One of the greatest challenges in astronomy is observing star and planetary formation, redshifted distant galaxies and molecular spectral ‘fingerprints’ in the far-infrared spectrum of light, using highly sensitive and large cameras. In this thesis we investigate superconducting resonators for photon detection. In superconductors the electrons are paired. The incoming light then breaks these pairs into unpaired electrons, so-called quasiparticles, influencing the superconductor’s inductance. Consequently, the resonance frequency shifts. These resonators are extremely sensitive, since they are operated at temperatures where less than a billionth of the electrons are unpaired. By giving each resonator (or pixel) a slightly different length, like the pipes in an organ, many can be read out simultaneously. This allows for the construction of large cameras. These cameras work best when pairing is slow – the quasiparticles eventually recombine and the signal is lost – and the noise is low. In this thesis we focus on two main topics: the quasiparticle recombination process as well as the frequency noise of these resonators. At low temperatures we find relaxation times as long as milliseconds for Al and several tens of microseconds for Ta. The relaxation times clearly saturate at low temperatures in both materials, indicating an additional recombination channel in the superconducting films. The low temperature relaxation is made faster by the implantation of magnetic as well as nonmagnetic atoms, indicating that it arises from an enhancement of disorder. In addition, we show that the frequency noise mainly arises at interfaces, whereas deviations in the temperature dependence of the resonance frequency arise from dipole defects in the volume of dielectrics. Finally, we significantly decrease the noise by widening the geometry of the resonator waveguide.
One of the greatest challenges in astronomy is observing star and planetary formation, redshifted distant galaxies and molecular spectral ‘fingerprints’ in the far-infrared spectrum of light, using highly sensitive and large cameras. In this thesis we investigate superconducting resonators for photon detection. In superconductors the electrons are paired. The incoming light then breaks these pairs into unpaired electrons, so-called quasiparticles, influencing the superconductor’s inductance. Consequently, the resonance frequency shifts. These resonators are extremely sensitive, since they are operated at temperatures where less than a billionth of the electrons are unpaired. By giving each resonator (or pixel) a slightly different length, like the pipes in an organ, many can be read out simultaneously. This allows for the construction of large cameras. These cameras work best when pairing is slow – the quasiparticles eventually recombine and the signal is lost – and the noise is low. In this thesis we focus on two main topics: the quasiparticle recombination process as well as the frequency noise of these resonators. At low temperatures we find relaxation times as long as milliseconds for Al and several tens of microseconds for Ta. The relaxation times clearly saturate at low temperatures in both materials, indicating an additional recombination channel in the superconducting films. The low temperature relaxation is made faster by the implantation of magnetic as well as nonmagnetic atoms, indicating that it arises from an enhancement of disorder. In addition, we show that the frequency noise mainly arises at interfaces, whereas deviations in the temperature dependence of the resonance frequency arise from dipole defects in the volume of dielectrics. Finally, we significantly decrease the noise by widening the geometry of the resonator waveguide.
Superconducting materials are useful for a wide range of applications, ranging from particle detectors to quantum computing. The presence of excitations (quasiparticles) in the superconductor can be a resource in some devices and a disturbance in others - in kinetic inductance detectors, the generation of quasiparticles by an incoming photon can be read out and used to calculate the energy of the photon, while the tunnelling of quasiparticles is a cause of decoherence in quantum computing. While early research mostly focused on superconductors close to the critical temperature, temperatures that are far below the critical temperatures are often used for current applications. At these low temperatures, the energy exchange between quasiparticles and phonons becomes slow, and even small disturbances may drive the energy distribution of the quasiparticles out of thermal equilibrium. In fact, experiments usually show a residual number of quasiparticles even at milikelvin temperatures, for which the thermal density of quasiparticles would be negligible. This thesis consists of two parts: In the first part, I model the energy distribution of quasiparticles in superconducting resonators: Quasiparticles absorb energy by absorbing photons and release it as phonons, which drives the superconductor out of thermal equilibrium. I solve a set of rate equations, both numerical and analytical, to calculate the energy distribution of the quasiparticles. For parameters typically used in kinetic inductance detectors made of aluminum, the microwave signal used to read out the resonator dominates the energy distribution of the quasiparticles, while their density is determined by other processes. At not too low temperatures, quasiparticles are mainly produced by thermal phonons, and my calculations reproduce recently measured quality factors of resonators at temperatures above 250 mK without free parameters. I show that even a very small number of photons of higher energy, which I ascribe to noise from the microwave generator, would dominate the quasiparticle density at lower temperatures. Under this assumption, my calculations also reproduce the quality factors at lower temperatures. In the second part of this thesis, I investigate the effects of spatial fluctuations of the superconducting energy gap on the dynamics of quasiparticles. Recently, it has been proposed that such fluctuations may lead to the localization of quasiparticles in states below the energy gap, which could cause a finite quasiparticle density even at very low temperatures. Using the Keldysh-Usadel formalism, I derive rates for the different processes (recombination/(de-) localization/generation) of quasiparticles in such systems. Using these rate equations I derive new upper limits for the quasiparticle density that could result from these localized states. These upper limits show that localization caused by weak magnetic impurities in typical aluminum systems does not lead to a relevant quasiparticle density. This contradicts previous theories, which only consider the recombination between two localized quasiparticles without examining their dynamics in detail.
