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Superconducting Nonlinear Kinetic Inductance Devices Superconducting Nonlinear Kinetic Inductance Devices Thesis by Aditya Shreyas Kher In Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2017 Defended August 30, 2016 ii © 2017 Aditya Shreyas Kher ORCID: 0000-0002-5994-428X All rights reserved except where otherwise noted iii ACKNOWLEDGEMENTS This has been a very fulfilling thesis project that has been impacted by many people around me during my time at Caltech. I must first thank Prof. Jonas Zmuidzinas for giving me the opportunity to work in his research group, and for coming up with such an interesting, novel topic for me to work on. I had struggled during my first two years at Caltech to find a research group that would suit me in the long run. During my search at the beginning of my third year, Prof. Sandra Troian, in her capacity as Option Representative of the Applied Physics department, suggested that I talk to Jonas about opportunities at JPL. I’m very grateful to Prof. Troian for her guidance, because I probably would have never approached Jonas otherwise, as I was under the impression that he was an astronomer, and that that field was distant from my interests in applied physics. Jonas ended up interviewing me for his own group, and although I’d been unprepared, he gave me the chance to think about joining. This is how I was introduced to the field of superconducting detectors, and I’ve found it to be one of the most interesting areas of applied physics. By joining, I became one of the few people during these years to enjoy the instruction of the very knowledgeable Prof. Zmuidzinas on topics such as superconductivity, microwave engineering, and noise. I have to also give Jonas credit for encouraging me to apply for the NASA Space Technology Research Fellowship, which I was awarded in 2012. I enjoyed four years of funding from this fellowship, including the opportunity to travel to conferences both in the US and abroad. Many colleagues at Caltech and JPL contributed greatly to this research. Dr. Pe- ter Day and Dr. Byeong Ho Eom’s contributions to this work are invaluable and too numerous to state. Peter must be given additional credit for serving as my de-facto advisor—despite not being a professor—while Jonas was busy with his duties as Chief Technologist of JPL. Our devices would not have existed without the fabrication expertise of Dr. H. G. “Rick” Leduc. The first TES that we used was obtained from Dr. Roger O’ Brient, with whom I also enjoyed many useful discus- sions. Dr. Andrew Beyer helped us get started using the wet dilution refrigerator. Dr. Pierre Echternach must be thanked for letting us borrow liquid helium so many times. Several postdocs, especially Dr. Chris McKenney, Dr. Loren Swenson, and Dr. Erik Shirokoff, helped in getting me up to speed on this field when I first joined the group. Dr. Ran Duan was a helpful officemate during my first year in this group, and his advisor, Prof. Sunil Golwala, graciously agreed to be my “advisor” on paper iv for the purpose of the NSTRF. Finally, I have to thank Sheri Stoll, our group admin, for helping with my funding issues and for holding so many packages for me when I went overboard with online shopping. Los Angeles has been a fantastic place to spend my twenties, and it was made better by the great friends I’ve been fortunate enough to make at Caltech and elsewhere. The many nights of role-playing games, board games, and everything else that I shared with Tejaswi Venumadhav, Paraj Titum, Scott Geraedts, and Utkarsh Mital helped keep me sane. I learned a lot during my many late-night, wine-fuelled conversations with Britton Sauerbrei. S. Bose was always a blast to hang out with, and was always up for trying something new. I’m also grateful for the friendships I’ve maintained outside Caltech, which also helped support me during my time here. I would especially like to thank Chris Blondefield and David Mandler, with whom I’ve somehow kept in touch as if high school never ended, and Max Dukarevich, who has encouraged me to adopt many new perspectives over the years, and has always shown an interest in my research and in learning about physics. Finally, I would like to thank my family for their unending support. My brother, Abhishek, has become a true friend, especially during my time at Caltech. My ex- tended family has always been supportive, and I’ve enjoyed indulging their curiosity about my research. And last, but certainly not least, I’d like to thank my parents, who introduced me to science at a very young age, and who have encouraged me throughout my journey. I wouldn’t be where I am without them. v ABSTRACT The transition-edge sensor (TES) is one of the most productive types of detectors currently used for observational