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Kinetic inductance detectors for measuring the polarization of the cosmic microwave background

D. Flanigan

Published Jan 1, 2018• 1 citation
Publisher

Abstract

Kinetic inductance detectors (KIDs) are superconducting thin-film microresonators that are sensitive photon detectors. These detectors are a candidate for the next generation of experiments designed to measure the polarization of the cosmic microwave background (CMB). I discuss the basic theory needed to understand the response of a KID to light, focusing on the dynamics of the quasiparticle system. I derive an equation that describes the dynamics of the quasiparticle number, solve it in a simplified form not previously published, and show that it can describe the dynamic response of a detector. Magnetic flux vortices in a superconducting thin film can be a significant source of dissipation, and I demonstrate some techniques to prevent their formation. Based on the presented theory, I derive a corrected version of a widely-used equation for the quasiparticle recombination noise in a KID. I show that a KID consisting of a lumped-element resonator can be sensitive enough to be limited by photon noise, which is the fundamental limit for photometry, at a level of optical loading below levels in ground-based CMB experiments. Finally, I describe an ongoing project to develop multichroic KID pixels that are each sensitive to two linear polarization states in two spectral bands, intended for the next generation of CMB experiments. I show that a prototype 23-pixel array can detect millimeter-wave light, and present characterization measurements of the detectors.

