We demonstrate an increased quasiparticle recombination time in superconducting resonators on a SiNx membrane, compared to identical resonators on a SiNx/Si wafer. An interpretation is given using a thermal model of the membrane. Using an array of tunnel junctions to cool or heat the membrane, we show that the resonators on the membranes are extremely sensitive to small changes of the phonon temperature, which renders them excellent phonon thermometers with a noise level equivalent to 5μK/Hz. The experimental set-up is in principle an ideal platform to study the interplay of quasiparticles and phonon populations in superconductors.
We demonstrate an increased quasiparticle recombination time in superconducting resonators on a SiNx membrane, compared to identical resonators on a SiNx/Si wafer. An interpretation is given using a thermal model of the membrane. Using an array of tunnel junctions to cool or heat the membrane, we show that the resonators on the membranes are extremely sensitive to small changes of the phonon temperature, which renders them excellent phonon thermometers with a noise level equivalent to 5μK/Hz. The experimental set-up is in principle an ideal platform to study the interplay of quasiparticles and phonon populations in superconductors.
We measure temperature-dependent quasiparticle fluctuations in a small Al volume, embedded in a NbTiN superconducting microwave resonator. The resonator design allows for readout close to equilibrium. By placing the Al film on a membrane, we enhance the fluctuation level and separate quasiparticle effects from phonon effects. When lowering the temperature, the recombination time saturates and the fluctuation level reduces by a factor $\ensuremath{\sim}100$. From this we deduce that the number of free quasiparticles is still thermal. Therefore, the theoretical, inverse relation between the quasiparticle number and recombination time is invalid in this experiment. This is consistent with quasiparticle trapping, where on-trap recombination limits the observed quasiparticle lifetime.
When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at $2\mathrm{\ensuremath{\Delta}}$. We show that a phonon band gap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon band gap can be realized and matched to the recombination energy with a phononic crystal, a periodically patterned dielectric membrane. We discuss in detail the nonequilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon band gap and a pair-breaking photon signal. Although intrinsically a nonequilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $exp({\mathrm{\ensuremath{\Omega}}}_{bg}/{k}_{B}{T}_{b})$, where ${\mathrm{\ensuremath{\Omega}}}_{bg}$ is the phonon band gap energy bandwidth above $2\mathrm{\ensuremath{\Delta}}$ and Tb is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic band gap on the performance of a superconducting circuit element and propose a microwave resonator to measure the enhancement in the quasiparticle lifetime.
Low temperature microwave superconducting resonators (SRs) are attractive candidates for producing quantum-sensitive, arrayable energy or power detectors for astrophysical and other precision measurement applications. Their readout uses a microwave probe signal with quanta of energy well below the threshold for pair-breaking in the superconductor. We have calculated the non-equilibrium quasiparticle and phonon distributions generated by the photons of the probe signal of a resonator operating well below its superconducting transition temperature T c as the absorbed probe power was changed using the coupled kinetic equations described by Chang and Scalapino. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from their thermal equilibrium value for typical readout powers. From the driven quasiparticle distribution functions, the driven quasiparticle number densities and lifetimes were calculated. An effective temperature to describe the driven quasiparticles was defined. The non-equilibrium lifetimes were compared to the distribution-averaged thermal lifetimes at the effective temperature and good agreement was found typically within a few per cent. We used the non-equilibrium quasiparticle distribution to model a representative SR. The complex conductivity and hence the frequency dependence of the experimentally measured forward scattering parameter S 21 of the SR as a function of absorbed power were found. The non-equilibrium S 21 cannot be accurately modeled by a thermal distribution even at its own elevated temperature, having a higher quality factor in all cases studied, although for low absorbed powers the two effective temperatures are similar. From the non-equilibrium lifetimes and number densities we determined the achievable noise equivalent power (NEP) of the resonator used as a power detector as a function of absorbed microwave power. Simpler expressions to evaluate the effective quasiparticle temperature as a function of absorbed power have also been derived. We conclude that multiple photon absorption from the microwave probe increases the quasiparticle number above the thermal background and ultimately limits the achievable NEP of the resonator at temperatures well below T c .
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.
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.
Disordered superconductors offer new impedance regimes for quantum circuits, enable a pathway to protected qubits, and can improve superconducting detectors due to their high kinetic inductance and sheet resistance. The performance of these devices can be limited, however, by quasiparticles—the fundamental excitations of a superconductor. While experiments have shown that disorder affects the relaxation of quasiparticles drastically, the microscopic mechanisms are still not understood. We address this issue by measuring quasiparticle relaxation in a disordered β-Ta film, which we pattern as the inductor of a microwave resonator. We observe that quasiparticle recombination is governed by the phonon scattering time, which is faster than conventional recombination in ordered superconductors. We interpret the results as recombination of localized quasiparticles, induced by disorder, which first delocalize via phonon absorption. We analyze quasiparticle relaxation measurements on superconductors with different degrees of disorder and conclude that this phenomenon is inherent to disordered superconductors. The authors study a disordered β-Ta film, finding that quasiparticle recombination is governed by the phonon scattering time, which is faster than conventional recombination in ordered superconductors. The authors interpret the results in terms of quasiparticle localization, which helps to understand the quasiparticle relaxation in disordered superconducting circuits.