W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei,and H. Yan, Phys. Rev. Lett. , 261803 (2018).[25] D. F. Jackson Kimball, A. Boyd, and D. Budker, Phys.Rev. A , 062714 (2010).[26] T. M. Leslie, E. Weisman, R. Khatiwada, and J. C. Long,Phys. Rev. D89 , 114022 (2014).[27] R. Essig et al. , “Dark sectors and new, light, weakly-coupled particles,” (2013), arXiv:1311.0029 [hep-ph].[28] P.-H. Chu, Y. J. Kim, and I. Savukov, Phys. Rev. D ,036002 (2016).[29] T. Karaulanov, I. Savukov, and Y. J. Kim, MeasurementScience and Technology , 055002 (2016).[30] ”QuSpin Inc.”, Available at [31] I. Savukov, Y. J. Kim, V. Shah, and M. G. Boshier,Measurement Science and Technology , 035104 (2017).[32] G. F. Dionne, Magnetic Oxides (Springer, 2009).[33] M. J. Geselbracht, A. M. Cappellari, A. B. Ellis, M. A.Rzeznik, and B. J. Johnson, Journal of Chemical Edu-cation , 696 (1994).[34] ”Quantum Design Inc.”, Available at .[35] L. Hunter, J. Gordon, S. Peck, D. Ang, and J.-F. Lin,Science339