YBCO microwave resonators for strong collective coupling with spin ensembles
Alberto Ghirri, Claudio Bonizzoni, Dario Gerace, Samuele Sanna, Antonio Cassinese, Marco Affronte
YYBCO microwave resonators for strong collective coupling with spinensembles
A. Ghirri, a) C. Bonizzoni, D. Gerace, S. Sanna, A. Cassinese, and M. Affronte Istituto Nanoscienze - CNR, Centro S3, via Campi 213/a, 41125 Modena,Italy Dipartimento Fisica, Informatica e Matematica, Universit`a di Modena e ReggioEmilia and Istituto Nanoscienze - CNR, Centro S3, via Campi 213/a, 41125 Modena,Italy. Dipartimento di Fisica, Universit`a di Pavia, via Bassi 6, 27100 Pavia, Italy. CNR-SPIN and Dipartimento di Fisica, Universit`a di Napoli Federico II, 80138 Napoli,Italy. (Dated: 23 February 2015)
Coplanar microwave resonators made of 330 nm-thick superconducting YBCO have been realized and char-acterized in a wide temperature ( T , 2-100 K) and magnetic field ( B , 0-7 T) range. The quality factor Q L exceeds 10 below 55 K and it slightly decreases for increasing fields, remaining 90% of Q L ( B = 0) for B = 7T and T = 2 K. These features allow the coherent coupling of resonant photons with a spin ensemble atfinite temperature and magnetic field. To demonstrate this, collective strong coupling was achieved by usingDPPH organic radical placed at the magnetic antinode of the fundamental mode: the in-plane magnetic fieldis used to tune the spin frequency gap splitting across the single-mode cavity resonance at 7.75 GHz, whereclear anticrossings are observed with a splitting as large as ∼
82 MHz at T = 2 K. The spin-cavity collectivecoupling rate is shown to scale as the square root of the number of active spins in the ensemble.PACS numbers: 03.67.Lx, 42.50.Pq, 33.90.+hKeywords: superconducting resonators, circuit-QED, molecular spins, electron spin resonanceThanks to pioneering experiments and theoretical pro-posals, quantum technologies have enormously advancedand the interest can now be turned to explore viableroutes for practical applications. Several pure quantumsystems, including cold atoms, photons, superconductingqubits, spin impurities in Si, or nitrogen vacancies (NV)in diamond - among many others - have been deeplyinvestigated in the last decade as potential candidatequbits for applications in quantum information process-ing, and techniques for their read out and manipula-tion have been developed. Advantages and limitationsof each system have been debated: whilst large marginsof improvement are still possible for the different tech-niques, fundamental limits are clear for each system. Apossible strategy to overcome these barriers is to combinequantum systems of different nature and take advantageof the best features of each of them in hybrid quantum de-vices. Of course, this opens new technological challenges.Along these lines, high-quality factor resonators play apivotal role, since photons can be coupled with a numberof other two-level systems (qubits) while begin optimalflying quantum bits themselves. Among them, planarresonators are particularly suitable to be coupled with avariety of atomic or solid state qubits, with the final goalof developing an on-chip hybrid quantum technology.
In fact, mm-length microwave resonators can be routinelyfabricated in a scalable arrangement and on differentsubstrates. In particular, state-of-art superconducting a) Electronic mail: [email protected].
FIG. 1. Characteristics of bare YBCO resonators. (a) Trans-mission spectrum measured at T = 2 K and B = 0. Theinput power is P inc = − . f , and (c) loaded quality factor, Q L . In theinset (d) a sketch of the YBCO coplanar resonator is shown. resonators allow the achievement of power-independentquality factors as high as 10 or above in planar geome-try at the single photon level. A key step to coherently transfer information betweencavity photons and stationary qubits is to achieve thestrong coupling regime: electric or magnetic dipole cou-pling between the qubit and the confined electromagneticfield should overcome their respective damping rates. Electric dipole coupling allowed the observation of thestrong coupling with single quantum emitters.
