Improving the performance of superconducting microwave resonators in magnetic fields

0.31 MB·English

by  Daniel Bothner

Improving the performance of superconducting microwave resonators in magnetic
fields
D. Bothner, T. Gaber, M. Kemmler, D. Koelle, and R. Kleiner
Physikalisches Institut – Experimentalphysik II and Center for Collective Quantum Phenomena,
Universita¨t Tu¨bingen, Auf der Morgenstelle 14, D-72076 Tu¨bingen, Germany
(Dated: January 18, 2011)
The operation of superconducting coplanar waveguide cavities, as used for circuit quantum elec-
trodynamics and kinetic inductance detectors, in perpendicular magnetic fields normally leads to
a reduction of the device performance due to energy dissipating Abrikosov vortices. We experi-
mentally investigate the vortex induced energy losses in such Nb resonators with different spatial
1
distributionsofmicropatternedpinningsites(antidots)bytransmissionspectroscopymeasurements
1
at 4.2 K. In comparison to resonators without antidots we find a significant reduction of vortex in-
0
ducedlossesandthusincreasedqualityfactorsoverabroadrangeoffrequenciesandappliedpowers
2
in moderate fields.

n
a PACSnumbers: 74.25.Qt,74.25.Wx,84.40.Dc,03.67.Lx
J

7
1 During the last decade coplanar microwave cavities trapping of ultracold atom clouds on a chip [18] or elec-
made of superconducting thin films have attained an in- trons in planar Penning traps [19]. We use strategically

] creasing importance for various experiments and appli- placed micropatterned holes (antidots) in the supercon-
n
cations. In circuit quantum electrodynamics, they form ducting film to provide well-known and highly control-
o
besides superconducting artificial atoms/qubits [1] the lable pinning sites for Abrikosov vortices [20–22]. The
c
- elementary building blocks for the fundamental investi- presentedresultsarealsotransferabletoothersupercon-
r
p gation of light-matter interaction on a chip [2–4]. These ducting microwave thin film devices, e.g. kinetic induc-
u integrated systems have also shown to be suitable can- tance detectors, mixers and filters, when operated in ex-
s didates for quantum information processing [5]. As low ternal magnetic fields.
.
t energylosses,thatishighqualityfactors,areanessential
a
m requirementtotheseresonators,therearecurrentlymany (a) 2 mm
efforts to identify and minimize the different dissipation B
-
mechanisms [6–9]. Recently, even more advanced hybrid
d
n systemshavebeenproposed[10–14],couplingrealatoms,
o moleculesorelectronstosuperconductingmicrowavecav- P P
app trans
c ities or combining artificial and real atoms. Here, micro-
+ +
[ Resonator
scopic particles need to be trapped and manipulated in

(b) (c) (d)
1 the vicinity of the resonator, thereby often requiring ex-
v ternal magnetic fields. 50 µm
5
Operating superconducting resonators in magnetic
8 0 1 3
fields can lead to considerable energy dissipation due to
1
3 Abrikosovvortexmotion[15]andthereforelowerquality FIG. 1: (Color online) Layout of a 12×4mm2 chip with a
. factors. Recently there have been some first approaches
1 capacitivelycoupled3.3GHztransmissionlineresonator(a),
toovercomethisproblemunderspecialexperimentalcon-
0 and optical images of resonators with 0 (b), 1 (c), and 3 (d)
1 ditions. Ifexperimentallyfeasible,themagneticfieldcan rows of antidots.
1 beappliedparalleltothethinfilm. Thisenabledthecou-
: plingofspinensemblesindiamondandrubytosupercon- We fabricated half wavelength transmission line res-
v
i ducting cavities in applied magnetic fields of ∼ 100mT onators with a resonance frequency fres ≈ 3.3GHz, ca-
X [16]. For the case of residual ambient fields it has been pacitively and symmetrically coupled to feed lines via
r shown, that energy losses due to a small number of vor- 70µm wide gaps at both ends. Figure 1 (a) shows a
a tices, caught while cooling through the superconducting sketch of the resonator layout. As the oscillating super-
transition temperature, can be reduced by trapping the currents are expected to mainly flow at the edges of the
vortices within a slot patterned into the resonator [17]. resonator, Abrikosov vortices located there will experi-
However, for magnetic fields with a considerable compo- ence a larger driving force than vortices far away from
nent(mTeslauptoTesla)perpendiculartothesupercon- the edges and therefore give a larger contribution to the
ducting chip, these approaches will not be sufficient. losses. Furthermore, if the magnetic field B is applied
In this letter we report on the experimental investiga- with the resonators in the superconducting state, as al-
tion of a method, which leads to a significant reduction ways in this work, the vortex density will be higher at
of microwave losses in superconducting Nb resonators in the edges, where the flux enters [23]. Hence, we placed
perpendicular magnetic fields, as required e.g. for the the antidots at the edges of the center conductor and
2

