arXiv:2501.13791 · Physical review. B./Physical review. B
Ab initio modeling of nonequilibrium dynamics in superconducting detectors and qubits
Alejandro Simon, Reed A. Foster, Mihir Sahoo, James Shi, Emma Batson, Francesca Incalza, Matteo Castellani, Owen Medeiros, Christoph Heil, Karl K. Berggren
Nonequilibrium quasiparticle and phonon dynamics are central to the operation of superconducting devices. Superconducting detectors, such as superconducting nanowire single-photon detectors, transition-edge sensors, or microwave kinetic inductance detectors, perform best when a large quasiparticle population is generated in response to small perturbations. Conversely, for superconducting qubits and topologically protected Majorana fermions, even relatively small quasiparticle densities can lead to significant performance degradation. Hence, ideal materials for these devices would be less susceptible to quasiparticle poisoning. However, existing models of these devices often rely on approximations and phenomenology. Therefore, they lack a rigorous description of the underlying quasiparticle and phonon dynamics that are responsible for device performance. In this article, we combine kinetic equations with density functional theory to model the nonequilibrium quasiparticle and phonon dynamics of a thin superconducting film ab initio. To demonstrate the universality of our model, we illustrate two independent example applications: (1) we develop a theoretical model describing the detection of single photons in superconducting nanowires, and (2) we calculate the energy-relaxation rate of a transmon qubit due to the presence of excess quasiparticles. Our examples demonstrate from first principles that niobium nitride is well suited to be used for single-photon detection and that tantalum transmon qubits possess reduced sensitivity to quasiparticle poisoning relative to other materials, which is likely in part responsible for their longer coherence times. In contrast to previous models of superconducting devices, our ab initio approach makes predictions of device performance without experimental input and thus can be used to accelerate progress in device development. Moreover, by considering the full-bandwidth electron-phonon coupling, our approach can incorporate strong-coupling effects. Our methods effectively integrate ab initio materials modeling with nonequilibrium theory of superconductivity to perform practical modeling of superconducting devices, providing a comprehensive approach that connects fundamental theory with device-level applications.
Nonequilibrium quasiparticle and phonon dynamics are central to the operation of superconducting devices. Superconducting detectors, such as superconducting nanowire single-photon detectors, transition-edge sensors, or microwave kinetic inductance detectors, perform best when a large quasiparticle population is generated in response to small perturbations. Conversely, for superconducting qubits and topologically protected Majorana fermions, even relatively small quasiparticle densities can lead to significant performance degradation. Hence, ideal materials for these devices would be less susceptible to quasiparticle poisoning. However, existing models of these devices often rely on approximations and phenomenology. Therefore, they lack a rigorous description of the underlying quasiparticle and phonon dynamics that are responsible for device performance. In this article, we combine kinetic equations with density functional theory to model the nonequilibrium quasiparticle and phonon dynamics of a thin superconducting film ab initio. To demonstrate the universality of our model, we illustrate two independent example applications: (1) we develop a theoretical model describing the detection of single photons in superconducting nanowires, and (2) we calculate the energy-relaxation rate of a transmon qubit due to the presence of excess quasiparticles. Our examples demonstrate from first principles that niobium nitride is well suited to be used for single-photon detection and that tantalum transmon qubits possess reduced sensitivity to quasiparticle poisoning relative to other materials, which is likely in part responsible for their longer coherence times. In contrast to previous models of superconducting devices, our ab initio approach makes predictions of device performance without experimental input and thus can be used to accelerate progress in device development. Moreover, by considering the full-bandwidth electron-phonon coupling, our approach can incorporate strong-coupling effects. Our methods effectively integrate ab initio materials modeling with nonequilibrium theory of superconductivity to perform practical modeling of superconducting devices, providing a comprehensive approach that connects fundamental theory with device-level applications.
Phonon-induced Cooper pair breaking, inciting nonequilibrium quasiparticle (QP) bursts, is known to deteriorate the performance of superconducting devices. However, a detailed understanding of QP-phonon dynamics is lacking due to the absence of a well-established theoretical framework. This paper presents a fully ab initio scheme of calculating nonequilibrium, polarization-dependent QP-phonon dynamics in superconductors. The authors find that with only an 8% deviation from the equilibrium phonon Bose–Einstein distribution, the resulting nonequilibrium QP population is 83 times larger than the equilibrium Fermi–Dirac distribution, and the longitudinal acoustic (LA) phonon polarization is most responsible for QP generation. The authors demonstrated that the qubit transition rate in Josephson junction-based transmon qubits is increased by orders of magnitude when taking these nonequilibrium distributions into account, compared to equilibrium distributions. This framework allows an in-depth exploration of nonequilibrium QP-phonon dynamics in various Josephson-junction-based superconducting devices. It paves the way for formulating advanced phonon shielding strategies to target the LA polarization, potentially leading to enhanced device performance, such as increased coherence time of transmon qubits or reduced thermal noise in cryogenics.
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.
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.
While experimental studies of kinetic-inductance sensors have been limited so far by the temperature range near the superconducting transition, these detectors can be very sensitivity at temperatures well below the transition, where the number of equilibrium quasiparticles is exponentially small. In this regime, a shift of the quasiparticle chemical potential under radiation results in the change of the kinetic inductance, which can be measured by a sensitive SQUID readout. We modeled the kinetic inductance response of detectors made from disordered superconducting Nb, NbC, and MoRe films. Low phonon transparency of the interface between the superconductor and the substrate causes substantial re-trapping of phonons providing high quantum efficiency and the operating time of approximately 1 ms at 1 K. Due to the small number of quasiparticles, the noise equivalent power of the detector determined by the quasiparticle generation-recombination noise can be as small as approximately 10(exp -19) W/Hz(exp 1/2) at He4 temperatures.
The response of superconducting pair-breaking detectors is dependent on the details of the quasiparticle distribution. In Kinetic Inductance Detectors (KIDs), where both pair breaking and non-pair breaking photons are absorbed simultaneously, calculating the detector response therefore requires knowledge of the often nonequilibrium distributions. The quasiparticle effective temperature provides a good approximation to these nonequilibrium distributions. We compare an analytical expression relating absorbed power and the quasiparticle effective temperature in superconducting thin films to full solutions for the nonequilibrium distributions, and find good agreement for a range of materials, absorbed powers, photon frequencies and temperatures typical of KIDs. This analytical expression allows inclusion of nonequilibrium effects in device models without solving for the detailed distributions. We also show our calculations of the frequency dependence of the detector response are in agreement with recent experimental measurements of the response of Ta KIDs at THz frequencies.
Quasiparticle poisoning following particle impacts poses a significant challenge to the development of fault-tolerant superconducting quantum computers, as a sudden excess of quasiparticles can simultaneously degrade the coherence of multiple qubits across large device arrays. In this work, we present a statistical analysis that models the time evolution of radiation-induced qubit energy relaxation through quasiparticle density dynamics. This study provides insight into quasiparticle loss processes by distinguishing between recombination and trapping decay channels and assessing their respective impact on qubit performance. We precisely measure quasiparticle recombination in multiple transmon qubits and uncover an unexpected dependence of qubit relaxation dynamics on deposited energy. By linking correlated relaxation events across qubits to ballistic phonon propagation, we introduce a statistical localization approach to extract the energy deposited in the substrate, which is in good agreement with Monte Carlo simulation. This work establishes the quantitative framework for using an arbitrary subset of superconducting transmon qubits in a QPU as energy-resolving witness particle detectors.