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Physical Review B

Dynamics of nonequilibrium quasiparticles in narrow-gap superconducting tunnel junctions

Alexander G. Kozorezov, R. A. Hijmering, Guy Brammertz, J. Keith Wigmore, Anthony J. Peacock, D. Martin, P. Verhoeve, Alexander A. Golubov, Horst Rogalla

Published Jan 2, 2008• 15 citations
Publisher

Abstract

The latest generation of high quality, narrow gap, superconducting tunnel junctions (STJs) exhibits a steady-state and time-dependent behavior which cannot be described satisfactorily by previous treatments of nonequilibrium quasiparticle (qp) dynamics. These effects are particularly evident in experiments using STJs as detectors of photons, over the range from near infrared to x ray. In this paper, we present a detailed theoretical analysis of the spectral and temporal evolution of the nonequilibrium qp and phonon distributions in such STJs excited by single photons, over a wide range of excitation energy, bias voltage, and temperature. By solving the coupled set of kinetic equations describing the interacting excitations, we show that the nonequilibrium qp distribution created by the initial photoabsorption does not decay directly back to the initial undisturbed state in thermal equilibrium. Instead, it undergoes a rapid adiabatic relaxation to a long-lived, excited state, the spectral distribution of which is nonthermal, maintained by a balance between qp creation, recombination, and trapping. The model is able to describe successfully photoabsorption data taken on several different aluminum STJs, using a single set of parameters. Of particular note is the conclusion that the local traps responsible for qp loss are situated specifically in the region of Nb contacts.