(a) Res 0 (c) resonance frequency fres(B) and FWHM ∆f(B) by fit-
µWP ()trans123 Papp i=n c-r2e0a sdiBngm B Q/1000 03+ tciniunlgFatiteghduertehcue2rqv(uecas)lwiftoyirthfathcateoLrroeQrseo(nnBtaz)tiao=nrs.fr0Wes(e(Bbsl)uu/be∆ssefqq(uuBaern)e,tslsy)hoacwnaldn-
3+ (red triangles). At B = 0 the resonator without an-
0 10
3.292 f (GHz) 3.293 tidotshasthehigherQ(0). However,forB ≥0.5mTthe
(b)3 qualityfactorofresonator3+significantlyexceedsQ(B)
Res 3+
W) P = -20 dBm of resonator 0 up to a factor of ∼ 2.5 at B = 4mT. We
µP (trans12 incarpepasing B n = 1 aptintrniibnugteofthviosrteinchesanbcyemtheenatnttoidaontse.ffective trapping and
3
T = 4.2 K

0
3.292 f (3G.2H93z) 3.294 0 1 B (m2T) 3 4 (a) n = 1 0 (b) B = 4 mT

3 1 3
FfIoGf.(2a:)(rCesoolonratoonrli0nea)nTdra(nbs)mreitstoendaptoorw3e+rPftorarnmsvasg.nferteiqcufieenlcdys 4Q x 10v2 133++ 4 x 10Qv2
0≤B ≤1.6mT (in 0.16mT steps); (c) shows corresponding 1/ 1/
quality factors Q(B) up to B =4mT. 1 1
P = -20 dBm
app
0 0
-4 -3 -2 -1 0 1 2 3 4 2 4 6 8 10 12 14
the ground planes in zero (reference sample), one and B (mT) f (GHz)
three rows, denoted as (resonator type) 0, 1 and 3, cf.
Fig. 1 (b), (c) and (d). The antidots have a diameter FIG. 3: (Color online) Vortex associated energy loss 1/Q
v
d = 2µm and an antidot-antidot distance a = 4µm as of five resonators with different antidot distributions (a) vs.
design parameters. As vortices in the feed lines will also appliedfieldB forfundamentalmode(n=1,f ≈3.3GHz)
res
contribute to the overall losses and lower the (loaded) and (b) vs. frequency f (n=1,2,3,4) at B =4mT.
quality factor Q(B), we implemented two different de-
signs for resonators 1 and 3: one with antidots only on In general many different field-dependent and field-
the resonator (1, 3) and one with additional antidots on independent mechanisms contribute to the total energy
the feed lines (1+, 3+), cf. Fig. 1 (a). The antidots loss 1/Q(B). To be able to quantitatively compare the
on the feed lines have the same configuration as on the different antidot structures with respect to their ability
respective resonator. to suppress vortex induced energy dissipation, we elimi-
Allstructureswerefabricatedonasingle330µmthick natedfieldindependentfactorsvia1/Q (B)=1/Q(B)−
v
2 inch sapphire wafer (r-cut) by optical lithography, dc 1/Q(0), cf. Refs. 15, 17. Figure 3 (a) shows the vor-
magnetronsputteringofa300nmthickNbfilmandlift- tex associated energy losses 1/Q (B) for n = 1 of five
v
offpatterning. TheNbhasacriticaltemperatureofT ≈ different resonators. The losses of all resonators with
c
9KandaresidualresistanceratioofR /R ≈3.6. antidots are significantly smaller than the losses of res-
300K 10K
The whole wafer was cut into single chips of 12×4mm2. onator0,althoughthemagnitudeofthereductionvaries
Each chip containing one resonator was mounted in a for the different antidot arrangements. The reduction of
brass box and contacted with Indium to SMA stripline lossesincreaseswithincreasingnumberofantidots;three
connectors. After zero-field cooling to T = 4.2K, we rows of antidots yield about twice the effect of one row
measured the frequency dependent transmitted power of antidots. The scaling of the loss reduction with the
P withaspectrumanalyzerfordifferentvaluesofap- numberofantidotrowsprobablymirrorsthenonuniform
trans
plied magnetic field |B| ≤ 4mT, which is perpendicular currentandvortexdistributionacrosstheresonator: vor-
to the resonator chip. Due to flux focusing we estimate tices near the edges contribute more to the losses than
the flux density seen by the resonator to be one order of those further away. The resonators 1+ and 3+ (open
magnitude larger than the applied field. Consequently, circlesandtriangles)showevenlowerlossescomparedto
the results presented below might be applicable to much their counterparts 1 and 3 without pinning sites on the
higherappliedfields, ifthegroundplaneareaisproperly feed lines (full circles and triangles). This suggests that
reduced. Figure 2 shows resonance curves P (f) for the ac vortex resistivity in the feed lines has a consider-
trans
the fundamental mode n = 1 of resonator 0 (a) and of able impact on the overall losses and can be reduced by
resonator 3+ (b) for different values of B and fixed ap- suitable pinning sites.
pliedpowerP . Forbothresonatorsf shiftstolower We note here, that the quality factor of the five res-
app res
