Using conventional superconductor theory we discuss and validate a model that
describes the energy-resolving performance of an aluminium LEKID to
single-photon absorption events. While aluminium is not the optimum material
for single-photon counting applications, this material is well understood and
is used to understand the underlying device physics of these detectors. We also
discuss data analysis techniques used to extract single-photon detections from
noisy data.Comment: 17th International Workshop in Low Temperature Detectors Conference
  Proceeding

Doyle, Simon

Papageorgiou, Andreas

Parrianen, Josie Dzifa Akua

Pascale, Enzo

English

arXiv

We present the first published results of near-infrared single-photon detection in aluminium lumped element kinetic inductance detectors (LEKIDs). Using aluminium as a well-understood material that follows conventional superconductor theory, we discuss and validate a model that describes the energy-resolving performance of a LEKID to single-photon absorption events. We also discuss data analysis techniques used to extract single-photon detections from noisy data. We measure an energy resolution of 662 meV for a 1550 nm photon source which is in close agreement to our model predictions for this non-optimised device limited by generation–recombination noise

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Journal of Low Temperature Physicshttps://doi.org/10.1007/s10909-018-2064-3Modelling the Performance of Single-Photon CountingKinetic Inductance DetectorsJosie Dzifa Akua Parrianen1 · Andreas Papageorgiou1 · Simon Doyle1 ·Enzo Pascale1,2Received: 6 November 2017 / Accepted: 28 August 2018© The Author(s) 2018AbstractWe present the first published results of near-infrared single-photon detection in alu-minium lumped element kinetic inductance detectors (LEKIDs). Using aluminium asa well-understood material that follows conventional superconductor theory, we dis-cuss and validate amodel that describes the energy-resolving performance of a LEKIDto single-photon absorption events. We also discuss data analysis techniques used toextract single-photon detections from noisy data. We measure an energy resolutionof 662 meV for a 1550 nm photon source which is in close agreement to our modelpredictions for this non-optimised device limited by generation–recombination noise.Keywords Single photon · Energy resolving · Kinetic inductance detectors1 IntroductionA principal goal of the next generation of space-based astronomy will be dedicatedto the characterisation of extra-solar planets (exoplanets). Of the 1000s discovered,only a handful have been spectrally analysed. As such, there is increasing interest innew exoplanet missions aiming to carry out spectroscopy on very low intensity lightand shallow transit light curves. Energy-resolving, single-photon counting detectorsprovide an elegant solution for carrying out imaging spectroscopy without the needfor gratings, prisms or combinations thereof. Kinetic inductance detectors (KIDs) area proven technology capable of energy-resolving single-photon events at optical andnear-infrared (NIR) wavelengths. Recent experiments such as ARCONS an opticalto NIR spectrophotometer [1] have achieved energy resolutions of order 300 meVat 400 nm. However, this is~10 times worse than the theoretical limit imposed byB Josie Dzifa Akua Parrianenjosie.parrianen@astro.cf.ac.uk1 School of Physics and Astronomy, Cardiff University, Cardiff, UK2 Dipartimento di Fisica, Sapienza Universita di Roma, Rome, Italy123Journal of Low Temperature PhysicsPoisson statistics. Similar experiments working at 1550 nm show the same deviationfrom theoretical limits achieving energy resolutions of order 220 meV [2]. Still, this isjust a factor of~2 worse than transition edge detectors in the same regime [3, 4]. Herewe present the first published results of NIR single-photon response in aluminium (Al)LEKIDs.2 Single-Photon ResponseModelKIDs are thin-film, superconducting microresonators [5]. Photon absorption leadsto the breaking of Cooper pairs to create quasiparticles (un-paired electrons in thesuperconductor). The quasiparticle population determines the resonance frequency, ofthe resonator, through its surface impedance. Changes to the surface impedance aregoverned by kinetic inductance.The absorption of a photon of energy hv creates a proportional number of excessquasiparticles; we assume the population is increased uniformly across the detector.A first-order estimate is given by Nqp,xs  ηhν/, where we assume η  0.4 is thequasiparticle generation efficiency for thin-film Al [6] and  is the superconductorenergy gap. Any change in the quasiparticle population corresponds to a change inthe detector’s resonance frequency d f0. Using conventional superconductivity theory,we simulate the detector response as a function of change in quasiparticle populationd f0/dNqp [7] to find the resonance frequency shift: d f0,max  Nqp,xs × d f0/dNqp.The expected response to single-photon absorption is a pulse with an exponentialdecayof the resonance frequency shiftd f0. Thedecay time is governedby the dominanttime constant of the detector. We assume this to be the quasiparticle lifetime τqp, suchthat d f0(t)  d f0,maxe−t/τqp . Note that τqp is longer than the detector ring-up/ring-down time