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. Posen, and A. GrassellinoFermi National Accelerator Laboratory, Batavia, IL 60510, USA

(Dated: October 10, 2018)

Very high quality factor superconducting radio frequency cavities developed for accelerators canoffer a path to a 1000-fold increase in the achievable coherence times for cavity-stored quantum statesin the 3D circuit QED architecture. Here we report the first measurements of several 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 special vacuum heat treatment.

Superconducting radio frequency (SRF) cavities inparticle accelerators routinely achieve [1, 2] very highquality factors Q > 1010 − 1011 corresponding to pho-ton lifetimes T1 as long as tens of seconds, much higherthan highest reported Q ∼ 108 used in various quantumregime studies [3, 4] with T1 ∼ 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. Recent investigations [5]revealed that the two-level systems (TLS) residing insidethe niobium oxide may play a significant role in the lowfield performance of SRF cavities, similarly to the 2Dresonators [6, 7]. Therefore, direct probing in the quan-tum regime is required to assess the performance of the“as-is” SRF cavities, as well as to guide any future Q im-provement directions. Up to now, no such investigationshave 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 (“quan-tum” regime). We achieve the highest reported photonlifetimes of more than 2 sec, and observe a Q decreasewhen going from previously explored temperatures of1.4 K down to below 20 mK. Our results demonstratethat SRF cavities can serve as the longest coherence plat-form for e.g. 3D cQED and quantum memory [4, 8]applications, as well as for various fundamental physicsexperiments, such as dark photon searches [9]. Further-more, it is the first direct study of the TLS in the 3D Nbresonators in the quantum regime, as well as the demon-stration of the drastic TLS-induced dissipation decreaseassociated with the oxide removal.

We have used fine grain high residual resistivity ra-tio (RRR)>∼200 bulk single cell niobium cavities of theTESLA shape [10] with resonant frequencies of theTM010 modes of 1.3, 2.6, and 5.0 GHz. One of the inves-tigated 1.3 GHz cavities has been heat treated in vacuumat 340◦C in a custom designed furnace as the last stepof the cavity preparation. This novel treatment [11] re-moves/modifies the niobium pentoxide and allows us to

directly investigate the associated improvement in theTLS dissipation.

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 BlueFors dilution refrigeratorat temperatures down to 10-20 mK.

For cavities in the vertical test dewar we have used thestandard SRF measurement techniques [12] at higher ac-celerating fields E, and the filtered decay method [5] atlower fields. The Q(E) results at temperatures down to1.4 K in a broad range of - higher - cavity fields areshown in FIG. 1. It is remarkable that the cavity afterthe 340◦C heat treatment has an extremely high qualityfactor Q >∼ 4 × 1011 in the broad range of fields, higherthan the previously reported highest results [2]. Thisindicates that the 340◦C heat treatment suppresses theresidual resistance at all fields, which may be also relatedto the TLS or other potential mechanisms, i.e. the possi-ble presence of the metallic niobium suboxide inclusionsinside the pentoxide layer.

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

Q

Eacc (MV/m)

1.4K < T < 1.5K

FIG. 1. 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.

arX

iv:1

810.

0370

3v1

[qu

ant-

ph]

8 O

ct 2

018

2

FIG. 2. Experimental setup: a) cavity placement inside thedilution refrigerator for one of the experiments; b) typical mi-crowave setup used for measurements (the attenuators andthe amplifiers were different in some cases for different fre-quencies and cooldown cycles).

For dilution refrigerator measurements, a custom de-signed magnetic shielding was used and the fluxgate mag-netometers placed directly on the outside cavity surfacesindicated that the DC ambient magnetic field level wasshielded to below 2 mG in all cases. A microwave setupwas different from the vertical test dewar, and includeda series of attenuators on the cavity input line, as wellas both cryogenic and room temperature amplifiers onthe pickup line. The measurement configuration includ-ing the low-noise cryogenic amplifier (from Low NoiseFactory) allows to measure reliably the photon lifetimesdown to the average cavity population n ∼10 photons.The cavity placement and a typical microwave schematicof the setup are shown in FIG.2.

The latter is calculated from the cavity stored energyU : n = U/hω, where U = PtQt/ω is extracted fromthe measured transmitted signal Pt at the pickup couplerwith the external quality factor Qt.

