Wireless Josephson Junction Arrays as Tunable Metamaterials: Inducing Discrete Frequency Steps with Microwave Radiation

1.9 MB·English

by  L. L. A. Adams

Wireless Josephson Junction Arrays as Tunable Metamaterials:
Inducing Discrete Frequency Steps with Microwave Radiation
L. L. A. Adams
School of Engineering and Applied Sciences, Department of Physics, Harvard University, Cambridge, MA 02138.
(Received textdate; Revised text)
Abstract
We report low temperature, microwave transmission measurements on a new switchable and tunable class of nonlinear
metamaterials. AwirelesstwodimensionalarrayofJosephsonjunctions(JJ)isprobedasametamaterialwhereeachplaquette
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in the array is considered as a meta-atom. In the presence of microwaves, this compact metamaterial of 30,000 connected
1
meta-atoms synchronizes the flow of Cooper pairs to yield a single robust resonant signal with a quality factor of 2800 at the
0
lowest temperature for our measurements. The transmission signal is switched on and off and its amplitude and frequency
2
are tuned with either temperature, incident rf power or dc magnetic field. Surprisingly, increasing the incident rf power above

n a threshold causes the resonance to split into multiple discrete resonances that extend over a range of 240 MHz for a wide
a temperature window. We posit that this effect is a new incarnation of the inverse ac Josephson effect where the Josephson
J plasma frequency locks to the rf drive frequency generating quantized frequency steps, instead of voltage steps, in the absence

3 of a dc bias. TEX .
2

] Prompted by theory [1],[2], extensive studies of care-
n
fully designed artificial materials, known as metamate-
o
c rials, are underway to find new electromagnetic phe-
- nomena such as amplification of evanescent waves [3]
r
p - [9], extraordinary transmission [10], [11], negative
u index of refraction [12], [13], and classical analogues
s
of electromagnetically-induced transparency [14] - [18].
.
t
a However,inspiteofrecentadvancesusingmetallicmeta-
m materials, requisites for practical applications such as
switching on and off a signal and modulating a signal’s
-
d frequency and amplitude using external control param-
n
eters still need to be addressed. Since fulfilling these
o
conditions with existing metallic structures is challeng-
c
[ ing, because of absorption losses, developing a new class

