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      Ultrasensitive Kilo-Pixel Imaging Array of Photon Noise-Limited Kinetic Inductance Detectors Over an Octave of Bandwidth for THz Astronomy

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          Abstract

          We present the development of a background-limited kilo-pixel imaging array of ultrawide bandwidth kinetic inductance detectors (KIDs) suitable for space-based THz astronomy applications. The array consists of 989 KIDs, in which the radiation is coupled to each KID via a leaky lens antenna, covering the frequency range between 1.4 and 2.8 THz. The single pixel performance is fully characterised using a representative small array in terms of sensitivity, optical efficiency, beam pattern and frequency response, matching very well its expected performance. The kilo-pixel array is characterised electrically, finding a yield larger than 90% and an averaged noise-equivalent power lower than 3  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document}  10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-19}$$\end{document}  W/Hz \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{1/2}$$\end{document} . The interaction between the kilo-pixel array and cosmic rays is studied, with an expected dead time lower than 0.6% when operated in an L2 or a similar far-Earth orbit.

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          Fluctuations in the electron system of a superconductor exposed to a photon flux

          In a superconductor well below its critical temperature, the majority of the electrons is bound in a condensate of Cooper pairs. The further the superconductor is cooled down, the closer it gets to its ground state, where all the quasiparticles are condensed to pairs. Due to the low gap energy, the superconductor is sensitive to disturbances from the environment to which it couples. In most experiments, this sensitivity is undesirable, but it is particularly suited for detection of radiation. The superconductor can interact with its environment due to either photons or phonons. Photons with an energy higher than the energy gap break up Cooper pairs into quasiparticles. The change in the number of quasiparticles and Cooper pairs changes the electrodynamic response of the superconductor, which can be measured using a microwave resonator1. Quasiparticles give rise to microwave losses and the Cooper pairs to a kinetic inductance2. In steady state, the number of quasiparticles fluctuates in time around a constant average value. A measurement of the spectrum of these fluctuations allows for a characterization of the quasiparticle system when exposed to pair-breaking photons, microwave photons or to changes in the bath temperature. The characteristic timescale of the fluctuations, the quasiparticle recombination time, is inversely proportional to the number of quasiparticles3, and is therefore a measure of this number. These fluctuation phenomena are a monitor of the superconducting state and reveal the physical mechanisms that are at the heart of pair breaking in a superconductor. We study these processes in a superconducting pair-breaking detector formed by a 50 nm thick Al film. The ideal pair-breaking detector can either count single photons while its sensitivity is limited by Fano noise, or is photon integrating and limited by photon noise, the noise from the photon source itself4. In both cases, a high optical efficiency is required. The principle of radiation detection due to pair breaking with superconducting microwave resonators was proposed in 2003 (refs 1, 5). Since then, the most important source of excess noise1, due to dielectric two level systems, has been thoroughly studied6 7 8 9. Here we report on an all-aluminium antenna-coupled microwave resonator detector (Fig. 1a) that is limited only by fluctuations in the electron system that are fundamentally connected to the physical process of pair breaking. Results Detector sensitivity We use a blackbody with a variable temperature (3–25 K) and eight optical filters, which define an optical band around 1.54 THz, as shown schematically in Fig. 1b. The radiation power can be changed from 3 × 10−21 W to 7 × 10−13 W. At powers ranging from 0.1–700 fW, the sensitivity is only limited by the random arrival rate of the photons, which is evident through the measured power dependence of the noise equivalent power (NEP) as shown in Fig. 1c. At lower radiation powers, we observe a power-independent NEP. This is consistent with generation-recombination noise due to the presence of excess quasiparticles10 11. Excess quasiparticles are a general concern for superconducting devices12 13 14 15 16 17 18. In this case, they are generated by the microwave readout power19 20. As shown in Fig. 1c, they impose a lower limit to the NEP of this detector of 3.8±0.6 × 10−19 WHz−1/2, which is the lowest reported so far for this type of detectors. Design of the experiment The detector is based on a lens antenna-coupled superconducting microwave resonator. The resonator is an open ended, half wave, coplanar waveguide resonator, where the central strip (with a width of 3 μm) is isolated from the ground plane. The resonators all have different lengths and therefore different resonant frequencies, enabling the readout of all resonators using a single coaxial line. Radiation is focused by a silicon lens onto an X-slot antenna21, optimized for broad band detection from 1.4–2.8 THz. Radiation coupled to the antenna is launched as a travelling wave into the waveguide21, where it is absorbed by breaking Cooper pairs (the gap energy Δ=188 μeV). The created