On theother hand, spin ensembles collectively coupled to mi- a r X i v : . [ qu a n t - ph ] M a y crowave resonators have been proposed for a hybrid quan-tum technology. Since the magnetic dipole coupling ofa single spin to a resonator mode, g s , is typically toosmall, a collective enhancement of the effective couplingrate of N spins , scaling as g s √ N , allows to overcomethe limitations due to both the decoherence rate of thespin system, γ s and the inverse photon lifetime in thecavity, κ = ω /Q (where f = ω / π is the resonant fre-quency and Q is the resonator quality factor). In thisway, collective strong coupling of spin ensembles and mi-crowave photons has been experimentally shown in copla-nar resonators, three-dimensional (3D) cavities, and microwave oscillators. While 3D resonators are lesssuited for on-chip integration, all of the previous achieve-ments employing planar resonators were obtained withconventional superconductors (typically Nb), which arelimited to operate at moderate magnetic fields. However,manipulation of spins may need application of finite mag-netic fields.
Microwave resonators made of high T c superconductors, such as YBCO, have shown excellentperformances from liquid Nitrogen temperatures down to mK range and single-photon regime. Thanksto the large value of their intrinsic upper critical field,these systems offer unprecedented possibilities for spinmanipulation.In this Letter, we show that YBCO coplanar resonatorshave excellent performances under strong magnetic fields,with quality factors significantly exceeding 10 up to T ∼
55 K. Therefore, they appear as a significant stepahead for quantum technology applications. Stimulatedby recent theoretical and experimental results,here we focused on the high photon number and hightemperature regimes, where we report the strong col-lective coupling of an electron spin ensemble to YBCOmicrowave coplanar resonators. Our major interest isto use molecular spins, which offer several advantageswith respect to spin impurities. Interesting and suffi-ciently long phase memory times have been reported forsimple radicals, mono-metallic Cu phthalocyaninemolecules, or (PPh ) [Cu(mnt) ] derivatives. In thepresent work, we employed commercial di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium (DPPH), which is regularlyused as field calibration marker in EPR spectroscopy.The decoherence time of DPPH is T = T = 62 ns, while the continuous wave linewidth is sharp ( γ s / π (cid:39) . due to the exchange narrowing effect. Below10 K the linewidth increases as an effect of antiferro-magnetic interactions [ γ s / π (cid:39)
14 MHz at 2 K]. Thestrong coupling between DPPH radicals and a confinedmicrowave field has been already demonstrated with 3Dcavities or microwave oscillators. Superconducting resonators were fabricated by opti-cal lithography upon wet etching (2% H PO solution)of commercial 10 x 10 mm double sided YBa Cu O (YBCO, in short) films (330 nm thick) on sapphire (430 µ m) substrates (Ceraco Gmbh). The film is gold-coatedon the back side to improve the contact to ground. Thepatterned coplanar structure is constituted by a 8 mm FIG. 2. (a) Transmission spectra as a function of frequencymeasured at 2 K for applied external magnetic fields up to7 T. Dependence of (b) the cavity mode resonant frequency, f , and (c) the loaded quality factor, Q L , on the externallyapplied magnetic field, B . central strip having width w = 200 µ m and separation s = 73 µ m from the lateral ground planes [Fig. 1 (d)]. The coupling of the resonator to the feed line can be ad-justed by finely tuning the position of the launchers. Wetested five YBCO planar resonators finding quite repro-ducible results. Low temperature measurements wereperformed using a Quantum Design PPMS cryo-magneticsystem equipped with 7 T magnetic field applied parallelto the plane of the resonator. Reflection [ S ( f )] andtransmission [ S ( f )] scattering parameters were mea-sured by means of an Agilent PNA Vector Network An-alyzer (VNA).We first show that coplanar resonators made