oftunable metamaterials,suchassuperconductingmeta-
1
materials, is arguably warranted. [19] - [26]
v
6 In this Letter, we show that tunable metamaterials FIG. 1: (Color online) Experimental set-up and sample a.)
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already exist in the form of superconducting Josephson Schematicoftheexperimentalsetupcontaininganetworkan-
7
junction, JJ, arrays. Most remarkable, however, isn’t alyzerandawaveguide. b.) Orientationofsampletoelectro-
5
0 their tunability per se, but discovering an unanticipated magneticwavesinwaveguide. c.) SEMimagesoftheJJmeta-
atom: above, image of the tunnel junction which is shown in
. rf power and temperature dependent manifestation of
1 the circular indentation in the image and below, two images
0 discrete frequency steps that, to our knowledge, has not of a single JJ meta-atom with 4 JJ per loop, left image, in
5 been previously reported. This physical phenomenon blackandwhite,andrightimage,incolor. d.) SEMimageof
1 opens up new possibilities for signal processing if scaled the JJ array showing only a small fraction, ˜80 meta-atoms,
:
v to THz frequencies [27], new opportunities for high fre- of the sample.
i quencydetectorsforradiotelescopes[28],andraisesnew
X
theoreticalquestionsabouttherelevanceoftheinverseac
r
Josephsoneffecttomicrowavetransmissionexperiments.
a
The inverse ac Josephson effect is the reverse of the ac frequency steps instead of voltage steps, and in between
Josephson effect. In the ac Josephson effect, an applied theseresonances,therearenarrowopaquewindowsinthe
dc voltage across a JJ generates a periodically oscillat- transmission line. The inverse ac Josephson effect only
ing supercurrent, pairs of electrons, that emits electro- appliesforunderdampedJJs[29]whichalsodescribesthe
magnetic radiation whereas in the inverse ac Josephson JJs studied here.
effect, shining electromagnetic radiation onto an unbi- TwodimensionalJosephsonjunctionarraysaremacro-
asedJJinducesadcvoltagedifferenceacrossthetunnel- scopic quantum materials with a highly tunable super-
ing barrier. Here we show that shining microwaves on a conducting current. We consider a wireless two dimen-
wireless Josephson junction array induces seven discrete sional network of 30,000 connected Josephson junction
1
(JJ)plaquetteswitheachplaquettehavingasquareloop
geometry containing 4 equally spaced JJs; we consider
theseplaquettesasmeta-atomswhichform,inaggregate,
aswitchableandtunablemetamaterial. Incontrasttore-
centmicrowavetransmissionreportsondiscrete splitring
JJ meta-atoms [30] , [31] , we find a sharp, robust reso-
nance. As with our previous measurements on this sam-
ple, abet at evanescent frequencies [9], the resonance is
clearlydistinctfromnoisewithoutprocessingthedataor
usinganyadditionalmicrowavecomponents,suchasam-
plifiers, attenuators, directional couplers or filters, which
also differentiates our work from others.
The experimental apparatus, described in detail else-
where[9],consistsofavectornetworkanalyzerconnected
toaX-bandwaveguideviaphase-maintainingco-axialca-
bles as seen in the schematic of Figure 1 a. The waveg-
uide, enclosed in a vacuum can, is cooled to cryogenic
temperatures; itismagneticallyshieldedby µ−metalto
reduce the ambient field. The JJ metamaterial is posi-
tioned in the center of the waveguide and oriented such
that the rf B-field is normal to the plane of the array as
seen in the schematic in Figure 1 b.
The sample is a portion of a much larger array [32],
[33]; its transport properties, before removing electri-
cal contact pads and reducing its size, have been ex-
tensively studied elsewhere. [34] Scanning electron mi-
croscope, SEM, images of a single tunneling junction,
Nb-amphoroussilicon-Nb, andofasinglemeta-atomare
seen in the upper and lower left images, respectively, of
Fig. 1 c. The 500 nm niobium thick square loop is 29
µm×29 µm with a linewidth of 5 µm. Each of the 4 JJs
in the loop has an area of 2.5 µm2 with an insulating
barrier of 10 nm. A colored optical microscope image of
a single meta-atom showing niobium coverage is seen in FIG.2: (Coloronline)Switchingaresonanceonandoffwith
the lower right image of Fig. 1 c; the non-continous cov- temperature and rf power. a.) Temperature dependence at
erageofniobiumindicatesthatresonanceoccursbecause fixed rf power, -55 dBm, for T = 2 K (red) and 10 K (black)
and b.) rf power dependence at fixed temperature, 2 K, for
chargedparticlesmusttunnelacrosscapacitivetunneling
rf power -55 dBm (red) and -5 dBm (black). Note that the
barriers to circulate throughout the network. A portion
range in transmission on the vertical axis is different in a
of the JJ metamaterial is seen in the SEM image of Fig.
and b. Also note that the transmission values above 0 dB
