Three-dimensional superconducting resonators at T < 20 mK with the photon lifetimeup to τ = 2 seconds∗

A. Romanenko,† R. Pilipenko, S. Zorzetti, D. Frolov, M. Awida, S. Belomestnykh, S. Posen, and A. GrassellinoFermi National Accelerator Laboratory, Batavia, IL 60510, USA

(Dated: December 25, 2019)

Very high quality factor superconducting radio frequency cavities developed for accelerators canenable fundamental physics searches with orders of magnitude higher sensitivity, as well as offer apath to a 1000-fold increase in the achievable coherence times for cavity-stored quantum states inthe 3D circuit QED architecture. Here we report the first measurements of multiple acceleratorcavities of f0 =1.3, 2.6, 5 GHz resonant frequencies down to temperatures of about 10 mK and fieldlevels down to a few photons, which reveal record high photon lifetimes up to 2 seconds, while alsofurther exposing the role of the two level systems (TLS) in the niobium oxide. We also demonstratehow the TLS contribution can be greatly suppressed by the vacuum heat treatments at 340-450◦C.

Superconducting radio frequency (SRF) cavities inparticle accelerators routinely achieve [1, 2] very highquality factors Q > 1010 − 1011 corresponding to photonlifetimes τ as long as tens of seconds. These are muchhigher than highest Q ∼ 108 reported in various quantumregime studies [3, 4] with τ ∼ 1 msec. Thus, adoptingSRF cavities for a 3D circuit QED architecture for quan-tum computing or memory appears to be a very promis-ing approach due to the potential of a thousand-fold in-crease in the photon lifetime and therefore cavity-storedquantum state coherence times. There is also a varietyof proposed fundamental physics experiments, i.e. darkphoton and axion searches [5–7], for which the availabil-ity of higher Q cavities in the lower photon regime woulddirectly translate into multiple orders of magnitude in-creases in search sensitivities.

Recent investigations [8] revealed that the two-levelsystems (TLS) residing inside the niobium oxide mayplay a significant role in the low field performance of SRFcavities, similarly to the 2D resonators [9, 10]. For fur-ther understanding of the physics involved, and to guideany future Q improvement directions, a direct probing ofSRF cavities in the quantum regime is required. Up tonow, no such investigations have been performed.

In this article, we report the first measurements of a se-lection of state-of-the-art SRF cavities down to very lowtemperatures (T < 20 mK) and very low fields of a fewphotons (“quantum” regime). We achieve the highest re-ported photon lifetimes of more than 2 sec, and observea Q decrease when going from previously explored tem-peratures of 1.4 K down to below 20 mK. It is also thefirst direct study of the TLS in the 3D Nb resonators inthe quantum regime, as well as the demonstration of thedrastic TLS-induced dissipation decrease associated withthe oxide removal. Our results demonstrate that SRFcavities can serve as the longest coherence platform fore.g. 3D cQED and quantum memory [4, 11] applications,as well as for various fundamental physics experiments,such as dark photon or axion searches [5–7].

We have used fine grain high residual resistivity ra-tio (RRR)>∼200 bulk single cell niobium cavities of the

TESLA shape [12] with resonant frequencies f0 of theTM010 modes of 1.3, 2.6, and 5.0 GHz.

The cavities utilized are shown in FIG. 1 along withthe calculated electric and magnetic field distributions.The fundamental frequency sets the radial dimension Rof the cavities: R ∝ 1/f0. Electromagnetic coupling tothe cavities is performed using axial pin couplers at bothends of the beamtubes.

We have also applied novel heat treatments in a customdesigned furnace [13] to remove the niobium pentoxide(Nb2O5) and to directly investigate the associated im-provement in the TLS dissipation on both 1.3 GHz and5 GHz cavities. The 1.3 GHz cavity has been heat treatedat 340◦C for several hours, whereas the 5 GHz cavity hasbeen treated similarly at 450◦C as the last step of thecavity preparation.