of YBCOallow expanding temperature, magnetic field, and powerranges with respect to the Nb cavities commonly usedin circuit-QED experiments. At T = 2 K, the trans-mission spectrum shows a well defined resonance cen-tered at f =7.7553 GHz [Fig. 1(a)]. The resonance dipis visible also in the S ( f ) spectrum. This indicatesthat the resonator is not undercoupled, and that theloaded quality factor ( Q L ) should be considered. Since S ( f ) = 20 log ( (cid:112) P ( f ) /P inc ), where P ( f ) and P inc are the transmitted and the input powers at the capacitorof the resonator, respectively, the transmission spec-trum can be fitted by S ( f ) = − IL −
10 log (cid:34) Q L (cid:18) ff − f f (cid:19) (cid:35) , (1)where Q L (2K) (cid:39) IL = − S ( f ) = 16 . Q L > The temperature dependence of the transmission reso-nance was investigated by measuring S ( f ) in the range2-100 K. To extract f and Q L we fitted each spectrumwith Eq. S1. Figure 1(b) shows a small shift of f be-tween 2 and 60 K. For higher temperature the resonancepeak shifts towards lower frequencies, and it disappearsin correspondence to the YBCO film critical temperature( T c = 87 K). The loaded quality factor [Fig. 1(c)] pro-gressively decreases with increasing T , while remaining Q L ( T ) > T <
55 K. This behavior is in linewith similar results reported in the literature. An applied magnetic field ( B ) generally gives rise bothto a decrease of the quality factor and to a hysteretic be-havior of the resonant frequency. While this behavior waseffectively observed for intermediate temperatures, atlow temperature the field dependence becomes progres-sively weaker. Figure 2(a) shows a series of S ( f ) spec-tra measured at 2 K for increasing B , up to 7 T. Thevalues of f and Q L extracted from Eq. S1 are plottedas a function of B in (b) and (c): they are remarkablystable up to 7 T, being Q L (7T) = 0 . × Q L (0T). Wenotice that for Nb resonators a drop of Q L is observedfor fields in the mT range. Degradation of the qualityfactor of the superconducting resonators against the ap-plied field is due to the dissipation mechanisms relatedto the vortex motion. This effect has been generally de-scribed in terms of increase of the surface resistivity ( R s )under applied magnetic field, whilst recent experimen-tal results have evidenced that more sophisticated mod-els are required for thin films. Surface resistivity mea-surements performed at 20 K by means of the dielectricresonator method have shown a weak dependence of R s with respect to a dc field up to 5 T applied parallel to theYBCO film. These findings, independently obtained bydifferent experimental techniques, corroborate the fielddependence of Q L we report in Fig. 2.Summarizing the results of the YBCO resonators char-acterization, the decay rate of the cavity remains reason-ably smaller than κ/ π ∼ . × . × .
05 mm ) was esti-mated under optical microscope, and it corresponds to atotal number of approximately N (cid:39) × radicals. InFig. 3 we report the evolution of the transmission peakin correspondence to the resonance field of the DPPHspin ensemble ( B r (cid:39) .
276 T). At 2 K two branches areobserved, which indicate the presence of a large anticross-ing between the resonator mode and the spin ensemble[Fig. 3(a)]. Cross-sectional S ( f ) spectra measured onresonance show two peaks separated by f + − f − (cid:39) f = 7 . Q L = 16000 and IL = − . κ (cid:39) . is N ph (cid:39) .For increasing temperature, the width of the anticross-ing decreases and the splitting is progressively reduced to (cid:39)
58 MHz (at 5 K) and (cid:39)
39 MHz (at 10 K) [Fig. 3(d)and (f)]. The splitting of the transmission peak in cor-
