Mem. S.A.It. Vol. 79, 953c© SAIt 2008 Memorie della

Microwave Kinetic Inductance Detectors forLong Duration Balloon experiments

M. Calvo1,2, C. Giordano1,2, R. Battiston3,4, A. Cruciani1, P. de Bernardis1,B. Margesin5, S. Masi1, and A. Monfardini6

1 Universita di Roma ’Sapienza’, Piazzale Aldo Moro 2, I-00185 Roma, Italy2 INFN Sezione di Roma, Piazzale Aldo Moro 2, I-00185 Roma, Italy

e-mail: martino.calvo@roma1.infn.it3 Universita di Perugia, I-06100 Perugia, Italy4 INFN Sezione di Perugia, I-06100 Perugia, Italy5 ITC-irst, Via Sommarive 13, I-38050 Povo (Tn), Italy6 CNRS - Institut Neel, 25 avenue des Martyrs, 38042 Grenoble cedex 9, France

Abstract. Long Duration Balloon experiments have played a key role in the study of theCosmic Microwave Background. The measurement of its temperature anisotropies has beenthe first step towards a deeper understanding of the structure of the Universe. Yet to datemany questions regarding its birth and evolution remain open. The polarization signal ofthe CMB can help us answer most of them. In particular, the so called B modes would be adirect test of the Inflation and could give information on the scale of energies at which it tookplace. The amplitude of the B modes is expected to be less then 1µK. In order to measurethis kind of signal one needs either a very long integration time, or a very fast mappingspeed. In the case of LDB and satellite missions the second is the only viable solution. Thisposes a serious technological challenge as large arrays of detectors are usually very hard toimplement.In this paper we present the working principle of the Microwave Kinetic InductanceDetectors and their status of development in Italy, focusing on the key aspects that makethem ideal for application in LDBs experiments and in particular for a high purity, ultra-sensitive, polarization mapper.

Key words. Microwave Kinetic Inductance Detectors – Cosmic Microwave Background –CMB polarization – Long Duration Balloons experiments

1. Introduction

Over the last decades there has been a huge de-velopment in the detectors for millimetric andsub-millimetric radiation. Spider web bolome-ters with germanium and transition edge sen-

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sors have already reached a noise level that iscomparable or less than the intrinsic noise ofthe CMB radiation itself. The increase in sen-sitivity that is mandatory for the measurementof the B modes of CMB polarization cannottherefore be attained by means of more sen-sitive detectors, but rather using large arrays

954 Calvo et al.: MKIDs for Long Duration Balloons experiments

of sensors in the focal plane, including fromhundreds to thousands of pixels. To reduce thethermal load on the cold stage of the experi-ment one has to develop a multiplexing strat-egy for the readout, to be able to read morepixels via a single cable. Such a system is verycomplex to implement for the detectors com-monly used today.

In this context we have started studyingthe Microwave Kinetic Inductance Detectors(Day et al. 2003; Mazin 2003). MKIDs work-ing principle is based on the dependance of thesurface impedance of a superconductor fromthe density ncp of Cooper Pairs. When a pho-ton of energy hν > 2∆ is absorbed by the su-perconductor it causes a decrease in ncp anda consequent increase in the kinetic inductaneLkin. The very small variation of Lkin can bemonitored by designing a resonating supercon-ducting component shunting a feedline. Sincethe losses in the superconductor are extremelylow, Q factors of up to 106 can be obtained.Therefore, even a small shift of the resonancedue to the variation of Lkin produces a signifi-cant effect both on the amplitude and the phaseof a fixed bias signal sent through the feedlineat the unperturbed resonant frequency.

The high Q value is of primary importancealso because it ensures that each resonator pro-duces an effect only in a very narrow range offrequencies around the resonant one. The idealbias frequency for MKID resonators is in thefew GHz range: such a high frequency allowsvery high Q factors, and thus the multiplex-ing of thousands of pixels with a single feed-line. Using one single coax cable all the pixelscan then be read out simultaneously, by meansof frequency domain multiplexing. These de-tectors therefore provide a solution that offersa high mapping speed, combined with a lowthermal input on the cold stage.

2. Experimental setup

The experimental setup needed to work withMKIDs consists of two main components, thecryogenic system and the RF readout.

2.1. Cryogenic system

For the MKIDs to work properly, they are to bekept at temperatures well below their criticaltemperature, Tc. In our laboratory setup this isaccomplished by a closed cycle 3He − 4He re-frigerator mounted on the Cold Head of a PulseTube cooler. In a typical balloon application, asimple liquid He dewar can be used in place ofthe pulse tube. Using the low ambient pressureas a very high efficiency pump, the baselinetemperature will be well below the superfluidtransition, and its stability will depend quiteweakly on the float altitude stability. A vaporcooled shield (see the contribution of L. Natiet al. in these proceedings) will provide the in-termediate temperature necessary for thermal-ization of the bias and readout cables.