frequencies with increasing magnetic field and the reso- onators in zero magnetic field varied between Q(0) ≈
nance peak becomes smaller and broader. The decrease 15000 (1) and Q(0)≈43000 (1+), but we neither found
of transmitted power and broadening of the resonance a correlation between zero field quality factor and anti-
peak though is much smaller for resonator 3+, indicat- dot configurations nor between Q(0) and 1/Q (B). This
v
ing reduced field dependent energy losses compared to leads to the conclusion, that the observed reduction of
resonator 0. For a quantitative analysis we determined 1/Q (B)canpurelybeattributedtoeffectivevortexpin-
v
3
ning by the antidots. pendent of P with a slight tendency of 1/Q to in-
app v
We also determined the losses 1/Q (B) for the first crease and Q to decrease with increasing applied power.
v
three higher order harmonics n = 2,3,4. Figure 3 (b) Note that the absolute quality factor Q(4mT) is dom-
shows 1/Q (f) for n = 1,2,3,4 of the five resonators at inated by the vortex induced losses, as it mirrors the
v
B =4mT.Wefoundthat1/Q (f)isnearlyconstantfor behaviour of 1/Q (4mT) almost independently of Q(0).
v v
all five resonators, with a small and surprising tendency Q(0) is nevertheless somewhat perceivable at B =4mT.
to decrease with frequency in contradiction to standard Resonator 1+ for example shows a higher Q than res-
models for the microwave response of vortices [24–26], onator 3 despite the higher vortex associated losses of
which predict a monotonous increase of the resistance resonator 1+. Essentially, the ratios of the vortex losses
with frequency. A detailed analysis of the data in terms and the quality factors of the five resonators and there-
of these models will be given elsewhere. Despite this fore the effectiveness of the antidots are almost constant
somewhat surprising behaviour it is important to note, for the investigated power range.
that the reduction of vortex associated losses by the in-
In conclusion, we demonstrated experimentally, that
troduction of antidots is quantitatively and qualitatively
energy losses in superconducting microwave resonators
stableoverabroadfrequencyrangeatleastfrom3.3GHz
due to the presence of Abrikosov vortices can be signifi-
to 13GHz.
cantly reduced by the introduction of antidots. Accord-
ingly, the quality factor Q(B) at finite applied fields in
(a) (b)
6 the mT range can be considerably increased with this
3 n = 1 5 method. We have demonstrated this result to hold for
410 004 a broad frequency range 3.3GHz ≤ f ≤ 13GHz and
Qx v 2 Q/103 four orders of magnitude of the applied power −40dBm
1/1 2 ≤ Papp ≤ 0dBm at a temperature of T = 4.2K.
0 1 1+
B = 4 mT 1 3 3+ Strategiesfortransferingtheseresultstohighermagnetic
0 0 fields might include the proper reduction of flux focus-
-40 -30 -20 -10 0 -40 -30 -20 -10 0
ing ground planes as well as the implementation of pin-
Papp (dBm) Papp (dBm) ningarrayswithtypicallenghthscaleswellinthesubmi-
cron range. As for many experiments incircuit quantum
FIG.4: (Coloronline)Experimentallydeterminedenergyloss
electrodynamics the resonators are operated in the Mil-
1/Q (a) and quality factor Q (b) vs. applied microwave
v likelvin and single photon regime, the effects presented
power P at B = 4mT and T = 4.2K of five resonators
app
here have to be investigated under these experimental
with different antidot distributions.
conditions in further studies.
We finally determined the power dependence of the This work has been supported by the Deutsche
quality factors Q(B) and energy losses 1/Q (B) for ap- Forschungsgemeinschaft (DFG) via the SFB/TRR 21.
v
pliedpowersfrom−40dBmto0dBm. ForP >0dBm D. Bothner acknowledges support by the Evangelisches
app
the resonance peak is cut off, indicating the ac supercur- Studienwerk Villigst e.V.. M. Kemmler acknowledges
rents to be overcritical near the maximum of the reso- support by the Carl-Zeiss Stiftung. We thank Stefan
nance. For smaller values of P the resonance curves Wu¨nschfromtheKarlsruheInsituteofTechnology(KIT)
app
showed no indication of nonlinearities. Figure 4 depicts for sharing his expertise in fabrication and characteriza-
(a)1/Q (P )and(b)Q(P )forthefivedifferentres- tion of superconducting resonators, and we thank Roger
v app app
onators at B = 4mT. Both quantities are almost inde- W¨ordenweber for inspiring discussions.
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