FIG. 3. Transmission spectra of a YBCO microwave resonatorloaded with a DPPH spin ensemble ( P inc = − . S ( f ) for different applied B . Temperature: 2K (a), 5 K (c) and 10 K (e). Dashed red lines display thecalculated curves. The right column shows the cross sectionsrelated to the corresponding right panel, either on resonance(cyan) or off resonance (blue). respondence to the resonance field of DPPH is observedup to 50 K. To evaluate the magnitude of the collectivecoupling constant g c , we fitted the resonance frequencyby using the usual expression for the vacuum field Rabisplitting (neglecting the damping rates, i.e. the imagi-nary parts of the split eigenfrequencies) ω ± = ω + ∆2 ± (cid:112) ∆ + 4 g c , (2)where ω ± = 2 πf ± , ∆ = gµ B ( B − B r ) / (cid:126) and g = 2 . g -factor of DPPH. The fitted rates g c / π are plotted as a function of temperature in Fig. 4 (blackcircles), spanning from 39 MHz at 2 K to 9 MHz at 40K. Hence, the strong coupling condition, g c (cid:29) γ s , κ , isclearly satisfied in our sample in the whole temperaturerange up to 40 K.To interpret the results in Fig. 4, we notice that thenumber of polarized s = 1 / N p ) varies with tem-perature as N p N = tanh (cid:18) hf k B T (cid:19) . (3)Simultaneously, g c rescales non-linearly as g c = g s (cid:112) N p , (4)where g s is the coupling of a single spin 1/2 to the res-onator mode. In Fig. 4 we calculated the behavior of g c by means of Eqs. 3 and 4 (solid red line). The best fitwas obtained by means g c / π [MHz]= 134 (cid:112) N p /N . Fromthe zero temperature limit ( N p = N ∼ × ), andthe finite temperature values, we estimated a single-spincoupling rate in a restricted range g s / π ∼ . − . besides being consistent with the values re-ported in the literature for different cavity geometries andspin systems. We also notice that even at the highesttemperatures at which strong coupling can be observed,when only a small fraction of spins is coupled to the mi-crowave mode, the condition N ph (cid:28) N p still holds, forwhich Eq. 4 is a safe assumption. To get further insight about the g c ( N p ) dependence,we removed a portion of DPPH sample from the res-onator and we repeated the measurements to extract thereduced coupling constant g ∗ c ( T ). The remaining sam-ple corresponds to approximatively 75% of the originalvolume. The total number of s = 1 / N ∗ = 0 . × N and g ∗ c = g s (cid:112) . × N p . Tocompare these results with g c ( T ), in Fig. 4 we plottedthe rescaled coupling constant g ∗ c / √ .
75 as function of T and (cid:112) N p /N (open squares). The very good agreementbetween g ∗ c ( T ) and g c ( T ) corroborates the behavior de-scribed from Eqs. 3 and 4.In summary, we have shown that YBCO microwaveplanar resonators constitute a viable route for the imple-mentation of on-chip quantum technologies. In particu-lar, we have shown their robustness against an externalmagnetic field up to 7 T and up to liquid Nitrogen tem-perature, which makes them ideal candidates for circuit-QED experiments with spin ensembles. To display theirpotentialities, we showed that the collective strong cou-pling regime of a DPPH ensemble coupled to coplanarYBCO resonators can be achieved up to 40 K. Acknowledgements.
The authors warmly acknowl-edge S. Carretta, A. Chiesa, A. Lascialfari, F. Troiani,and M. Barra for useful discussions, T. Orlando for sup-plementary EPR measurements and S. Marrazzo for fab-rication expertise. This work was funded by the ItalianMinistry of Education and Research (MIUR) through“Fondo Investimenti per la Ricerca di Base” (FIRB)project RBFR12RPD1, and by the US AFOSR/AOARDprogram, contract FA2386-13-1-4029. Z.-L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Rev. Mod. Phys. , 623 (2013). C. Grezes, B. Julsgaard, Y. Kubo, M. Stern, T. Umeda, J. Isoya,H. Sumiya, H. Abe, S. Onoda, T. Ohshima et al., Phys. Rev. X , 021049 (2014). A. Megrant, C. Neill, R. Barends, B. Chiaro, Y. Chen, L. Feigl,J. Kelly, E. Lucero, M. Mariantoni, P. J. J. O’Malley et al., Appl.Phys. Lett. , 113510 (2012). Z. K. Minev, I. M. Pop, and M. H. Devoret, Appl. Phys. Lett. , 142604 (2013). D. F. Walls and G. J. Milburn,
Quantum Optics (Springer, NewYork, 2008). R. J. Thompson, G. Rempe, and H. J. Kimble, Phys. Rev. Lett. , 1132 (1992). FIG. 4. Dependence of the collective coupling constant g c ( T )(black circles) with respect to T and (cid:112) N p ( T ) /N (inset). Theblue open squares display g ∗ c ( T ) / √ .