DOI
10.1103/physrevb.77.014501

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The latest generation of high quality, narrow gap, superconducting tunnel junctions (STJs) exhibits a steady-state and time-dependent behavior which cannot be described satisfactorily by previous treatments of nonequilibrium quasiparticle (qp) dynamics. These effects are particularly evident in experiments using STJs as detectors of photons, over the range from near infrared to x ray. In this paper, we present a detailed theoretical analysis of the spectral and temporal evolution of the nonequilibrium qp and phonon distributions in such STJs excited by single photons, over a wide range of excitation energy, bias voltage, and temperature. By solving the coupled set of kinetic equations describing the interacting excitations, we show that the nonequilibrium qp distribution created by the initial photoabsorption does not decay directly back to the initial undisturbed state in thermal equilibrium. Instead, it undergoes a rapid adiabatic relaxation to a long-lived, excited state, the spectral distribution of which is nonthermal, maintained by a balance between qp creation, recombination, and trapping. The model is able to describe successfully photoabsorption data taken on several different aluminum STJs, using a single set of parameters. Of particular note is the conclusion that the local traps responsible for qp loss are situated specifically in the region of Nb contacts.
We present a full theoretical and experimental study of the dynamics and energy distribution of nonequilibrium quasiparticles in superconducting tunnel junctions (STJ's). STJ's are often used for single-photon spectrometers, where the numbers of quasiparticles excited by a photon provide a measure of the photon energy. The magnitude and fluctuations of the signal current in STJ detectors are in large part determined by the quasiparticle dynamics and energy distribution during the detection process. We use this as motivation to study the transport and energy distribution of nonequilibrium quasiparticles excited by x-ray photons in a lateral, imaging junction configuration. We present a full numerical model for the tunneling current of the major physical processes which determine the signal. We find that a diffusion framework models the quasiparticle dynamics well and that excited quasiparticles do not equilibrate to the lattice temperature during the time scales for tunneling. We extract physical time scales from the measured data, make comparisons with existing theories, and comment on implications for superconducting mesoscopic systems and single-photon detectors.
We recently predicted the formation of a highly non-equilibrium quasiparticle (qp) distribution in low TC multiple tunnelling superconducting tunnel junctions (STJs) [1]. The situation arises through qp energy gain in cycles of successive forward and back tunnelling events in the absence of relaxation via sub-gap phonon emission. The qps can acquire sufficient energy to emit phonons, which break more Cooper pairs and release additional qps. In this paper we report theoretical and experimental studies of the effect of this process on photon detection by such an STJ. We derived a set of energy-dependent balance equations [2], which describe the kinetics of the qps and phonons, including the qp multiplication process described above. Solution of the balance equations gives the non-equilibrium distribution of the qps as a function of time and energy, and hence the responsivity of the STJ as a function of bias voltage. We compared the theoretical results with experiments on high quality, multiple-tunnelling Al STJs cooled to 35mK in an adiabatic demagnetisation refrigerator, and illuminated with monochromatic photons with wavelengths between 250 and 1000 nm. It was found that in the larger junctions with the longest qp loss time, both responsivity and signal decay time increased rapidly with bias voltage. Excellent agreement was obtained between the observed effects and theoretical modelling.
We recently predicted the formation of a highly non-equilibrium quasiparticle (qp) distribution in low TC multiple tunnelling superconducting tunnel junctions (STJs) [1]. The situation arises through qp energy gain in cycles of successive forward and back tunnelling events in the absence of relaxation via sub-gap phonon emission. The qps can acquire sufficient energy to emit phonons, which break more Cooper pairs and release additional qps. In this paper we report theoretical and experimental studies of the effect of this process on photon detection by such an STJ. We derived a set of energy-dependent balance equations [2], which describe the kinetics of the qps and phonons, including the qp multiplication process described above. Solution of the balance equations gives the non-equilibrium distribution of the qps as a function of time and energy, and hence the responsivity of the STJ as a function of bias voltage. We compared the theoretical results with experiments on high quality, multiple-tunnelling Al STJs cooled to 35mK in an adiabatic demagnetisation refrigerator, and illuminated with monochromatic photons with wavelengths between 250 and 1000 nm. It was found that in the larger junctions with the longest qp loss time, both responsivity and signal decay time increased rapidly with bias voltage. Excellent agreement was obtained between the observed effects and theoretical modelling.
Nonequilibrium quasiparticles (QPs) generated by stray infrared and ionizing radiation can limit the performance of superconducting quantum processors and present challenges for quantum error correction schemes. Models of QP-induced energy relaxation commonly assume that the characteristic energy of the QPs and the qubit transition energy are both small relative to the superconducting gap. Under these assumptions, certain qubits such as the fluxonium would exhibit protection against QP-induced dissipation at specific bias points. Here, we show that this is not necessarily the case, numerically analyzing the predicted rate of QP-induced dissipation in fluxonium qubits for different QP energy distributions and for QPs created via photon-assisted tunneling processes. We find that accounting for small numerical factors, existing theoretical models predict sensitivity to QP-induced errors at bias points previously thought to be protected. We find that inclusion of asymmetry in the superconducting gap energy across the junction can reintroduce suppression of QP-induced relaxation, as expected. Additionally, for QPs created by photon-assisted tunneling, we predict that T1T_1T1​ protection will only occur for a specific energy of pair-breaking radiation. This understanding of fluxonium sensitivity to QP-induced dissipation informs the development of fluxonium-based processors and future QP-mitigation strategies.
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.
Quasiparticle (QP) effects play a significant role in the coherence and fidelity of superconducting quantum circuits.The Andreev bound states of high-transparency Josephson junctions can act as low-energy traps for QPs, providing a mechanism for studying the dynamics and properties of both the QPs and the junction.Using locally injected and thermal QPs, we study QP loss and QP poisoning in epitaxial Al-InAs Josephson junctions incorporated in a superconducting quantum interference device (SQUID) galvanically shorting a superconducting resonator to ground.We observe changes in the resonance line shape and frequency shifts consistent with QP trapping into and clearing out of the ABSs of the junctions when the junctions are phase biased.By monitoring the QP trapping and clearing mechanisms in time, we find a time scale of O(1 µs) for these QP dynamics, consistent with the presence of phonon-mediated QP-QP interactions.Our measurements suggest that electron-phonon interactions play a significant role in the relaxation mechanisms of our system, while electron-photon interactions and electron-phonon interactions govern the clearing mechanisms.Our results highlight the QP-induced dissipation and complex QP dynamics in superconducting quantum circuits fabricated on superconductor-semiconductor heterostructures.