Superconducting microwave resonators have the potential to revolutionize submillimeter and far-infrared astronomy, and with it our understanding of the universe. The field of low-temperature detector technology has reached a point where extremely sensitive devices like transition-edge sensors are now capable of detecting radiation limited by the background noise of the universe. However, the size of these detector arrays are limited to only a few thousand pixels. This is because of the cost and complexity of fabricating large-scale arrays of these detectors that can reach up to 10 lithographic levels on chip, and the complicated SQUID-based multiplexing circuitry and wiring for readout of each detector. In order to make substantial progress, next- generation ground-based telescopes such as CCAT or future space telescopes require focal planes with large-scale detector arrays of 104–106 pixels. Arrays using microwave kinetic inductance detectors (MKID) are a potential solution. These arrays can be easily made with a single layer of superconducting metal film deposited on a silicon substrate and pattered using conventional optical lithography. Furthermore, MKIDs are inherently multiplexable in the frequency domain, allowing ∼ 103 detectors to be read out using a single coaxial transmission line and cryogenic amplifier, drastically reducing cost and complexity. An MKID uses the change in the microwave surface impedance of a superconducting thin-film microresonator to detect photons. Absorption of photons in the superconductor breaks Cooper pairs into quasiparticles, changing the complex surface impedance, which results in a perturbation of resonator frequency and quality factor. For excitation and readout, the resonator is weakly coupled to a transmission line. The complex amplitude of a microwave probe signal tuned on-resonance and transmitted on the feedline past the resonator is perturbed as photons are absorbed in the superconductor. The perturbation can be detected using a cryogenic amplifier and subsequent homodyne mixing at room temperature. In an array of MKIDs, all the resonators are coupled to a shared feedline and are tuned to slightly different frequencies. They can be read out simultaneously using a comb of frequencies generated and measured using digital techniques. This thesis documents an effort to demonstrate the basic operation of ∼ 256 pixel arrays of lumped-element MKIDs made from superconducting TiNx on silicon. The resonators are designed and simulated for optimum operation. Various properties of the resonators and arrays are measured and compared to theoretical expectations. A particularly exciting observation is the extremely high quality factors (∼ 3 × 107) of our TiNx resonators which is essential for ultra-high sensitivity. The arrays are tightly packed both in space and in frequency which is desirable for larger full-size arrays. However, this can cause a serious problem in terms of microwave crosstalk between neighboring pixels. We show that by properly designing the resonator geometry, crosstalk can be eliminated; this is supported by our measurement results. We also tackle the problem of excess frequency noise in MKIDs. Intrinsic noise in the form of an excess resonance frequency jitter exists in planar superconducting resonators that are made on dielectric substrates. We conclusively show that this noise is due to fluctuations of the resonator capacitance. In turn, the capacitance fluctuations are thought to be driven by two-level system (TLS) fluctuators in a thin layer on the surface of the device. With a modified resonator design we demonstrate with measurements that this noise can be substantially reduced. An optimized version of this resonator was designed for the multiwavelength submillimeter kinetic inductance camera (MUSIC) instrument for the Caltech Submillimeter Observatory.
In a superconductor, in which electrons are paired, the density of unpaired electrons should become zero when approaching zero temperature. Therefore, radiation detectors based on breaking of pairs promise supreme sensitivity, which we demonstrate using an aluminium superconducting microwave resonator. Here we show that the resonator also enables the study of the response of the electron system of the superconductor to pair-breaking photons, microwave photons and varying temperatures. A large range in radiation power (at 1.54 THz) can be chosen by carefully filtering the radiation from a blackbody source. We identify two regimes. At high radiation power, fluctuations in the electron system caused by the random arrival rate of the photons are resolved, giving a straightforward measure of the optical efficiency (48±8%) and showing an unprecedented detector sensitivity. At low radiation power, fluctuations are dominated by excess quasiparticles, the number of which is measured through their recombination lifetime. Electromagnetic radiation detectors based on superconducting resonators have a range of potential uses from astronomy to quantum computing. De Visser et al.demonstrate a superconductor detector with unprecedented sensitivity limited only by fluctuations in the electron system of the superconductor.
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.
We present measurements of the quasiparticle relaxation time in Ta superconducting films shaped as planar resonators using the response of the complex conductivity to photon flux. These films have been implanted with magnetic (Mn) as well as non-magnetic atoms (Al). We find a significant decrease of the relaxation time with increasing impurity concentration for both cases, observing a reduction of the low temperature relaxation time, from 25 μs to 10 μs when implanting 100 ppm Mn. This indicates that impurities enhance quasiparticle relaxation in superconductors, regardless of their magnetic moment.
The quasiparticle relaxation time in superconducting films has been measured as a function of temperature using the response of the complex conductivity to photon flux. For tantalum and aluminum, chosen for their difference in electron-phonon coupling strength, we find that at high temperatures the relaxation time increases with decreasing temperature, as expected for electron-phonon interaction. At low temperatures we find in both superconducting materials a saturation of the relaxation time, suggesting the presence of a second relaxation channel not due to electron-phonon interaction.