75. Solid red lines showthe calculated curves. M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J.M. Raimond, and S. Haroche, Phys. Rev. Lett. , 1800 (1996). A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang,J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, Nature , 162 (2004). K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atat¨ure,S. Gulde, S. F¨alt, E. Hu, and A. Imamoˇglu, Nature , 896(2007). R. H. Dicke, Phys. Rev.
99 (1954). A. Imamoˇglu, Phys. Rev. Lett. , 083602 (2009). M. Tavis and F. W. Cummings, Phys. Rev. , 379 (1968). Y. Kubo, F. R. Ong, P. Bertet, D. Vion, V. Jacques, D. Zheng,A. Dr´eau, J. F. Roch, A. Auff`eves, F. Jelezko et al. Phys. Rev.Lett. , 140502 (2010). R. Ams¨uss, C. Koller, T. N¨obauer, S. Putz, S. Rotter, K. Sand-ner, S. Schneider, M. Schramb¨ock, G. Steinhauser, H. Ritsch etal., Phys. Rev. Lett. , 060502 (2011). D. I. Schuster, A. P. Sears, E. Ginossar, L. DiCarlo, L. Frunzio,J. J. L. Morton, H. Wu, G. A. D. Briggs, B. B. Buckley, D. D.Awschalom, and R. J. Schoelkopf, Phys. Rev. Lett. , 140501(2010). G. R. Eaton and S. S. Eaton
Multifrequency Electron Paramag-netic Resonance
Ed. S. K Misra, (Wiley-VCH, Weinheim, 2011). D. Zilic, D. Pajic, M. Juric, K. Molcanov, B. Rakvin, P. Planinic,and K. Zadro, J. Mag. Reson.
34 (2010). A. M. Prokhorov and V. B. Fedorov, Sov. Phys. JEPT , 1489(1963). I. Chiorescu, N. Groll, S. Bertaina, T. Mori, and S. Miyashita,Phys. Rev. B E. Abe, H. Wu, A. Ardavan, and J. J. L. Morton, Appl. Phys.Lett. , 251108 (2011). S. Probst, H. Rotzinger, S. W¨unsch, P. Jung, M. Jerger, M.Siegel, A.V. Ustinov, and P. A. Bushev, Phys. Rev. Lett. ,157001 (2013). A. W. Eddins, C. C. Beedle, D. N. Hendrickson, and J. R. Fried-man, Phys. Rev. Lett. , 120501 (2014). G. Boero, G. Gualco, R. Lisowski, J. Anders, D. Suter, and J.Brugger, J. Magn. Reson. , 133 (2013). M. J. Lancaster,
Passive Microwave Device Applications of HighTemperature Superconductors (Cambridge University Press,Cambridge, 1997). M. Hein,
High-Temperature-Superconductor Thin Films at Mi-rowave Frequencies (Springer, Berlin, 1999). G. Ghigo, D. Botta, A. Chiodoni, R. Gerbaldo, L. Gozzelino, F.Laviano, B. Minetti, E. Mezzetti and D. Andreone, Supercond.Sci. Technol. , 977 (2004). Th. Kaiser, B.A. Aminov, A. Baumfalk, A. Cassinese, H.J.Chaloupka, M.A. Hein, S. Kolesov, H. Medelius, G. Muller, M.Perpeet et al.,J. Supercond. 12, 343 (1999). M. Arzeo, F. Lombardi and T. Bauch, IEEE Trans. Appl. Super-cond. , 1700104 (2015). Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, andY. Nakamura, Phys. Rev. Lett. , 083603 (2014). X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Phys. Rev. Lett. , 156401 (2014). E. I. Baibekov, Opt. and Spect. , 889 (2014). A. Ghirri, F. Troiani, and M. Affronte,
Quantum Computationwith Molecular Nanomagnets: Achievements, Challenges, andNew Trends, Structure and Bonding (Springer, Berlin, 2014). S. Nakazawa, S. Nishida, T. Ise, T. Yoshino, N. Mori, R. D.Rahimi, K. Sato, Y. Morita, K. Toyota, D. Shiomi et al. Angew.Chem. Int. Ed. , 9860 (2012). A. Collauto, M. Mannini, L. Sorace, A. Barbon, M. Brustolon,and D. Gatteschi, J. Mater. Chem. , 22272 (2012). M. Warner, S. Din, I. S. Tupitsyn, G. W. Morley, A. M. Stone-ham, J. A. Gardener, Z. Wu, A. J. Fisher, S. Heutz, C. W. M.Kay, and G. Aeppli, Nature , 504 (2013). K. Bader, D. Dengler, S. Lenz, B. Endeward, S. Jiang, P. Neuge-bauer, and J. van Slageren, Nat. Comm. , 5304 (2014). See Supplementary Information. D. Bothner, T. Gaber, M. Kemmler, D. Koelle, R. Kleiner, S.Wunsch, and M. Siegel, Phys. Rev. B , 014517 (2012). J. Krupka, J. Judek, C. Jastrzebski, T. Ciuk, J. Wosik, and M.Zdrojek, Appl. Phys. Lett. , 102603 (2014). K. Sato, S. Sato, K. Ichikawa, M. Watanabe, T. Honma, Y.Tanaka, S. Oikawa, A. Saito, and S. Ohshima, J. Phys. Conf.Ser. , 012045 (2014). J. M. Sage, V. Bolkhovsky, W. D. Oliver, B. Turek, and P. B.Welander, J. Appl. Phys. , 063915 (2011).