cosmology. It is the detector technology used in modern experiments such as POLARBEAR, SPIDER, and BICEP2 for studies of the polarization of the cosmic microwave background radiation. Next-generation instruments demand larger arrays of detectors to increase the sensitivity of the measurement. However, the size of TES arrays is currently limited to ∼104 due to the complexity of the readout system. A TES needs to be read out by a sensitive ammeter, and the most sensitive ammeters available are superconducting quantum interference devices (SQUIDs). Large detector arrays require multiplexed readouts, and SQUIDs are not inherently easy to multiplex. Thus, a large effort has taken place over the past decade to develop SQUID multiplexers for TES-based instruments. However, these multiplexers are complicated, requiring feedback electronics or other tricks in order to deal with the peculiarities of SQUIDs, such as their nonlinear, periodic transfer function. In addition, the SQUIDs themselves are complicated and expensive to fabricate, requiring up to 10 layers in the process. SQUID-based readout systems appear daunting for the arrays of 104–106 detectors that are needed for the focal planes of next-generation instruments. In this thesis we present a class of devices called kinetic inductance parametric up-converters (KPUPs) that provide a potential solution to the TES readout prob- lem. Broadly, a KPUP is a superconducting device operating in the microwave band that has a nonlinear kinetic inductance. Since the kinetic inductance of a super- conductor is a function of the current flowing through it, a low-frequency current signal can be detected by being strongly up-converted to the microwave band by the nonlinearity of the KPUP device, and then measured using a combination of microwave and low-frequency electronics. This can be done with a microresonator, where the superconducting kinetic inductance provides a portion of the resonator’s inductance. A large kinetic inductance can be achieved by using a thin film of a high-resistivity superconducting material such as TiN or NbTiN. Nanowires used as lumped-element kinetic inductors in a resonator are of particular interest: a small current in the nanowire changes its inductance and therefore shifts the resonance frequency. A device using this principle is demonstrated with a current sensitivity of p 8 pA/ Hz, making it potentially useful for TES readout and other current-sensing applications. Since this device is a microwave resonator, it can be easily multiplexed vi in the frequency domain, offering the potential of a considerably simplified readout compared to SQUID-based systems. We document efforts to integrate this device with a TES, including a successful measurement of the TES bias curve at several different temperatures of the heat bath. A two-stage TES multiplexing scheme is developed, where an array of TESs is read out by a single KPUP device, and an array of such KPUPs is read out in a microwave transmission measurement. Another version of the device is a transmission line, where its nonlinear kinetic inductance contributes to the total inductance of the line. A DC signal current in the line changes its kinetic inductance, which in turn changes the microwave phase length of the line. The change in phase length can be detected via a microwave transmission measurement of the transmission line. This type of device is demonstrated with a p current sensitivity of 5 pA/ Hz, meaning it is also suitable for TES readout as well as other current-sensing applications. This version of the device has the advantage of greater dynamic range and multi-gigahertz bandwidth, meaning that many more TESs can be read out by a single KPUP device. Also demonstrated is a transmission-line resonator version of the KPUP, which retains much of the dynamic range advantage of the transmission line KPUP while still being naturally easy to multiplex in the frequency domain, similar to the lumped-element device. A strong current response is demonstrated for this version of the device, and efforts to integrate it with a TES array are described. The current sensitivity of the transmission-line resonator could in principle reach levels as low as that of the other two devices. We also demonstrate a lumped-element resonator in a loop configuration that is natively sensitive to magnetic fields, similar to a SQUID but having the advantage of being easy to multiplex in the frequency domain. A magnetic field signal per- pendicular to the loop induces a loop current, changing the kinetic inductance of the nanowires that form part of the loop and in turn changing the resonance frequency of the resonator. A strong periodic response to the external magnetic field is observed for this device.
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