given by Q/π f0. This is demonstrated in Fig. 2 where the rise time ofthe pulse is determined by the resonator ring-up time and the far slower decay isdetermined by τqp.This first-order model assumes that single-photon absorption results in a uni-form rise in the quasiparticle distribution across the detector’s meander, producingan expected maximum pulse height of~120 Hz.3 Energy ResolutionThe energy resolution of a single-photon detector is given byE  hν × noisesignal. (1)In a KID, the noise equivalent power (NEP) for a given detector volume andtemperature is fundamentally limited by the random fluctuation in the quasiparticle123Journal of Low Temperature Physicspopulation, known as generation–recombination (GR) noise. This limit is describedby [8]NEPGR  2√Nqp/τqp. (2)We multiply Eq. (2) by the detector time constant τqp to convert to noise equivalentenergy NEEGR  2√Nqpτqp, which gives the energy resolution in 0.5 s of integra-tion time. For single-photon events, the response is measured over the detector timeconstant; in our case, it is dictated by τqp. Taking into consideration the quasiparticlegeneration efficiency, the GR noise-limited energy resolution is approximated byσGR  η√2Nqp. (3)The fundamental noise for a detector capable of single-photon detection is governedby the Fano limit and is given byσphoton √hνFη, (4)where F  0.2 is the Fano factor [9]. For a KID, the Fano factor takes into accountthe variance in the number of quasiparticles generated due to single-photon absorptionevents.We therefore propose a limit on the energy resolution of a single-photon KID as acombination of the two fundamental limits from Eqs. (3) and (4). The convention is toquote the full-width-at-half-maximum (FWHM) energy resolution, where FWHM 2.355σ so thatElim  2.355√2η22Nqp +hνFη. (5)The devices were measured at 100 mK and have meander volumes of~1400 µm3.Based on the theory outlined above, we predict σGR  1.3 meV, and thus, Elim 21 meV for our test devices following Eq. (5). This suggests the detector is atthe fundamental photon limit. However, the quasiparticle lifetime (and equivalentlythe quasiparticle density) has been shown to saturate at some temperature due tomicrowave heating [10, 11]. We have measured this saturation in our device, seeFig. 2, showing a saturation temperature of approximately 190 mK. This adjustsour GR-limited 1-sigma energy resolution to σGR  142 meV, and thus, we predictElim  335 meV, putting our detectors very firmly in the GR noise limit.4 Experimental Set-Up andMeasurementWe used a 624-pixel lumped element (LE) KID array developed for part of theSpaceKIDs project [12], optimised as a 350 GHz narrowband Earth observation123Journal of Low Temperature PhysicsFig. 1 Left: Schematic of LEKID architecture. Interdigitated capacitor (IDC) and meander have linewidth4 µm with meander volume~1400 µm3. Right: Image of fibre-chip interface (Colour figure online)demonstrator. The array is formed of a 30 nm Al film (TC 1.3 K) on a 320-µmsilicon (Si) substrate. There is an additional low TC titanium aluminium (TiAl) bi-layer on the backside of the substrate, designed as a phonon-absorbing layer to limitthe effects of cosmic ray events in the array. The pixel design follows standard LEKIDarchitecture [13]with the inductivemeander patterned into a third-orderHilbert fractal,shown in Fig. 1.The array was cooled down, to a base temperature of 100 mK, using a miniaturedilution refrigerator. A standard homodyne readout technique was used to measurethe detector response. Measurements were made with a 1550 nm laser diode mountedon the 4 K stage. The incident photons are carried by a 9 µm single-mode fibreoptic cable up to the ultra-cold stage and are attenuated before entering the deviceholder. A modified plate, shown in Fig. 1, ensures roughly half of the pixels aredirectly illuminated. The device is flood illuminated at a constant DC power level.The time-dependent fluctuations in resonant frequency are measured and analysedunder illuminated and non-illuminated conditions.5 ResultsThe analysis of the data produced in this work has two main aims: (1) to measure theimpulse response decay time constant τ and (2) to identify single-photon absorptionevents and measure the pulse amplitude of such events.The impulse response time constant wasmeasured by illuminating the detector withoptical square-wave pulses and fitting to the pulse decay time. Several pulses werestacked to increase the signal-to-noise ratio (SNR). At temperatures above 200 mK,the SNR became too low, at which point we use the method of fitting to the noise123Journal of Low Temperature PhysicsFig. 