Supplementary Information
I. EXPERIMENTAL SECTION
Experiments with YBCO resonators and applied magnetic fields up to 7 T were carried out by means of the lowtemperature set-up shown in Fig. S1. The external magnetic field is applied parallel to the YBCO film, and usedto tune the DPPH spin gap. The coplanar resonators were installed into an oxygen free high conductivity copperbox that allows installation, grounding, as well as thermalization down to 2 K. The resonator box is installed on adedicated probe wired with cryogenic coaxial cables (Micro-Coax UT-085B-SS), and inserted in a Quantum DesignPPMS cryo-magnetic set-up. The temperature is monitored by means of a RuO thermometer located close to theresonator box. Reflection ( S ) and transmission ( S ) scattering parameters were measured by means of a VectorNetwork Analyzer (Agilent PNA 26.5 GHz). The microwave launchers are constituted by a SMA connector on thecoaxial cable side, and a gold-plated pin on the device side. The relative length of the pin can be regulated to tunethe effective coupling between resonator and feedline.To calibrate the transmission spectrum and to remove the insertion loss of the coaxial line ( IL coax ), we measuredthe S ( f ) spectrum of a calibration device constituted by a superconducting waveguide without capacitive gaps,which was installed in place of the coplanar resonator. The incident power at the input capacitor of the resonatorwas estimated as P inc = P out − IL coax /
2, where P out is the output power of the Vector Network Analyzer. II. CHARACTERIZATION OF THE YBCO COPLANAR RESONATORS
We fabricated and tested five YBCO/sapphire coplanar resonators (named resonator f ) and qualityfactor ( Q L ) from temperature ( T ) and applied magnetic field ( B ). The strong coupling between microwave field andDPPH radicals has been reproducibly obtained with all the tested resonators.The measured values of resonant frequency f and loaded quality factor Q L are shown in Fig. S2 for resonator f and Q L show a weak dependence from T . Fig. S3 shows the dependence ofthe loaded quality factor measured as a function of the applied magnetic field. These experimental data have beenmeasured on resonator f has been observed by repetitively cycling the magnetic field between +0.5 and -0.5 T. Its shape qualitativelyresembles the hysteresis reported for Nb resonators . For the YBCO/sapphire resonator, the maximum variationof f ( B ) is very small (0.44 MHz), and it corresponds to 0.006% of the resonance frequency at zero field. Thedegradation of the internal quality factor of high temperature superconductors under applied magnetic field has beenwidely investigated and different models have been proposed . The generalized two fluid model, which includesquasi-particle excitations and vortex motion, has been often used to interpret the microwave surface resistance ofYBCO superconducting thin films under high dc magnetic field . The complex conductivity approach has been VNAresonatorthermalization stage2 Kvacuum B resonatorSMASMAlauncherscopper box FIG. S1. Left. Photograph of the YBCO coplanar resonator installed into the copper box. Right. Schematic of theexperimental set-up. The base temperature is 2 K and the maximum field strength is 7 T.
