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Kinetic Inductance Detectors for Measuring the Polarization of the Cosmic Microwave Background

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Kinetic Inductance Detectors for Measuring the Polarization of the Cosmic Microwave Background Kinetic inductance detectors for measuring the polarization of the cosmic microwave background Daniel Flanigan Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2018 © 2018 Daniel Flanigan All rights reserved ABSTRACT Kinetic inductance detectors for measuring the polarization of the cosmic microwave background Daniel Flanigan 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. Contents List of Figures vi List of Tables x 1 Introduction and notation 1 2 The cosmic microwave background 6 2.1 Physics ......................................... 6 2.1.1 Before recombination ............................. 6 2.1.2 During recombination ............................. 10 2.1.3 After recombination .............................. 12 2.2 Experiment ...................................... 13 2.2.1 Goals ..................................... 13 2.2.2 Signals .................................... 14 2.2.3 Detectors ................................... 16 3 Kinetic inductance detectors: basic theory 17 3.1 The BCS theory and the ground state ........................ 19 3.1.1 The Cooper pair condensate ......................... 19 i 3.1.2 Fiducial parameters .............................. 20 3.1.3 Radiation detection using superconductors . 22 3.2 Quasiparticle excitations ............................... 22 3.2.1 The quasiparticle density of states ...................... 22 3.2.2 Generation .................................. 27 3.2.3 Pair recombination .............................. 27 3.2.4 Phonons .................................... 29 3.2.5 Single-quasiparticle decay .......................... 31 3.2.6 Inhomogeneity and diffusion ......................... 32 3.3 Electrodynamics .................................... 34 3.3.1 The two-fluid model ............................. 34 3.3.2 The Mattis-Bardeen theory .......................... 35 3.3.3 Surface impedance .............................. 36 3.4 Nonequilibrium perturbations to the ground state . 37 3.4.1 Nonequilibrium occupancy .......................... 37 3.4.2 First-order response functions ........................ 38 3.5 The quasiparticle number model ........................... 41 3.5.1 Steady-state .................................. 43 3.5.2 Dynamics ................................... 43 3.5.3 The quasiparticle relaxation time ....................... 46 3.6 Resonators ....................................... 49 3.6.1 A generic model for a shunt-coupled resonator . 49 ii 3.6.2 The effective kinetic inductance fraction ................... 51 3.7 Detector response and responsivity .......................... 54 3.7.1 Photodetection ................................ 54 3.7.2 Optical quasiparticle generation ....................... 56 3.7.3 Quasiparticle number ............................. 57 3.7.4 Complex conductivity ............................. 58 3.7.5 Surface impedance .............................. 60 3.7.6 Resonator parameters ............................. 61 3.7.7 The forward scattering parameter ....................... 61 3.7.8 Summary ................................... 63 3.7.9 Time-ordered data ............................... 65 4 Sources of loss 67 4.1 Dielectrics ....................................... 68 4.2 Near-field coupling .................................. 69 4.3 Magnetic flux vortices ................................. 70 4.3.1 Introduction .................................. 71 4.3.2 Experiment .................................. 72 4.3.3 Results .................................... 75 4.3.4 Discussion ................................... 78 5 Sensitivity and noise 79 5.1 Photon noise and noise-equivalent power ....................... 80 iii 5.2 Quasiparticle generation and recombination noise . 82 5.3 Two-level system noise ................................ 86 5.4 Readout noise ..................................... 87 5.5 Measuring photon noise with KIDs .......................... 88 5.5.1 Introduction .................................. 89 5.5.2 Experiment .................................. 89 5.5.3 Results .................................... 91 5.5.4 Discussion ................................... 97 5.5.5 Supplemental material ............................ 99 6 Multichroic detectors 103 6.1 Overview .......................................103 6.2 Optical coupling ....................................105 6.3 Prototype resonators: simulation and testing . 107 6.4 The 23-pixel design ..................................111 6.5 Fabrication ......................................113 6.6 MKIDArray01-0101: a 23-pixel array on intrinsic silicon . 115 6.7 MKIDArray02-0001: a 23-pixel array on SOI . 118 6.8 Conclusions and future work .............................125 References 127 Appendix A Connections to other work 138 iv Appendix B First-order response functions 140 Appendix C Hardware 149 C.1 KID readout ......................................149 C.2 Millimeter-wave source ................................151 C.3 Cryostat ........................................152 v List of Figures 2.1 A map of the CMB temperature anisotropies from the Planck satellite. 7 2.2 Planck measurements of the CMB temperature power spectrum. .......... 9 2.3 Recent measurements of the CMB E-mode and B-mode power spectra. 11 2.4 The CMB monopole spectrum from FIRAS on COBE. 13 3.1 A schematic that shows how KIDs are read out and multiplexed. 17 3.2 The amplitude and phase of the forward transmission past a resonator, versus frequency. 18 3.3 The quasiparticle energy and density of states. .................... 24 3.4 The reduced thermal quasiparticle density versus reduced temperature. 26 3.5 The quasiparticle group velocity versus quasiparticle energy. 33 3.6 The first-order response functions for the real and imaginary parts of the conductivity at fmc. ......................................... 40 3.7 The decay of perturbations to the quasiparticle density versus time. 42 3.8 Time-ordered data showing the detuning response as a millimeter-wave signal is turned off, and a fit. .................................. 46 3.9 The quasiparticle relaxation time versus bath temperature, showing saturation at low temperature. ...................................... 47 3.10 Complex transmission data from a frequency sweep across a resonator, normalized and fit to a resonator model. .............................. 52 vi 3.11 The number of quasiparticles excited per photon and the pair-breaking efficiency versus photon frequency. ............................... 55 3.12 The normalized response ratios of the real and imaginary conductivity to the thermal quasiparticle density. ................................. 59 3.13 Theoretical predictions for the S21 response to an increase in the quasiparticle number. 62 3.14 MKIDArray02-0001: the internal loss and fractional frequency shift versus temper- ature for a multichroic 3410 MHz resonator. ..................... 63 3.15 Time-ordered data showing the response to millimeter-wave light. 66 4.1 Photographs and drawings of the magnetic flux vortex experiment. 70 4.2 The measured magnetic field of the magnet array versus distance along its center axis. 73 4.3 Forward scattering parameter data at different magnetic fields. 74 4.4 The inverse internal quality factor of three resonators versus magnetic field. 76 4.5 The spectral density of the fractional frequency detuning time series data from one resonator at different magnetic fields. ......................... 77 5.1 Schematics of the photon noise experiment. ..................... 89 5.2 Primary results of the photon noise experiment. ................... 92 5.3 Dark noise data and fits. ................................100 6.1 Drawings of the multichroic detector module and of one multichroic pixel. 104 6.2 Simulations of the spectral bands for the multichroic KID pixels. 105 6.3 A schematic of the microstrip-to-coplanar-waveguide coupler for the multichroic KID project. ......................................106 6.4 MKIDArray01-0101: a photograph of one resonator. 109 6.5 A photograph and a drawing of a chip with eight prototype resonators. 110 vii 6.6 A
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