The measurements have been performed first at thevertical test facility where the cavities are submerged inliquid helium and temperatures down to 1.4 K can beachieved, and then in the dilution refrigerator at tem-peratures down to 10-20 mK.

For cavities in the vertical test dewar we have usedthe standard SRF measurement techniques [14] at higheraccelerating fields E, and the filtered decay method [8]at lower fields. The Q(E) results at temperatures downto 1.4 K in a broad range of - higher - cavity fields areshown in FIG. 2. It is remarkable that the 1.3 GHz cavityafter the 340◦C heat treatment has an extremely highquality factor Q >∼ 4 × 1011 in the broad range of fields,higher than the previously reported highest results [2].This indicates that the 340◦C heat treatment suppressesthe residual resistance at all fields, which may be alsorelated to the TLS or other potential mechanisms, i.e. tothe elimination of the possible metallic niobium suboxideinclusions inside the pentoxide layer.

For dilution refrigerator measurements, the doublelayer magnetic shielding around the full cryostat was usedand the magnetometers placed directly on the outsidecavity surfaces indicated that the DC ambient magneticfield level was shielded to below 2 mG in all cases. Themicrowave setup included a series of attenuators on the

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This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.

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FIG. 1. a) Single cell cavities of TESLA geometry used for the measurements; b) distribution of the magnetic and electricfields in the utilized TM010 mode (half of the rotationally symmetric cavity is shown); the coupling to the mode is performedusing the pin couplers on cavity axis on both sides; c) typical microwave setup used for measurements (the attenuators and theamplifiers were different in some cases for different frequencies and cooldown cycles).

0 5 10 15 20 25 30 35 40109

1010

1011

1012

1.3 GHz 2.6 GHz 5 GHz 1.3 GHz - after heat treatment 5 GHz - after heat treatment

Q

Eacc (MV/m)

1.4K < T < 1.5K

FIG. 2. Intrinsic cavity quality factors of the investigated 1.3,2.6, and 5 GHz cavities as a function of the accelerating fieldat temperatures 1.4 < T < 1.5 K.

cavity input line, as well as both cryogenic and roomtemperature amplifiers on the pickup line. For one ofthe runs with the 5 GHz cavity the Josephson Paramet-ric Amplifier (JPA) has been used in the output line aswell. The measurement configuration including the low-noise cryogenic amplifier allows to measure reliably thephoton lifetimes down to the average cavity populationn ∼10 photons, while JPA enabled extending it further tosingle photon levels. The cavity placement and a typical

microwave schematic of the setup are shown in FIG.1.The average photon number is calculated from the cav-

ity stored energy U : n = U/hω, where U = PtQt/ω isextracted from the measured transmitted signal Pt at thepickup coupler with the external quality factor Qt.

0 1 2 3 410-1100101102103104105106107108109

1010101110121013

n

Time (seconds)

5 GHzT <20 mK

n(t) = n0e-t/t

After heat treatment

Before heat treatment

HEMT+JPA

HEMT onlytL =0.07 sec

tL =0.23 sec

FIG. 3. Average photon population decay upon switching theRF power off measured in the 5 GHz cavities before and afterheat treatment at 450◦C. Blue and black curves correspond tothe decays from different starting fields and with the differentfiltering bandwidths (100 Hz and 10 Hz respectively). Thered lines show linear fits for both. Magenta and dark yellowlines show stored energy decays of the 450◦C treated cavitywith the much longer photon lifetime.