1d. TheindividualJJmeta-atomsareabout1500times correspondto0dB:thisoffsetisduetothecalibrationbeing
smallerthanthemicrowavewavelength,whichisapproxi- done at room temperature while the measurements are at
mately 40 mm, placing them in the deep sub-wavelength liquid helium temperatures.
limit.[35] The superconducting transition temperature,
T , of the individual niobium islands is 9.2 K. [36]
c
If we consider that each JJ contributes a capacitance,
ing rf frequency should be significantly larger than the
C, estimated to be 0.9 pF, a normal state resistance, R, (cid:113)
estimated to be 510 Ω, and a critical current, Ic, which natural Josephson plasma frequency, f= 21π 2(cid:126)eCIc ∼ 15
is estimated to be 0.165 µA, [37], we can estimate the GHz. [39] The resonant frequency, which is the plasma
degree of damping in a junction, using the dimensionless frequency[9],alsodepends,inpart,onthesample’sloca-
McCumber parameter, βc, which is βc = 2eIc(cid:126)R2C ∼ 118, tion in the waveguide indicating the need for additional
where e is the electron charge and (cid:126) is Planck’s constant capacitive terms [40], which would lower the resonant
divided by 2π. Since β > 1, the junction is said to be frequency but not by enough to satisfy this second con-
c
underdamped meaning that there are inertial effects of dition. Nevertheless, we will show that the mechanism
the ”phase” particle [38] which satisfy one of the condi- responsible for the transmission features seen here are
tions required for the inverse ac Josephson effect [29]. A due to the inverse ac Josephson effect.
second condition that needs to be met is that the driv- Cooling the sample to temperatures below the su-
2
FIG.4: (Coloronline)RFpowerdependenceatfixedtemper-
FIG. 3: (Color online) Tuning the resonance with temper- ature, T=1.1 K. The black arrows indicate multiple discrete
ature and rf power. Temperature dependence when the rf resonances that appear below the central resonance and at
power is fixed at a. )-55 dBm and b.) -49 dBm for tempera- highrfpower; thesearespacedabout0.04GHzapart. Inset:
tures: T=2.0K(black),T=3.0K(red),T 4.0K(green),T RF power dependence at fixed temperature, T = 1.24 K for
=5.0K(blue)=6.0K(purple),andT=7.0K(brown). Ag- -49.5 dBm (blue) and -49 dBm (red).
gregation of temperature-dependent data at fixed power: c.)
-55 dBm and d.) - 49 dBm. Each color represents a different
temperature.
ers, -55 dBm, as seen in Fig. 3 a, and -49 dBm, as seen
in Fig. 3b. At -49 dBm, the higher rf power, the res-
onance also shifts to lower frequencies while broadening
perconducting transition temperature and applying low with increasing temperature; however, the overall ampli-
powermicrowavestotheJJarrayresultsinasharpreso- tude decreases and the resonance dip splits into two for
nanceatf =8.08GHzappearingintransmissionasseen T < 6 K.
in the plots of Fig. 2. Extinguishing the resonance is
To elucidate the effect of the resonances splitting at -
achieved by either increasing the temperature above the
49 dBm, we compare two large sets of temperature data,
superconductingtransitiontemperatureasseeninFig. 2
one at -55 dBm and the other at -49 dBm as seen in
a, or by increasing input power as seen in Fig. 2 b.
Fig. 3 c and 3 d. The aggregate temperature data at
Increasing temperature, at fixed rf power, shifts the -49 dBm and for T < 5.2 K clearly show a simple ”egg
resonance to lower frequencies and broadens the reso- crate” pattern in transmission that is not present at -55
nance. Thisisseeninthetransmissionvsfrequencyplots dBm. Withincreasingrfpower,screeningcurrentsbegin
for different temperatures in Fig 3 a-d. As temperature to slosh back and forth generating an ac magnetic field
increases, Cooper pairs break lowering the critical cur- which cancels the applied RF field. Furthermore, when
rent,Ic,andthusshiftingtheresonancetolowerfrequen- these induced ac supercurrents, driven by external mi-
cies. While the density of Cooper pairs decreases, the crowave radiation, lock to the natural oscillations of the
density of normal conduction electrons increases, lead- array there is a range of DC currents for which there are
ing to more dissipation and insertion loss; for instance, constant frequency steps. This current range is depicted
a jump of - 5 dB in insertion loss is measured when the in the number of resonances, with different amplitudes,
temperature reaches 7 K as seen at 7.2 GHz in Fig. 3a appearing at the same frequency.
and 3b. While these behaviors are reminiscent of those Frequency locking is also manifested when increasing
seenwithsuperconductingmetamaterials[22],[42],they the RF power at fixed temperature, T= 1.1 K, as seen
arenotidentical. Here,theresonancesaremoresensitive in the transmission vs frequency plot in Fig. 4. As the
to temperature increases due to Cooper pairs tunneling RF power increases, the number of dips also increase.