quasiparticles, which can diffuse over several millimetres before they recombine, are confined to the central strip. The central strip layer is 50 nm thick, and the ground plane layer 100 nm. The thin central strip layer gives higher response and ensures that most of the radiation is absorbed in that central strip, due to its higher resistance (see Methods). The thick ground plane reduces antenna losses. An advantage of the geometry, shown in Fig. 1a, is that it can also be used at other radiation frequencies by only changing the antenna. The sample is cooled in a pulse tube precooled adiabatic demagnetization refrigerator. The sample stage is carefully shielded from stray light from the 3 K stage of the cooler, using a box-in-a-box concept with optical filters at each stage, as well as coax cable filters in the outer box22. The photon source is a blackbody with a variable temperature between 3 and 25 K (Methods). The system is schematically depicted in Fig. 1b. Eight optical filters in series define an optical band-pass of 0.1 THz centred around 1.54 THz. Three filter stacks are essential to eliminate filter heating. The filter transmission of the three filter stages is shown in Fig. 2a. The curves of spectral radiance for high and low blackbody temperature indicate a large tuning range in radiation power (P rad). In fact, P rad can be varied between 3 zW (1 zW=10−21 W) and 1 pW (Supplementary Fig. S1). Practically, this experiment allows us to switch from a regime where the number of quasiparticles is fully determined by the radiation to a regime with a negligible number of optically created quasiparticles. We put a polarizing wire grid just before the detector to make sure the detector only receives radiation in the polarization direction of the antenna. Operation principle The number of quasiparticles is measured through a measurement of the complex conductivity of the superconductor. The real part of the conductivity, σ 1, is due to the quasiparticles and resistive. The imaginary part, σ 2, is due to the kinetic inductance of the Cooper-pair condensate2. When the radiation power or the bath temperature is increased, more quasiparticles are generated, which changes both σ 1 and σ 2. The kinetic inductance increases, which leads to a lower resonant frequency f 0=1/2l , where l is the length of the resonator, L g the geometrical inductance, L k the kinetic inductance and C the capacitance of the line, all per unit length. The losses at microwave frequencies also increase, leading to a shallower resonance curve. Measurements of the resonance curves for various radiation powers are shown in Fig. 2b. In a practical detection scheme, one typically uses an amplitude, A, and a phase, θ, referred to the resonance circle in the complex plane6, as shown in Fig. 2c. The amplitude response originates from a change in resistance, whereas the phase changes due to the kinetic inductance. We have only used the amplitude response in this experiment, because the phase noise is too high for this resonator (Supplementary Note 1). The NEP is a convenient quantity to compare the spectra of quasiparticle fluctuations in different regimes, as shown in Fig. 1c. The NEP of the resonator amplitude is experimentally determined from a measurement of the noise spectrum (S A ) and the responsivity to radiation (dA/dP rad) and given by with P rad the radiation power and f the modulation frequency. dA/dP rad is obtained experimentally by a linear fit to a measurement of A where P rad is slowly varied around the power of interest (see Methods). The measured microwave response upon a change in P rad is shown in Fig. 2c. The last factor in equation (1) arises because the quasiparticle system cannot respond to fluctuations that are faster than the quasiparticle recombination time, τ qp. Photon-induced quasiparticle fluctuations If the average number of quasiparticles is dominated by the absorbed optical photons, the number of quasiparticles fluctuates in time due to two contributions. One is fundamental to every power-integrating detector and due to the random arrival rate of the photons, which induces a random generation of quasiparticles. The power spectral density of fluctuations in the resonator amplitude due to this photon noise is given by4 where the first term is the spectrum of the photon (power) fluctuations and the second term describes the resonator response upon a change in the radiation power. F is the frequency of the optical photons and h Planck's constant. The factor (1+η opt B) is the correction to Poissonian statistics due to photon bunching for a single mode, with η opt the optical efficiency and B the mode occupation23. The photon bunching contribution is negligible for the here measured power range (Supplementary Fig. S1c). Equation (2) is valid as long as τ qp>>τ res, which holds in this experiment since the response time of the resonator, given by τres=Q/πf 0, is 6 μs. Q is the quality factor of the resonator. Because of the pair-breaking nature of the radiation absorption, a second noise mechanism arises due to random recombination of the quasiparticles that are generated by the photons. This is half the generation-recombination noise that arises in thermal equilibrium24, because generation noise is already contained in equation (2). The spectrum is given by with N qp the number of quasiparticles and dA/dN qp the responsivity of A to a change in N qp. Quasiparticle number fluctuations can be converted to power fluctuations through η pb η opt P rad=N qpΔ/τ qp. η opt is the optical efficiency, the efficiency with which power in front of the lens is absorbed in the detector. η pb≈0.57 is the pair-breaking