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arXiv:1306.4992 · Physical Review Letters

Evidence of a Nonequilibrium Distribution of Quasiparticles in the Microwave Response of a Superconducting Aluminum Resonator

Pieter de Visser, D. J. Goldie, P. Diener, S. Withington, J. J. A. Baselmans, T. M. Klapwijk

Published Jan 28, 2014• 138 citations
arXivHTMLPDF

Abstract

In a superconductor, absorption of photons with an energy below the superconducting gap leads to redistribution of quasiparticles over energy and thus induces a strong nonequilibrium quasiparticle energy distribution. We have measured the electrodynamic response, quality factor, and resonant frequency of a superconducting aluminium microwave resonator as a function of microwave power and temperature. Below 200 mK, both the quality factor and resonant frequency decrease with increasing microwave power, consistent with the creation of excess quasiparticles due to microwave absorption. Counterintuitively, above 200 mK, the quality factor and resonant frequency increase with increasing power. We demonstrate that the effect can only be understood by a nonthermal quasiparticle distribution.

DOI
10.1103/physrevlett.112.047004

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LOSS IN SUPERCONDUCTING QUANTUM DEVICES FROM NON-EQUILIBRIUM QUASIPARTICLES AND INHOMOGENEITY IN ENERGY GAP

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This dissertation describes energy dissipation and microwave loss due to non-equilibrium quasiparticles in superconducting transmon qubits and titanium nitride coplanar waveguide resonators. During the measurements of transmon T1 relaxation time and resonator quality factor QI, I observed reduced microwave loss as the temperature increased from 20 mK to approximately Tc/10 at which the loss takes on a minimum value. I argue that this effect is due to non-equilibrium quasiparticles. I measured the temperature dependence of the relaxation time T1 of the excited state of an Al/AlOx/Al transmon and found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK with a best T1 of 0.2 ms. I present an argument showing this unexpected temperature dependence occurs due to the behavior of non-equilibrium quasiparticles in devices in which one electrode in the tunnel junction has a smaller volume, and slightly smaller superconducting energy gap, than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with the smaller gap, leading to a relatively high density of quasiparticles at the junction and a short T1. Increasing the temperature gives the quasiparticles enough thermal energy to occupy the higher gap electrode, reducing the density at the junction and increasing T1. I present a model of this effect, extract the density of quasiparticles and the two superconducting energy gaps, and discuss implications for increasing the relaxation time of transmons. I also observed a similar phenomenon in low temperature microwave studies of titanium nitride coplanar waveguide resonators. I report on loss in a resonator at temperatures from 20 mK up to 1.1 K and with the application of infrared pair breaking radiation (λ=1.55 μm). With no applied IR light, the internal quality factor increased from QI = 800,000 at T < 70 mK up to QI=(2×10^6 ) at 600 mK. The resonant frequency f0 increased by 2 parts per million over the same temperature range. Above 600 mK both QI and f0 decreased rapidly, consistent with the increase in the density of thermally generated quasiparticles. With the application of IR light and for intensities below 1 aW μm^(-2) and T < 400 mK, QI increased in a similar way to increasing the temperature before beginning to decrease with larger intensities. I show that a model involving non-equilibrium quasiparticles and two regions of different superconducting gaps can explain this unexpected behavior.