across barriers as described by the Ambegaokar-Baratoff While an increase in the current decreases the depth of
current-temperature relation. [43] the dip, it does not explain multiple dips. We surmise
Similar temperature dependent resonant responses that the increase in the number of dips is analogous to
persistwhencomparingresponsesattwodifferentrfpow- Shapiro steps observed in dc current-biased experiments
3
step represented by a different color, in Fig. 5 a. Con-
sidering the temperature to be proportional to the dc
current and the frequency proportional to dc voltage, by
the Josephson relation, V = n((cid:126)ω )/2e , then these
DC RF
stepslooksimilartothosefoundinI(V)curvesforspon-
taneousemissioninbiased, underdampedJJarrays. [45]
TherangeofphaselockingandDCcurrentsinourexperi-
mentsisindicatedbytheplateausforeachfrequency;the
width of the plateau becomes smaller with higher order
stepsbecausethecurrentisexpressedintermsofaBessel
function. [38] Between resonant frequencies, the phase is
unlocked leaving narrow electromagnetically opaque re-
gions. A diagonal line is draw in the plot to show the
linear behavior between frequency and temperature at
temperatures close to T , the transition temperature of
co
thearray,˜6.5K.Comparingresonantfrequenciesfor-55
dBm and -49 dBm reveals two main differences: first is
the appearance of steps at -49 dBm and second, is the
systematic higher shift in the frequency vs temperature
at -55 dBm below the transition temperature as shown
in the lower inset of Fig. 5 a. This shift is due to the
induced rf currents being lower.
Thestrengthoftheresonance,transmissionamplitude
of S , is dependent on rf power as seen in Fig. 5 b.
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However, we find that it also varies with temperature, in
contrast to split ring resonantors with JJs [31], except
at temperatures between ˜5 K and 6 K which coincides
totemperatureswherefrequencystepsnolongerprevail.
Since the resonance splits at -49 dBm, we label the two
resonances either left as seen in green in Fig. 5 b or
FIG.5: (Coloronline)a.) Resonantfrequencyversustemper- right as seen in red in Fig. 5 b. The -55 dBm and -
atureat-49dBm. SevenstepsareclearlyvisibleforT<5K. 49 dBm curves crossover at ˜6.5 K which is the same
Each of the different colors correspond to separate dips con-
temperature that the resonant frequency flattens out as
tainingmultipleresonances. Alineisdrawtoshowthelinear
seen in Fig. 5 a. This is indicated by a vertical dash line
dependence at temperatures close to the transition tempera-
in Fig. 5. There is still a resonance beyond 6.5 K that
ture of the array. Inset: Comparison between -49 dBm (red)
and - 55 dBm (blue). b.) Transmission Amplitude, S , ver- doesn’t change in frequency suggesting superconducting
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sus temperature at -49 dBm (red and green) and - 55 dBm quasiparticles tunneling until T ˜ 8.5 K.
(blue). In conclusion, our results demonstrate that a wire-
less JJ array in a waveguide can controllably switch on
and off a microwave signal with temperature and input
power. The array can also modulate the signal over a
withamicrowaveirradiatedJJ.[44]Here,however,there rangeoffrequenciesandamplitudesbyvaryingeitherin-
isnoappliedbias,onlyaninduceddcvoltagebias. Since putpower, temperature, ordcmagneticfield(notshown
the device is nonlinear, locking occurs not only at ωRF, here). Modulating signals with temperature is tradition-
but also at harmonics of the RF frequency - that is, ally considered to be quite slow; however, for JJ arrays,
at multiples of ωRF, such that nωRF = ωJ - giving rise the response occurs rapidly and without noticeable de-
to discrete dips appearing at lower frequencies and sep- lay. The signal is sharp and robust without processing
arated by 0.04 GHz as indicated by the black arrows in the data and does not require the aid of amplifiers and
Fig. 4. A close-up image of a resonance splitting into filters in the experimental configuration. Moreover, our
two with higher RF power for T =1.24 K is seen in the results reveal qualitatively new phenomena for tunable
inset of Fig. 4. metamaterials that occur as the input power increases,
Wealsoanalyzetheseresultsbystudyinghowthereso- breaking the central resonance down to discrete frequen-
nant frequency and transmission amplitude change with cies. Finally, this alternative perspective on metamate-
temperature and rf power. These results are shown in rials may provide new strategies for future metamaterial
the plots of Fig. 5. There are seven steps in resonant design and tunability.
frequencybelow5Kthatareclearlyobserved, witheach Acknowledgements. None of this work would have
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