efficiency25, the efficiency with which absorbed radiation power is converted into quasiparticles. For small changes in the quasiparticle number, dP rad/dN qp=Δ/(τ qp η pb η opt) and therefore dA/dP rad=τ qp η pb η opt/Δ·(dA/dN qp). From equations (2) and (3), the relative contribution of photon noise compared with recombination noise is given by hF(1+mB)η pb η opt/Δ=10 at all P rad, for F=1.54 THz and η opt=0.5. The NEP due to photon noise and recombination noise (equations (1, 2, 3)), for f 1 fW) however, the measured photon noise NEP stays the same, as expected from equation (4) (Supplementary Fig. S4). Therefore, when photon noise dominates the noise spectrum, one can safely use high readout powers to suppress amplifier noise (Supplementary Note 4). At the lowest readout power where τ qp was determined, P read=−102 dBm, the quasiparticle recombination time is 3.5 ms, which corresponds to a quasiparticle density n qp=24 μm−3. This density is still high in comparison with the lowest reported values for superconducting qubits and Cooper-pair transistors17 18 (less than 0.1 μm−3), but inherent to the relatively high microwave powers we need in this type of experiments. The measured limit in optical NEP due to excess quasiparticles is comparable with the lowest observed optical NEP in other detectors for similar wavelengths29 30 31. A reduction in N qp is possible by using a parametric amplifier with high bandwidth and dynamic range32. This allows a reduction of the readout power by about a factor 10. In the current design, however, the detector would become too slow for practical use at low readout power due to the long recombination time. The most feasible route towards lower NEP with aluminium, the most reliable material so far, is to choose geometries in which the active volume is dramatically reduced, which could also be the route towards single photon counting at terahertz frequencies. Methods Sample design A layer of aluminium with a thickness of 100 nm is sputtered onto a sapphire substrate and serves as the ground plane for the microwave resonators. The microwave resonator is a coplanar waveguide resonator with a central strip width of 3 μm and slit widths of 1.5 μm. The central strip of the resonator is made of a second layer of 50 nm thick Al. The critical temperature of the 50 nm layer is measured to be T c=1.24 K, from which the energy gap Δ=1.76k B T c=188 μeV. From the normal state resistivity, (ρ=2.2 μΩcm for the central strip and 0.28 μΩcm for the ground plane) the skin depth for radiation at 1.54 THz is 60 nm in the central strip and 21 nm in the ground plane. The X-slot antenna would be ineffective for a layer thinner than the skin depth, therefore the ground plane layer is 100 nm thick. The microwave sheet resistance of the central line is 0.46 Ω and that of the ground plane 0.13 Ω. Taking this effect into account, together with the participation ratios of the central line and the ground plane33, we estimate that 90% of the radiation is absorbed in the central line. The current distribution along the length of the resonator peaks at the antenna and decreases as sin(x) to zero at the open ends. Therefore, the responsivity changes with sin2(x). Since the diffusion length within a typical quasiparticle recombination lifetime of 2 ms is more than half the resonator length, optically created quasiparticles can move into the non-responsive regime. Therefore, for calculating the number of quasiparticles in the sensitive volume, we take half the central strip volume, V=0.6 × 103 μm3. Noise measurement The signal from the microwave generator is first attenuated, sent through the sample and amplified with a HEMT amplifier at 4 K and with a room temperature amplifier. The output is mixed with the original signal using an IQ mixer, the output of which can be sampled at a maximum frequency of 2 MHz. The spectrum of fluctuations in the resonator amplitude is measured by recording the resonator amplitude as a function of time and computing the power spectral density. Peaks in the time domain stream that occur due to high energy impacts are filtered out before the spectrum is computed, as described in ref. 11. We use the amplitude direction because fluctuations in the phase direction are dominated by two level system noise in the dielectrics surrounding the resonator6 (Supplementary Fig. S5 and Supplementary Note 1). Optical system and radiation power The photon source used in the experiment is a blackbody that is formed by a 40 mm diameter copper cone, coated with carbon-loaded epoxy (EPOTEK 920 1LB part A, with 3% by weight carbon black and 3% by weight EPOTEK 920 1LB part B) that is covered with 1 mm SiC grains. The temperature of the blackbody is varied in this experiment from 3–25 K. There are three metal-mesh filter stacks (QMC Instruments, Cardiff), the characteristics of which are given in Fig. 2a. The measured transmission of the whole filterstack as a function of optical frequency, Tr(F), is also shown in Fig. 2a. Since there is no aperture limitation in between the blackbody and the detector, the optical throughput is assumed to be (c/F)2, with c the speed of light. The total radiation power that arrives in front of the lens of the detector can now be calculated by numerically integrating Planck’s law over the throughput and the measured filter characteristic at each blackbody temperature T BB. The radiation power is here given for one polarization. The optical window around 1.54 THz, together with the blackbody temperature range of 3–25 K gives a large tuning range in radiation power, as shown in Supplementary Fig. S1b. With the present device, we can verify the