FIG. S2. Temperature dependence of resonant frequency (upper panel) and loaded quality factor (lower panel) of resonator shown to better describe the properties of YBCO films under applied magnetic field . Magnetic flux penetratesin the superconductor through vortices, with the size of about few nanometers in YBCO ; their motion producesdissipation resulting in an increase of the surface resistance (flux flow). In a real system defects are always presentand cause the vortices to become pinned at particular positions. In addition, in layered structures such as the high- T c superconductors the vortex can be pinned by the block interspacing between the superconducting CuO layers whenthe field is perpendicularly applied. However, vortex lines can move between these pinning centers with thermallyactivated jumps (flux creep process). This is expected to be the main process causing both the large reduction of thequality factor as the temperature is increased, as well as the sensitive degradation as a function of the applied field athigh temperature, as displayed in Fig. S3. Quantum tunneling may also cause flux motion at very low temperature(quantum creep process) . The occurrence of these effects has a strong dependence on temperature and appliedmagnetic field, as well as on the characteristics of the superconducting material. FIG. S3. Q L -vs- B curves measured for different temperatures on the bare resonator III. ESTIMATION OF THE NUMBER OF PHOTONS
Figure S4 (a) shows the dependence from the incident power of the transmission spectrum of resonator S ( f ) = − IL −
10 log (cid:34) Q L (cid:18) ff − f f (cid:19) (cid:35) , (S1)we extracted f = 7 . IL = 31 . Q L = 33500 for P inc < − . Q L decreases [Fig. S4 (b)]. The number of photons N ph = P circ hf (S2)can be calculated from the circulating power P circ = 1 π P inc Q L − IL/ , (S3)and results comprised in the range 10 -10 respectively for P inc varying between -42.5 and 7.5 dBm [Fig. S4 (b)]. IV. ESTIMATION OF THE NUMBER OF RADICALS
The total number of spins in our sample can be estimated from the known radicals density in DPPH, ρ = 1 . . Knowing the molar mass m mol = 394 .
32 g/mol, we get the density as ρ V ∼ × cm − . Then, thenumber of radicals in a sample of known volume, V , is simply N = ρ V V . V. LINEWIDTH OF DPPH ORGANIC RADICAL
Spin-phonon relaxation ( T ) and dephasing ( T ) times of DPPH organic radicals are reported in the literature.For concentrated samples T = T = 62 ns . By considering the homogeneous broadening, the linewidth can becalculated from γ s = 12 T + 1 T (cid:113) γ B T T (S4)where γ = gµ B / (cid:126) is the gyromagnetic ratio and B is the amplitude of the microwave field. Due to the effect ofthe exchange narrowing , the calculated linewidith is overestimated respect to that obtained experimentally. Recentmeasurements report γ s = 3 . . For T <
10 broadening of the EPR line occurs due toantiferromagnetic interactions between the DPPH radicals. The reported linewidth is γ s = 14 MHz at 2 K . FIG. S4. (a) S ( f ) spectra measured for resonator P inc (open circles). The temperature is 2 K.Solid lines show the fit curve calculated from Eq. 1. (b) dependence of the fitted Q L and of the number of photons calculatedfrom Eq. 2. VI. ESTIMATION OF THE SPIN-PHOTON COUPLING RATE