DOI
10.7916/d84f336t

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•Oct 1, 2019•0 citations
Kinetic inductance detectors (KIDs) are superconducting thin-film microresonators that are sensitive photon detectors. These detectors are a candidate for the next generation of experiments designed to measure the polarization of the cosmic microwave background (CMB). I discuss the basic theory needed to understand the response of a KID to light, focusing on the dynamics of the quasiparticle system. I derive an equation that describes the dynamics of the quasiparticle number, solve it in a simplified form not previously published, and show that it can describe the dynamic response of a detector. Magnetic flux vortices in a superconducting thin film can be a significant source of dissipation, and I demonstrate some techniques to prevent their formation. Based on the presented theory, I derive a corrected version of a widely-used equation for the quasiparticle recombination noise in a KID. I show that a KID consisting of a lumped-element resonator can be sensitive enough to be limited by photon noise, which is the fundamental limit for photometry, at a level of optical loading below levels in ground-based CMB experiments. Finally, I describe an ongoing project to develop multichroic KID pixels that are each sensitive to two linear polarization states in two spectral bands, intended for the next generation of CMB experiments. I show that a prototype 23-pixel array can detect millimeter-wave light, and present characterization measurements of the detectors.
Focal plane arrays consisting of low-noise, polarisation-sensitive detectors have made possible the pioneering advances in the study of the cosmic microwave background (CMB). To make further progress, the next generation of CMB experiments (e.g. CMB-S4) will require a substantial increase in the number of detectors compared to current instruments. Arrays of kinetic inductance detectors (KIDs) provide a possible path to realising such large-format arrays owing to their intrinsic multiplexing advantage and relative cryogenic simplicity. In this paper, we report on the design of a variant of the traditional KID design: the antenna-coupled lumped-element KID. A polarisation-sensitive twin-slot antenna placed behind an optimised hemispherical lens couples power onto a thin-film superconducting microstrip line. The power is then guided into the inductive section of an aluminium KID, where it is absorbed and modifies both the resonant frequency and quality factor of the KID. We present the various aspects of the design and preliminary results from the first set of seven-element prototype arrays and compare to the expected modelled performance.
Future ground-based cosmic microwave background (CMB) experiments will require more than 10510^5105 polarization sensitive pixels covering multiple atmospheric bands. The scientific potential for such an experiment is impressive; however, the technical challenges are daunting: such an instrument will require square meters of focal plane covered in background limited cryogenic detectors and a dramatic increase in readout capability. We are developing novel kinetic inductance detectors (KIDs) optimized for this purpose. These devices use a twin-slot microwave antenna, superconducting Nb transmission line, and a novel coupling scheme that deposits mm-wavelength power onto a high-resistivity meander deposited as the first layer on a bare Si wafer. This architecture allows us to independently adjust the detector and antenna properties and to pursue multi-band designs. We have fabricated superconducting resonators made from atomic layer deposited (ALD) titanium nitride (TiN), with thicknesses ranging from 3 to 40 nm. We find a strong dependence of transition temperature on thickness, from 0.6 to 4.2 K for our thinnest and thickest films, respectively. In dark measurements, we find internal quality factors that range from 10410^4104 to 7×1057\times 10^57×105 depending on film thickness, and kinetic inductance as high as 8 nH/square. The very small volumes and high kinetic inductance make it possible to engineer extremely sensitive detectors with inductor volumes approaching a few cubic microns that operate at readout frequencies of tens to hundreds of MHz. By taking advantage of the large fractional bandwidth available at low frequencies, we expect to achieve multiplexing densities that exceed that of state of the art TES arrays even without further improvements in film quality factor. We will present the characterization of film properties and dark devices, as well as well as initial optical results for antenna coupled single-band and single-pol devices. We will also discuss designs and sensitivity projections for future dual-pol and multi-band arrays ready for deployment in near-future CMB instruments.
Kinetic inductance detectors (KIDs) provide an attractive solution to the production of large detector arrays for use in ground and space based 200μm astronomy. KIDs work by measuring the change in quasi-particle density upon photon absorption in a high Q superconducting resonator. A change in quasi-particle density is measured by a shift in phase of a microwave probe signal of frequency equal to that of the resonant frequency of the KID. Such detectors have a fundamental noise limit owing to the quasi-particle recombination rate, which, in a KID fabricated from a high quality Niobium film can give sensitivities of 10-18W√Hz at 1K. Constructing KIDs of varying resonant frequencies coupled to a single transmission line provides a multiplexed detector array with simple low temperature electronics. Here we discuss the theoretical requirements for both ground and space based 200μm cameras with various radiation coupling schemes for this wavelength range using distributed and lumped element high Q resonators.
Microwave kinetic inductance detector (MKID) provides a way to build large ground-based sub-mm instruments such as NIKA and A-MKID. For such instruments, therefore, it is important to understand and characterize the response to ensure good linearity and calibration over a wide dynamic range. We propose to use the MKID readout frequency response to determine the MKID responsivity to an input optical source power. A signal can be measured in a KID as a change in the phase of the readout signal with respect to the KID resonant circle. Fundamentally, this phase change is due to a shift in the KID resonance frequency, in turn due to a radiation induced change in the quasiparticle number in the superconducting resonator. We show that the shift in resonant frequency can be determined from the phase shift by using KID phase versus frequency dependence using a previously measured resonant frequency. Working in this calculated resonant frequency, we gain near linearity and constant calibration to a constant optical signal applied in a wide range of operating points on the resonance and readout powers. This calibration method has three particular advantages: first, it is fast enough to be used to calibrate large arrays, with pixel counts in the thousands of pixels; second, it is based on data that are already necessary to determine KID positions; third, it can be done without applying any optical source in front of the array.
In this thesis I describe work on developing theoretical and numerical models of supercon- ducting thin-film microwave resonators. Superconducting resonators are used in a variety of applications, one of which is as kinetic inductance detectors (KIDs). KIDs are ultra-low noise, highly sensitive, multiplexable detectors, with uses in a wide variety of fields including astrophysics, medical imaging, and particle physics. Resonators are also crucial for supercon- ducting qubit readout, superconducting mixers and parametric amplifiers, and as multiplexers for other devices. The results described in this thesis apply to all thin film resonators, but are primarily described in the context of KIDs. I develop models of how constant absorbed power affects superconducting thin films, driving them out of thermal equilibrium with the bath. Using the Chang & Scalapino equations, I calculate numerically the steady-state quasiparticle and phonon distributions for various sources of power (sub-gap and above-gap photons and phonons, single frequency and broadband). Many new results emerge, a few of which are: the quasiparticle heating effects of microwave power, explaining the experimentally measured saturation of resonator performance; the frequency dependence of the quasiparticle generation efficiency in the sub-mm wavelength range; and the importance of phonon trapping in thin films at low temperatures. I then use these nonequilibrium results in higher-level device models. Starting from a generic framework for resonators, I present and implement a model of a KID with variable thermal isolation. I calculate the effects of quasiparticle heating on both the large-signal and small-signal behaviour, highlighting the effects of electrothermal feedback caused by readout power. Electrothermal feedback is shown to be able to increase or decrease the magnitude and bandwidth of the responsivity and noise, depending on the operating point. Finally, I propose an experimental measurement of quasiparticle heating effects in a new device – a four-port ring resonator. In such a device, unlike in the standard two-port resonator, the device can be heated and read out independently. I develop detailed models for the thermal and electrical behaviour of these devices, and suggest a scheme by which the quasiparticle heating effects of microwave power, predicted in this thesis, can be measured.
Microwave kinetic inductance detectors (MKID) are superconducting broadband direct detectors. If a superconducting thin film patterned into a resonator is illuminated with photons, Cooper pairs break up and the kinetic inductance of the film changes. This shifts the resonance frequency downwards and the dissipation of the resonator increases, which can be detected in the phase and amplitude of a transmitted signal. \n \nIn this thesis, a waveguide coupled MKID is designed and simulated. 350 GHz radiation is coupled into a copper waveguide via a horn antenna. A waveguide probe leads the signal onto a 9 µm silicon membrane where it is absorbed in a 40 nm superconducting aluminum film which is the inductive part of a superconducting resonator. The capacitor of the resonator is made of niobium. Two versions of the device are developed, a transmission line resonator and a lumped element resonator design. The new design will enable an accurate understanding of the optical sensitivity of MKIDs and allow comparison of different resonator materials. Since two different resonator types are used, the direct comparison of transmission line and lumped resonators will also be possible. \n \nA measurement setup is developed including an ADR cryostat to cool MKID devices down to below 40 mK. An analog readout system using either a vector network analyzer or an IQ mixer is designed and built. The necessary software to control the ADR, the temperature monitoring, the readout signal generation and detection and the signal acquisition of the setup is also developed. \n \nThe waveguide coupled MKID design is fabricated in our in-house microfabrication laboratory and measured in the new setup. In my measurements, the devices do not show a resonance feature. The VNA and DC measurements are analyzed to determine a plausible hypothesis of the failure. The devices are diagnosed for critical issues during fabrication which will be addressed in a future iteration. \n \nTo verify the measurement setup, a test device of the IRAM NIKA 2 MKID camera is measured and the complete analysis pipeline is exercised. The quasi-particle lifetime in the aluminum thin films is measured and a dark and optical noise equivalent power are determined. The results are within the uncertainty comparable to measurements of IRAM themselves. \n \nA test chip designed in my master thesis that contains eight NbTiN resonators is measured in the new setup and non-linear effects under strong readout power are studied. Parametric amplification and oscillation of a resonator are shown qualitatively.