To send the RF signal to the MKID, mini-mizing the thermal load, a series of 3 low ther-mal conductivity coax cables has been used,thermalized at the 2 intermediate tempera-ture stages that are available (30K and 3K).Furthermore, DC blocks have been added onevery stage. A DC block consists of a verysmall break in the center pin of the coax cable.This strongly reduces the thermal conductivitythrough it, still allowing high frequency signalsto travel through.

Thanks to all these precautions the baseworking temperature reached in our setup isapproximately 310mK. This is reasonably lowfor Aluminum (Tc = 1.25K) resonators, andideal for Niobium Nitride (Tc ' 13K) ones.

2.2. RF system

The basic idea to readout the MKIDs is to com-bine the signal sent into the cryostat with theone getting out of it, in order to measure the ef-fect of the detector on its amplitude and phase.This can be accomplished in two ways. Thefirst one is using a Vector Network Analyzer:this option is very good for characterizing thedevices in terms of resonant frequency and Qfactor, but it is too slow for many applications.

If one wants to study fast signals, the so-lution is based on a RF synthesizer and anIQ mixer. The synthesizer produces a constanttone, which is split in two branches, one used

Calvo et al.: MKIDs for Long Duration Balloons experiments 955

Table 1. Resonant frequency and Q factors of the resonators on the Al chip at T = 310mK.

Resonator # fres [GHz] σ fres [GHz] Q [·104] σQ [·104]

1 2.765257 0.000007 7.0 0.12 2.83595 0.00001 8.0 1.83 2.89025 0.00002 14.0 1.14 3.298130 0.000007 1.44 0.045 3.944696 0.000009 7.2 1.36 4.91196 0.00002 11 3

as a reference and the second sent into thecryostat. The signal coming out of the cryostatand the reference one are then mixed togethervia an IQ mixer, which produces two outputsignals, proportional to the phase and quadra-ture components of the inputs product. If thetwo inputs are at the same frequency, the out-puts are DC signals.

The advantage of this scheme is that it canbe upgraded with relative ease to a multipixelsystem, if a comb of frequencies is generatedvia a fast DAC that is then up-converted to RFfrequencies and sent into the cryostat; an IQmixer is then used to recover the signals of allthe pixels.

To control the power which is used to read-out the MKIDs, a variable warm attenuator hasbeen added to the fixed value ones which areinside the cryostat. The output signal is thenboosted by a cold amplifier and a by a warmamplifier, for a total gain of 60dB.

3. First measurements

The first chip that we have used is made ofAluminum on a Silicon substrate, produced atthe IRST-ITC in Trento. The resonator is a dis-tributed one, in which the resonant frequency isdetermined by the length of the superconduct-ing strip coupled to the feedline. The chosengeometry is that of a coplanar waveguide.

The first fridge cycle has been devoted tothe determination the main properties of theresonator. Even though, given the limitationsof our cryogenic system, the temperature wasslightly higher then the ideal one, the obtainedQ values were nonetheless very high, and theresonant frequency has been determined with

high accuracy, as it is shown in table 1. Alreadyat this temperature, 1000 pixels could easily fitinto a 1GHz bandwidth, a good proof of thefeasibility of this multiplexing scheme.

We then moved to study the effect of in-creasing temperature on our resonators. As Tis raised, more and more Cooper Pairs willbreak due to thermal excitations and becomeunbound electrons or, as they are usually calledin this context, Quasi Particles. The conse-quent increase of Lkin and of the residual re-sisitivity of the QPs, Rqp, should affect the res-onance figure by shifting it towards lower fre-quencies (since Fres ∝ 1/

√Lkin) and making it

broader and shallower. One of the temperaturesweeps is presented in figure 1.

The variation of the surface impedance ofa superconductor can be evaluated using theMattis-Bardeen theory (Mattis and Bardeen1958), which gives the real and complex com-ponents of the surface conductivity. The kineticinductance represents only a fraction α of thetotal inductance, which has also a componentdue to the magnetic field energy, Lmag, whichdoesn’t vary with the value of ncp. Startingfrom

fres ∝ 1/√

Ltot

and variating it, one therefore finds

δ fres(T )fres(0)

= −12αδLkin(T )Lkin(0)

Thus an estimate of the fraction α of the ki-netic inductance can be obtained easily by fit-ting the data to the theoretical prediction ofMattis-Bardeen theory. The value of α we getis α = 0.024 ± 0.001. The graph is shown isfigure 2. This parameter has to be maximized

956 Calvo et al.: MKIDs for Long Duration Balloons experiments

-6

-5

-4

-3

-2

-1

0

2.7642 2.7644 2.7646 2.7648 2.765 2.7652 2.7654 2.7656 2.7658

Nor

mal

ized

S21

(dB

)

Frequency (GHz)

Effect of increasing T on the resonance of MKID 1

319 mK332 mK342 mK351 mK363 mK372 mK382 mK393 mK402 mK412 mK422 mK432 mK442 mK453 mK463 mK472 mK

Fig. 1. Variation of the resonance peak as the temperature is increased from 320mK to 470mK. Both thefrequency shift and the degradation of the Q factor are clearly visible. Notice how such a large increase ofT shifts the resonance center by less then 1MHz.

to get more sensitive devices, as the larger thefraction of inductance which is of kinetic ori-gin, the larger the effect its variation will have.