The single spin-photon coupling rate in the resonator, g s , can be assumed to be equal to half the Rabi frequencyof a spin 1/2 under the resonator vacuum magnetic field g s = gµ B B vac h , (S5)where g = 2 . µ B = 9 . − J/T the Bohr magneton, and h = 6 . − J s the Planck constant. An approximate expression to evaluate B vac from the resonator parameterscan be given as B vac (cid:39) µ I vac w , (S6)where we µ = 4 π × − N A − is the vacuum magnetic permeability, I vac = 8 . × − is the zero-point current in theresonator, which can be estimated as I vac = π (cid:112) h/Z f , Z being the characteristic impedance of the transmissionline (see also Ref. 22), and we assumed w = 400 µ m (taking into account the transverse extension of the B -fieldlines on the coplanar resonator surface, including the central strip line of 200 µ m, the gaps and part of the groundplanes). From these values we obtain B vac (cid:39) . × − T. Hence, the single spin coupling rate results from Eq. S5 g s (cid:39) . g c , considering that the simple analysis above neglects any average on the spatial distribution of the spins within themagnetic field profile. D. Bothner, T. Gaber, M. Kemmler, D. Koelle, and R. Kleiner, S. Wunsch and M. Siegel, Phys. Rev. B , 014517 (2012). M. W. Coffey and J. R. Clem, Phys. Rev. B , 342 (1993). M. J. Lancaster,
Passive Microwave Device Applications of High Temperature Superconductors (Cambridge University Press, Cambridge,1997). O. G. Vendik, I. B. Vendik and D. I. Kaparkov, IEEE Trans. Micr. Theory Tech., , 469 (1998). G. Blatter, M. Y. Feigelman, Y. B. Geshkenbein, A. I. Larkin and V. M. Vinokur, Rev. Mod. Phys. , 1125 (1994). S. Ryu and S. Stroud, Phys. Rev. B, , 1320 (1996). S. Ohshima, K. Kitamura, Y. Noguchi, N. Sekiya, A. Saito, S. Hirano and D. Okai, J. Phys. Conf. Ser. , 551 (2006). T. Honma, S. Sato, K. Sato, M. Watanabe, A. Saito, K. Koike, H. Kato, S. Ohshima, Physica C,
46 (2013). K. Sato, S. Sato, K. Ichikawa, M. Watanabe, T. Honma, Y. Tanaka, S. Oikawa, A. Saito, and S. Ohshima, J. Phys. Conf. Ser. ,012045 (2014). J. Krupka, J. Wosik, C. Jastrzebski, T. Ciuk, J. Mazierska, and M. Zdrojek, IEEE Trans. Appl. Supercond., , 1501011 (2013). J. Krupka, J. Judek, C. Jastrzebski, T. Ciuk,1 J. Wosik, and M. Zdrojek, Appl. Phys. Lett., , 102603 (2014). B. L. T. Plourde, D. J. Van Harlingen, N. Saha, R. Besseling, M. B. S. Hesselberth, and P. H. Kes, Phys. Rev. B , 054529 (2002). F. S. Wells, A. V. Pan, X. Renshaw Wang, S. A. Fedoseev and H. Hilgenkamp, Scie. Rep. , 867 (2015). A. F. Th. Hoekstra, A. M. Testa, G. Doornbos, J. C. Martinez, B. Dam, R. Griessen, B. I. Ivlev, M. Brinkmann, K. Westerholt, W. K.Kwok, and G. W. Crabtree, Phys. Rev. B , 7222 (1999). J. M. Sage, V. Bolkhovsky, W. D. Oliver, B. Turek and P. B. Welander, J. Appl. Phys. , 063915 (2011). C. T. Kiers, J. L. De Boer, R. Olthof, and A. L. Spek, Acta Cryst. B , 2297 (1976). G. R. Eaton and S. S. Eaton, Multifrequency Electron Spin-Relaxation Times, Multifrequency Electron Paramagnetic Resonance: Theoryand Applications, ed S. K. Misra, Wiley, 2011. J. A. Weil and J. R. Bolton, Electron Paramagnetic Resonance, Wiley (2007). P. W. Anderson and P. R. Weiss, Rev. Mod. Phys.
269 (1953). D. Zilic, D. Pajic, M. Juric, K. Molcanov, B. Rakvin, P. Planinic and K. Zadro, J. Mag. Reson.