radiation power down to 0.1 fW using the measured quasiparticle recombination time (Fig. 5b). The trend of increasing optical responsivity and recombination time with decreasing microwave power, without any sign of saturation, suggests that the optical system is well characterized down to even lower radiation powers. The excess quasiparticles in the present device limit us to verify that. Right in front of the detector, after the last optical filter, we place a polarizer to select the polarization for which the antenna is designed. The polarizer consists of a copper wire grid on top of a 1.5-μm thick Mylar film. The grid lines are 10 μm wide and the spacing between the lines is 20 μm. Responsivity fit The responsivity dA/dP rad is obtained from a linear fit to the response A measured as a function of P rad. The blackbody temperature is swept slowly around the P rad of interest. Each measured point is integrated for 500 ms. At very low radiation power (P rad<0.3 aW) there is no response (due to the excess quasiparticles). Therefore, the responsivity at 3 zW is estimated by a fit of the response in the range 0.3–9 aW, for example. Note that this reflects the saturation in the sensitivity of the detector. At the highest power P rad=724 fW, the fit range is 705–743 fW. The fit range is chosen by hand, because it differs widely from the saturation regime to the regime in which the number of quasiparticles is dominated by the absorbed P rad. The fit range is chosen small enough to stay in the linear response regime and large enough to limit the standard deviation of the fit. Lens antenna efficiency The radiation power is focused by an elliptical silicon lens of 2 mm in diameter onto the antenna that is in the second focus of the lens34. The major and minor axes of the ellipse are 1.037 and 0.992 mm, respectively. The lens has an antireflection coating of 130 μm of Parylene C, which is not optimized for 1.54 THz. The antenna is an in-line X-slot antenna, designed to receive radiation in a broad band around 1.54 THz as described in ref. 21. To obtain the optical efficiency, a simulation in CST Microwave Studio is performed of the whole structure: the lens with the coating, the antenna and a piece of coplanar waveguide transmission line. The aperture is chosen to be 30 degrees, the angle from which the detector can see the blackbody (single-side angle). The optical efficiency is shown as a function of frequency in Supplementary Fig. S6. The total efficiency is the multiplication of the front-to-back ratio, the spill over losses, the efficiency of an impedance mismatch between the antenna and the CPW line and the reflection losses at the anti-reflection-coated lens surface. All together, we expect an efficiency of 48% for one polarization in the filter transmission band, which is in good agreement with the measured optical efficiency of 48±8%. The antenna was not designed to have a perfect optical efficiency, but to have a large bandwidth. The agreement of the measured optical efficiency with the CST-simulation shows that the optical system is understood. Author contributions J.J.A.B. conceived the experiment. P.J.V., J.J.A.B. and J.B. performed the experiments. N.L. analysed and simulated the optical system. P.J.V., J.J.A.B. and T.M.K. analysed the data and composed the article. Additional information How to cite this article: de Visser, P. J. et al. Fluctuations in the electron system of a superconductor exposed to a photon flux. Nat. Commun. 5:3130 doi: 10.1038/ncomms4130 (2014). Supplementary Material Supplementary Information Supplementary Figures 1-7, Supplementary Notes 1-4 and Supplementary References
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              SPACEKIDS: kinetic inductance detectors for space applications

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                Author and article information

                Contributors
                j.bueno@sron.nl
                Journal
                J Low Temp Phys
                J Low Temp Phys
                Journal of Low Temperature Physics
                Springer US (New York )
                0022-2291
                1573-7357
                29 May 2018
                29 May 2018
                2018
                : 193
                : 3
                : 96-102
                Affiliations
                [1 ]ISNI 0000 0004 0646 2222, GRID grid.451248.e, SRON Netherlands Institute for Space Research, ; Utrecht, The Netherlands
                [2 ]ISNI 0000 0001 2097 4740, GRID grid.5292.c, Terahertz Sensing Group, , Delft University of Technology, ; Delft, The Netherlands
                Article
                1962
                10.1007/s10909-018-1962-8
                6190645
                30839749
                924c0f8a-ea51-404a-a5a9-a5f557823860
                © The Author(s) 2018

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International 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 the source, provide a link to the Creative Commons license, and indicate if changes were made.

                History
                : 11 October 2017
                : 10 May 2018
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100000781, European Research Council;
                Award ID: 648135
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/100011203, FP7 Space;
                Award ID: 313320
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                © Springer Science+Business Media, LLC, part of Springer Nature 2018

                kinetic inductance detectors,kilo-pixel array,thz astronomy

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