As a last step we illuminated the chip witha 145GHz light source, namely a Gunn diode,to check that the detectors were actually sen-sitive to photons of high enough energy (for

Fig. 2. Evaluation of the kinetic inductance fractionα obtained relating the data to the theoretical predic-tions of Mattis-Bardeen integrals.

Aluminum, νgap ' 90GHz). To take the data inthis case we used the system based on IQ mix-ers. The relevant variables in this case are theinphase and quadrature output of the mixers,which are plotted in the complex plane and arerelated to the complex value of the S 21 param-eter commonly used to describe RF devices.Sweeping the frequency across the resonanceone gets a circle in this plane, whose radius isproportional to the depth of the resonance it-self.

To readout the MKIDs we used a constantfrequency signal at fres,dark and measured theoutput variation due to the Gunn. Since thiswas the first run of chips we made, they werenot optimized for coupling to radiation, andthe throughput of our optical system was notwell defined. Nevertheless we clearly saw asignal synchronous to the on/off frequency ofthe Gunn diode. We expect the effect of lightto be analogous to that of an increase in tem-perature, as in both cases there is a decrease ofncp. In particular we should see the signal com-ing out of the cryostat less attenuated when theGunn is on, and with a different phase, as theresonance has shifted. Both these effects are

Calvo et al.: MKIDs for Long Duration Balloons experiments 957

Fig. 3. Effect of 145GHz radiation shone on the de-tectors. Even though the optical coupling is not atall optimized, the signal is clearly visible showingthat the sensors can be used for radiation of thiswavelength, particularly interesting for many fieldsof Cosmology.

evident in the measured data plotted in figure3.

4. Future prospects

The test-bench we have setup will be modifiedin the near future to reach lower temperatures(below 100mK), by means of a dilution refrig-erator. This will allow better measurements onthe Aluminum KIDs , on which we would liketo concentrate, as they are the best ones to useat the ”CMB” frequencies around 150GHz. Inthe meantime we have begun the optimizationof the chips, in particular as far as the opticalcoupling is concerned: we are designing a newmask with Lumped Element KIDs (Doyle et al.2008), a kind of KID detectors whose geom-etry can be tuned to match the impedance offree space. This improve enormously the cou-pling to the incoming radiation.

Until now all the resonators have beenstudied one at a time. The multiplex RF elec-tronics is under development at the Universityof Perugia, and as soon as the readout systemis ready we will include it in the Rome test fa-cility.

5. Use of MKIDs in LDB experiments

Several balloon and space missions have beenrecently proposed in the mm/sub-mm range.

All need a cryogenic system optimized forextremely long hold-time. The issue of theheat load from the readout is especially im-portant for a space mission with consumableliquid He, where the duration of the missionis limited by the hold time of the cryogen.For this reason MKIDs could be the detec-tors of choice for the future B-Pol mission (seehttp://www.b-pol.org). This mission is aimedat the detection of B-modes in CMB polar-ization, and a set of several thousand detec-tors will be needed. In view of this mission,a balloon-borne survey (B-B-Pol) is needed tovalidate all the involved technologies (see thepaper by P. de Bernardis in these proceedings).MKIDs could represent the detectors of choicefor the high-frequency instrument of B-B-Pol(140 and 220 GHz bands).

6. Conclusions

The first MKIDs chip that we have used isworking as expected, and though we are still atthe beginning of the development process theresults obtained make us optimistic: the Q val-ues are of order 105 even at relatively high tem-peratures, and we have managed to see lightwithout yet having optimized the coupling. Weare therefore confident that the optimizationprocess that is ongoing will lead us to the de-velopment of sensors that could play a key rolein future LDB and satellite missions.

Acknowledgements. We are grateful to prof. P.Mauskopf and dr. S. Doyle of University of Cardifffor enlightening discussions and suggestions, andfor sharing their experience on many topics and is-sues of this research. This research is supported bythe RIC program of INFN (Istituto Nazionale diFisica Nucleare), commission 5, and by Universityof Rome La Sapienza.

References

Day P. et al., 2003, Nature, 425, 817Doyle S. et al., 2008, J. Low Temp. Phys., 151,

530Mattis D. C. and Bardeen J., 1958, Phys. Rev.,

111, 412Mazin B., 2004, PhD thesis