The typical decay curves for 5 GHz cavities before and

3

0.01 0.1 1108

109

1010

1011

1012

1.3 GHz 2.6 GHz 5 GHz 1.3 GHz - after 340C 5 GHz - after 450C TLS model fits

Q

Temperature (K)

Temperature rangeexplored in SRF

TLS-dominated regime

FIG. 4. Intrinsic cavity quality factor Q of the investigated1.3, 2.6, and 5 GHz cavities as a function of temperature. Pre-viously, SRF cavities have only been studied at temperaturesabove about 1.3 K. Below about 1 K a significant decrease inQ is observed consistent with the TLS dissipation - the redlines show TLS model fits. A dramatic increase in Q associ-ated with the oxide-modifying heat treatment is apparent onthe 1.3 GHz and 5 GHz cavities.

after 450◦C vacuum heat treatment for different startingcavity photon populations are shown in FIG. 3. Blue andblack curves correspond to two different starting powerlevels, as well as the different resolution bandwidths ofthe spectrum analyzer. As the exponential decay fits (redlines) indicate, the time constant and therefore the qual-ity factor Q remains constant down to the noise floor ofabout 10 photons and ∼2 photons. We have also ob-served no rf field amplitude dependence of the Q factorfor all the cavities in the dilution refrigerator setup. Itis consistent with our previous studies and higher tem-perature/higher field measurements in the current study,which showed that the “critical” TLS saturation fieldEc for niobium oxide is much higher - of the order ofEc ∼ 0.1 MV/m - and therefore TLS are not saturatedby the microwave fields from about n ∼ 1020 all the waydown to n ∼ 2.

Q(T ) measurements, which represent the main find-ings of our paper, are shown in FIG. 4. A characteristic∝ 1/ tanh

(α hω

2kT

)temperature dependence of the qual-

ity factors Q(T ) for all the cavities is clearly observedwith the Q decreasing towards lower temperatures. Theamount of Q degradation is drastically suppressed by theheat treatments - 340◦C for the 1.3 GHz and 450◦C forthe 5 GHz cavity respectively. This is consistent withthe removal of the significant number of TLS, which arehosted by the pentoxide layer of SRF cavities - as shownin our previous work [8].

TABLE I. Summary of TLS model fitting results.

f0 (GHz) Oxide treatment Fδ0 F δ01.3 No 5.2 × 10−10 1.0 × 10−7 0.172.6 No 8.2 × 10−10 2.4 × 10−8 0.135 No 9.1 × 10−10 1.2 × 10−8 0.08

1.3 340◦C 3 hrs 6.7 × 10−11 unknown n/a5 450◦C 3 hrs 5.6 × 10−11 unknown n/a

Below about 1 K the contribution to the surface resis-tance caused by the thermally excited quasiparticles be-comes negligible and the Q(T ) curves appear to be dom-inated by a dissipation caused by the TLS. The TLS dis-sipation increases as the temperature is further lowereddue to the decreased thermal saturation and therefore anincreased number of the TLS systems participating in theresonant absorption of the microwave power.

In the TLS-dominated regime, an excellent fit is ob-tained using the “standard” TLS model [9, 10] dissipa-tion with δ0 as the loss tangent of the TLS at T = 0 K, anadditional coefficient α to account for temperature mea-surement efficicency, and a fixed residual (Rres) surfaceresistance:

1

Q(T )= Fδ0 tanh

(αhω

2kT

)+Rres

G(1)

where F is the calculated filling factor [4, 15, 16], G =268 Ohm is the geometry factor of the TM010 mode forTESLA shape extracted from the finite element simula-tions [12].

In Table I the obtained fit Fδ0 values are shown for allthe cavities investigated. A dramatic - about an orderof magnitude - decrease in Fδ0 is associated with theheat treatments. For cavities before the heat treatments(with the pentoxide layer) the participation ratios can becalculated as in Ref. [8] assuming the ∼5 nm oxide layer,and the δ0 values can then be estimated as well. Theseare listed in Table I wherever applicable.

While the presence of TLS leads to the decrease ofQ from its values at higher temperatures, even in theworst case (5 GHz without heat treatment) we obtainthe photon lifetime τ = 32 msec, which is several timeshigher than the previous record of ∼10.2 msec [17]. Afterthe heat treatments, the achieved photon lifetimes of 0.5-2 sec correspond to a ∼50-200 times improvement.