•Jan 1, 2020•1 citation
In a superconductor, absorption of photons with an energy below the superconducting gap leads to redistribution of quasiparticles over energy and thus induces a strong nonequilibrium quasiparticle energy distribution. We have measured the electrodynamic response, quality factor, and resonant frequency of a superconducting aluminium microwave resonator as a function of microwave power and temperature. Below 200 mK, both the quality factor and resonant frequency decrease with increasing microwave power, consistent with the creation of excess quasiparticles due to microwave absorption. Counterintuitively, above 200 mK, the quality factor and resonant frequency increase with increasing power. We demonstrate that the effect can only be understood by a nonthermal quasiparticle distribution.
We have illuminated a thin-film superconducting Al lumped-element microwave resonator with 780 nm light and observed the resonator quality factor and resonance frequency as a function of illumination and microwave power in the 20 to 300 mK temperature range. The optically induced microwave loss increases with increasing illumination but decreases with increasing microwave power. Although this behavior may suggest the presence of optically activated two-level systems, we find that the loss is better explained by the presence of nonequilibrium quasiparticles generated by the illumination and excited by the microwave drive. We model the system by assuming that the illumination creates an effective source of phonons with energy higher than double the superconducting gap and solve the coupled quasiparticle-phonon rate equations. We fit the simulation results to our measurements and find good agreement with the observed dependence of the resonator quality factor and frequency shift on temperature, microwave power, and optical illumination. Examination of the model reveals approaches to reducing optically induced loss and improving the relaxation time of superconducting quantum devices.
We have measured the number of quasiparticles and their lifetime in aluminium superconducting microwave resonators. The number of excess quasiparticles below 160 mK decreases from 72 to 17 μm−3 with a 6 dB decrease of the microwave power. The quasiparticle lifetime increases accordingly from 1.4 to 3.5 ms. These properties of the superconductor were measured through the spectrum of correlated fluctuations in the quasiparticle system and condensate of the superconductor, which show up in the resonator amplitude and phase, respectively. Because uncorrelated noise sources vanish, fluctuations in the superconductor can be studied with a sensitivity close to the vacuum noise.
In the superconducting state, the presence of a finite gap in the excitation spectrum implies that the number of excitations (quasiparticles) is exponentially small at temperatures well below the critical temperature. Conversely, minute perturbations can significantly impact both the distribution in energy and the number of quasiparticles. Typically, the interaction with the electromagnetic environment is the main perturbation source driving quasiparticles out of thermal equilibrium, while a phonon bath is responsible for restoration of equilibrium. Here we derive approximate analytical solutions for the quasiparticle distribution function in superconducting resonators and explore the impact of nonequilibrium on two measurable quantities: the resonator's quality factor and its resonance frequency. Applying our results to experimental data, we conclude that while at intermediate temperatures there is clear evidence for the nonequilibrium effects due to heating of the quasiparticles by photons, the low-temperature measurements are not explained by this mechanism.
Many superconducting devices rely on the finite gap in the excitation spectrum of a superconductor: thanks to this gap, at temperatures much smaller than the critical one the number of excitations (quasiparticles) that can impact the device’s behavior is exponentially small. Nevertheless, experiments at low temperature usually find a finite, non-negligible density of quasiparticles whose origin has been attributed to various non-equilibrium phenomena. Here, we investigate the role of photons with energy exceeding the pair-breaking threshold 2\Delta 2 Δ as a possible source for these quasiparticles in superconducting resonators. Modeling the interacting system of quasiparticles, phonons, sub-gap and pair-breaking photons using a kinetic equation approach, we find analytical expressions for the quasiparticles’ density and their energy distribution. Applying our theory to measurements of quality factor as function of temperature and for various readout powers, we find they could be explained by assuming a small number of photons above the pair-breaking threshold. We also show that frequency shift data can give evidence of quasiparticle heating.
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 .
This dissertation describes energy dissipation and microwave loss due to non-equilibrium quasiparticles in superconducting transmon qubits and titanium nitride coplanar waveguide resonators. During the measurements of transmon T1 relaxation time and resonator quality factor QI, I observed reduced microwave loss as the temperature increased from 20 mK to approximately Tc/10 at which the loss takes on a minimum value. I argue that this effect is due to non-equilibrium quasiparticles. I measured the temperature dependence of the relaxation time T1 of the excited state of an Al/AlOx/Al transmon and found that, in some cases, T1 increased by almost a factor of two as the temperature increased from 30 mK to 100 mK with a best T1 of 0.2 ms. I present an argument showing this unexpected temperature dependence occurs due to the behavior of non-equilibrium quasiparticles in devices in which one electrode in the tunnel junction has a smaller volume, and slightly smaller superconducting energy gap, than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with the smaller gap, leading to a relatively high density of quasiparticles at the junction and a short T1. Increasing the temperature gives the quasiparticles enough thermal energy to occupy the higher gap electrode, reducing the density at the junction and increasing T1. I present a model of this effect, extract the density of quasiparticles and the two superconducting energy gaps, and discuss implications for increasing the relaxation time of transmons. I also observed a similar phenomenon in low temperature microwave studies of titanium nitride coplanar waveguide resonators. I report on loss in a resonator at temperatures from 20 mK up to 1.1 K and with the application of infrared pair breaking radiation (λ=1.55 μm). With no applied IR light, the internal quality factor increased from QI = 800,000 at T < 70 mK up to QI=(2×10^6 ) at 600 mK. The resonant frequency f0 increased by 2 parts per million over the same temperature range. Above 600 mK both QI and f0 decreased rapidly, consistent with the increase in the density of thermally generated quasiparticles. With the application of IR light and for intensities below 1 aW μm^(-2) and T < 400 mK, QI increased in a similar way to increasing the temperature before beginning to decrease with larger intensities. I show that a model involving non-equilibrium quasiparticles and two regions of different superconducting gaps can explain this unexpected behavior.