The typical decay curves for a 5 GHz cavity for photonoccupations up to about 107 photons are shown in FIG. 3.Two curves correspond to two different starting powerlevels, as well as the different resolution bandwidths ofthe spectrum analyzer. As the exponential decay fit (redline) indicates, the time constant and therefore the qual-ity factor Q remains constant down to the noise floor ofabout 10 photons. We have also observed no rf field am-plitude dependence of the Q factor for all the cavitiesin the dilution refrigerator setup. It is consistent withour previous studies and higher temperature/higher fieldmeasurements of this work, which showed that the “crit-ical” TLS saturation field Ec for niobium oxide is muchhigher - of the order of Ec ∼ 0.1 MV/m - and there-fore TLS are not saturated by the microwave fields fromabout n ∼ 1020 all the way down to n ∼ 10.

0.0 0.2 0.4 0.6 0.8 1.0100

101

102

103

104

105

106

107

108

109

n

Time (seconds)

5 GHzT = 18 mK

n(t) = n0e-t/t

FIG. 3. Average photon population decay in the 5 GHz cavityafter switching the RF power off. Blue and black curves cor-respond to the decays from different starting fields and withthe different filtering bandwidths (100 Hz and 10 Hz respec-tively). The red line shows a linear fit for both.

0.01 0.1 1

109

1010

1011

1012

1.3 GHz 2.6 GHz 5 GHz 1.3 GHz - oxide freeTLS model fit

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 decreasein Q is observed consistent with the TLS dissipation - thered line shows a TLS model fit for the 5 GHz cavity. A dra-matic increase in Q associated with the oxide-modifying heattreatment is apparent on the 1.3 GHz cavity.

Q(T ) measurements, which represent the main find-ings of our paper, are shown in FIG. 4. A peculiar tem-perature dependence of the quality factors Q(T ) for allthe cavities is clearly observed with the Q decreasing to-wards lower temperatures. The amount of Q degradationis drastically different between the 1.3 GHz cavities be-fore and after the 340◦C treatment. This is consistentwith TLS hosted by the oxide layer of SRF cavities, as

3

shown in our previous work [5].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 [6, 7] dissipationwith δ0 as the loss tangent of the TLS at T = 0 K, an ad-ditional coefficient α, and a fixed residual (Rres) surfaceresistance:

1

Q(T )= Fδ0 tanh

(αhω

2kT

)+

G

Rres(1)

where F is the calculated filling factor [4, 13, 14], G =268 Ohm is the geometry factor of the TM010 mode forTESLA shape extracted from the finite element simula-tions [10].

For a 5 GHz cavity the fit is shown in FIG. 4, andtaking the calculated F ≈ 1.2 × 10−8 with the ∼5 nmoxide layer, we obtain a loss tangent δ0 ≈ 7.6 × 10−2.

While the presence of TLS leads to the decrease of Qfrom its values at higher temperatures, even in the worstcase (5 GHz) we obtain the photon lifetime τ = 32 msec,which is several times higher than the previous recordof 7 msec [4]. In the case of the cavity with the re-moved/modified niobium pentoxide, the photon lifetimeof 2 sec corresponds to a ∼300 times improvement.

It is intriguing that the cavity after 340◦C heat treat-ment still has some non-zero Q degradation at tempera-tures lower than 1 K. One possibility is that some fractionof the oxide - likely very thin - has re-grown, which never-theless has a noticeable contribution to low temperaturelosses. This in turn would suggest that the TLS-inducedlosses in the oxide are more localized at the interface(s),with the bulk contribution being relatively smaller. Itis also possible that a different (dry) niobium oxide isre-grown under a prolonged vacuum exposure, which hasfewer TLS than the regular oxide formed on SRF cavitysurfaces after air exposure and subsequent high pressurewater rinsing. Yet another possibility is that the remain-ing TLS are of a different nature, e.g. surface adsorbates.

In summary, we have performed the first measure-ments of the state-of-the-art SRF accelerator cavities inthe quantum regime and have demonstrated the pho-ton lifetimes as high as τ = 2 sec - about a factor of300 higher than the records so far in this regime. Thisopens up a pathway of exploring e.g. coupled SRF cavity-transmon structures as the highest coherence supercon-ducting quantum circuits for quantum computing andother potential applications. In particular, implementingthe protocol from Ref. [15] would allow direct generationof very long-lived Fock states in SRF cavities. We have

also revealed the quality factor decrease at lower tem-peratures, consistent with the contribution of the TLShosted by niobium oxide and demonstrated its mitiga-tion by the in situ heat treatment resulting in the oxideremoval/modification.

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 of theaspects of this work, as well as Joe Lykken and SergeyBelomestnykh for their support of this work.

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

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