To reveal the underlying material changes happeningduring the vacuum treatment in the temperature rangeof interest (340-450◦C) we have performed the directstudies on the niobium cavity cutout using the in-housetime-of-flight secondary ion mass spectrometry (TOF-SIMS) system. TOF-SIMS allows obtaining the depthprofiles of various elements within the sample with thesub-nanometer depth and better than parts-per-millionconcentration resolution and has been actively used inrecent years to guide the SRF cavity near-surface struc-

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0 10 20 30 40 50

0

100

200

300

400

500

600

Nb 2

O5- (c

ount

s) Before heat treatment After 400C 1hr

~5 nm

Niobium pentoxideelimination

Nitrogenpeak emergence

NbN

- (cou

nts)

Sputtering time (sec)

FIG. 5. TOF-SIMS depth profiles obtained on the cavitycutout revealing the changes in the niobium pentoxide andnitrogen-related signals after 400◦C in situ heat treatment.About 5 nm thick Nb2O5 pentoxide layer is completely dis-solved after the 400◦C treatment. Another apparent changeis the increase in the nitrogen level within ∼10 nm from thesurface.

ture tailoring [18]. Shown in FIG. 5, the comparisonbefore and after the 400◦C vacuum treatment (withoutsubsequent air exposure) has confirmed the removal ofthe Nb2O5, likely explaining the reduced TLS dissipationafter 340-450◦C treatments. Furthermore, we have dis-covered the emergence of the strong near-surface nitrogenenrichment, which is the likely cause of the “doping”-likeeffect we have found at higher cavity fields after theseheat treatments [19].

It is intriguing that the cavities after 340-450◦C heattreatments still have some non-zero Q degradation attemperatures lower than 1 K (FIG. 4). Since SIMS stud-ies suggest that there is no Nb2O5 after these treatments,an additional source of TLS should be present as well.Some potential examples could be other types of nio-bium oxides (e.g. NbO) and their interfaces with theunderlying bulk, or e.g. surface adsorbates. Pinpointingthese remaining sources would be a key goal of the futuredetailed investigations.

Practically, our findings open up a pathway of ex-ploring coupled SRF cavity-transmon structures as thehighest coherence superconducting quantum circuits forquantum computing. In particular, implementing theprotocol from Ref. [20] would allow direct generation ofvery long-lived Fock states in SRF cavities. One impor-tant question is what is the best way to insert the trans-

mon in the SRF cavity to provide enough coupling to thecavity mode of interest while not degrading the ultra-highQ. A possible solution is using the low-loss dielectric rod(such as sapphire) to hold the transmon in the relevantfield area of the cavity. Corresponding electromagneticdesign work and the mechanical and microwave measure-ments to validate this concept are currently on the way.

For new physics searches, using SRF cavities with theQ factors we have demonstrated allows for a sensitivityincrease of multiple orders of magnitude. A prototypedark photon “light-shining-through-the-wall” search ex-periment of the type as in Ref. [5] but now with muchhigher Q SRF cavities has been assembled and is cur-rently being commissioned with the results to be reportedin future publications.

In summary, we have performed the first measurementsof the state-of-the-art SRF accelerator cavities in thequantum regime and have demonstrated the photon life-times as high as τ = 2 sec - about a factor of 200 higherthan the records so far in this regime. We have also re-vealed the quality factor decrease at lower temperatures,consistent with the contribution of the TLS hosted by theniobium oxide, and demonstrated its mitigation by thein situ heat treatments at 340-450◦C resulting in the re-moval of niobium pentoxide, as witnessed by TOF-SIMS.

Fermilab is operated by Fermi Research Alliance, LLCunder Contract No. DE-AC02-07CH11359 with theUnited States Department of Energy. The authors wouldlike to acknowledge Dmitri Sergatskov, Oleksandr Mel-nychuk, and Damon Bice for participation in some ofthe aspects of this work, Joe Lykken for his support ofthis work, as well as David Pappas, Haozhi Wang, andMustafa Bal for providing a JPA used for one of the mea-surements.

∗ This work was supported by the US Department of En-ergy, Office of High Energy Physics.

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