2 Left: Averaged normalised stacked impulse response found in the illuminated detector response. Anexponential (red line) is fitted with τ 1.9 ms. Right: The quasiparticle lifetime as a function of bathtemperature, using two methods for extracting the time-constant. Kaplan theory [14] is fitted to the noiseroll-off data (blue) (Colour figure online)Fig. 3 Left: Impulse detection counts as a function of impulse amplitude; detection counts shown for bothdark (LEDoff) and illuminated (LEDon) detector. Dark detections are false detections and represent the sen-sitivity limits of the detection algorithm. Right: Normalised expected photon absorption event distribution,which shows a peak at approximately 120 Hzroll-off from the detector response power spectral density (PSD) [10]. Figure 2 showsthe combined detector time constant fitting results.The time constant was validated by fitting to detector impulse responses to single-photon absorption events. Potential absorption eventswere identified by a step functionmatched filter. Such events were stacked and averaged, as shown in Fig. 2, which hasbeen fitted with an exponential of τ 1.9 ms, matching the same value found forsquare-wavemeasurementsmade at 100mK.We take this as the quasiparticle lifetime.Having obtained an estimate of the impulse response, 20 s response time streamswere Wiener filtered—with bandwidth~2 kHz—and potential photon absorptionevents were identified by matched filter. The same procedure was applied to bothilluminated and dark detector data; the extracted counts are shown in Fig. 3. The darkdetector has only “false” events due to the limitations of the impulse extraction proce-dure, while the illuminated detector counts comprise both “true” and “false” events.The illuminated detections significantly outnumber the false detections, picked outfrom the dark detector, for impulses of amplitude>200 Hz. This surplus of detections123Journal of Low Temperature Physicsis attributed to true photon absorption events. Given the extraction method employedhere, photon absorption events with amplitude<200 Hz are more difficult to discernbetween true and false detections. This uncertainty is depicted by the vertical error barsshown in Fig. 3. Note that counts below 50 Hz have been set to zero due to excessivenoise.The expected photon absorption distribution is then measured by subtracting thedark data detections from the detections of the illuminated data (using a coefficientof 1), resulting in the plot shown in Fig. 3. Notice the photon absorption distributionpeaks at an amplitude of~120Hz,matching our expected pulse height. Theremay alsobe a peak at~240 Hz with very small error bars, suggestive of two-photon absorptionevents.As an initial estimate for the energy resolution of our measurements, we refer toEq. (1), taking our noise as the FWHM of the right plot from Fig. 3 and the peak valueas our signal, such that Ecalc  662 meV. This is~2 times worse than expected.However, the Weiner filtering process reduces the integration time to~ τqp/4 leadingto a√4 increase in GR noise contributions: Elim  668 meV. Accounting for thereduced effective integration time, our measured value is in rough agreement withour predicted theoretical limit. Measuring such low energy photons in the presenceof relatively high GR noise has resulted in poor SNR (as depicted by the error barsin Fig. 3), with the absorption distribution being not well defined. As such the truepeak value is not easily discerned and the Gaussian width used to calculate energyresolution is likely skewed by the apparent~240-Hz peak. We also note it is likely thedistribution includes responses from photons absorbed in the capacitor section of thedevice where reduced response is observed, as has been seen in similar devices [2].6 Conclusions and FutureWorkWe show confirmation of single-photon detection which corroborates our first-ordersensitivity model in the presence of GR noise, using η  0.4 for thin-film Al. Wehave also shown the limiting effects of microwave heating on such devices thatcomplies with theory and measurement. We plan to fully confirm this model by mea-suring devices of varying volumes over a range of optical frequencies and operatingtemperatures enabling clearmapping of theFano andGRnoise contributions to energy-resolving LEKIDs.Acknowledgements Weacknowledge the Science and Technology Facilities Council (STFC)ConsolidatedGrant Ref: ST/N000706/1 and studentship funding for supporting this work. We also take the opportunityto thank the reviewers of this paper for their insightful comments.Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 Interna-tional License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,and reproduction in any medium, provided you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate if changes were made.123Journal of Low Temperature PhysicsReferences1. B.A. Mazin et al., Publ. Astron. Soc. Pac. 125(933), 1348–1361 (2013)2. W. Guo et al., Appl. Phys. Lett. 110(21), 212 (2017)3. A.E. Lita, A.J. Miller, S.W. Nam, Opt. Express 16(5), 3032–3040 (2008)4. A.J. Miller, S.W. Nam, J.M. Martinis, Appl. Phys. Lett. 83(4), 791 (2003)5. P.K. Day et al., Nature 425(6960), 817–821 (2003)6. T. Guruswamy, D.J. Goldie, S. Withington, Supercond. Sci. Technol. 27(5), 55 (2014)7. S.M. Doyle, Lumped Element Kinetic Inductance Detectors (Cardiff University, Cardiff, 2008)8. A.V. Sergeev, V.V. Mitin, B.S. Karasik, Appl. Phys. Lett. 80(5), 817–819 (2002)9. U. Fano, Phys. Rev. 72(1), 26–29 (1947)10. P.J. de Visser et al., J. Low Temp. Phys. 167(3–4), 335–340 (2012)11. P.J. de Visser et al., Phys. Rev. Lett. 112(4), 047004 (2014)12. Griffin, M., et al., SPACEKIDS: kinetic inductance detectors for space applications, in Proceedings ofSPIE—The International Society for Optical Engineering (2016)13. S. Doyle et al., J. Low Temp. Phys. 151(1–2), 530–536 (2008)14. S.B. Kaplan et al., Phys. Rev. B 14(11), 4854–4873 (1976)123

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