Kinetic-equation approach to nonequilibrium superconductivity

Chang, Joon-Hyuk; Scalapino, D. J.

doi:10.1103/physrevb.15.2651

Cited by 153 publications

(79 citation statements)

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“…The response measurements, complemented with quasiparticle recombination time measurements, are explained consistently by a model based on a microwave-induced nonequilibrium fðEÞ. Redistribution of quasiparticles [5,6] due to microwave absorption [7] has been shown earlier to cause enhancement of the critical current [8], the critical temperature (T c ), and the energy gap [9]. These enhancement effects are most pronounced close to T c and were observed for temperatures T > 0.8T c .…”

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confidence: 82%

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

et al. 2014

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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 PACS numbers: 74.25.nn, 07.57.Kp, 74.40.Gh, 74.78.-w A superconductor can be characterized by the density of states, which exhibits an energy gap due to Cooper pair formation, and the distribution function of the electrons, which in thermal equilibrium is the Fermi-Dirac distribution. When a superconductor is driven by an electromagnetic field, nonlinear effects in the electrodynamic response can occur, which are usually assumed to be due to a change in the density of states, the so-called pair-breaking mechanism [1]. These nonlinear effects can be described along the lines of a current dependent superfluid density n s ðT; jÞ ∝ n s ðTÞ½1 − ðj=j c Þ 2 , where j is the actual current density, j c the critical current density, and T the temperature. Observations such as the nonlinear Meissner effect [2] and nonlinear microwave conductivity [3,4] can be explained by a broadening of the density of states and a decreased n s . The quasiparticles are assumed to be in thermal equilibrium and a Fermi-Dirac distribution fðEÞ ¼ 1=½expðE=k B TÞ þ 1 is assumed, with E the quasiparticle energy and k B Boltzmann's constant.Here we demonstrate that a microwave field also has a strong effect on fðEÞ in the superconductor, and induces a nonlinear response. We present measurements of the electrodynamic response, quality factor, and resonant frequency of an Al superconducting resonator (at 5.3 GHz) as a function of temperature and microwave power at low temperatures T c =18 < T < T c =3. The response measurements, complemented with quasiparticle recombination time measurements, are explained consistently by a model based on a microwave-induced nonequilibrium fðEÞ. Redistribution of quasiparticles [5,6] due to microwave absorption [7] has been shown earlier to cause enhancement of the critical current [8], the critical temperature (T c ), and the energy gap [9]. These enhancement effects are most pronounced close to T c and were observed for temperatures T > 0.8T c . A representation of gap suppression and gap enhancement is shown in the inset to Fig. 1(b) [8]. The consequences of the redistribution of quasiparticles for the electrodynamic response were only studied theoretically for T > 0.5T c [10]. Redistributi...

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confidence: 82%

“…We solve the full nonlinear kinetic equations as presented in Ref. [5], together with Eq. (1), in steady state dfðEÞ=dt ¼ dnðΩÞ=dt ¼ 0 for all energies, with a self-consistency equation for Δ, given by…”

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confidence: 99%

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

et al. 2014

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“…We note that I qp describes the rate at which quasiparticles with energy E are changing occupancy due to the rf drive. We can write the power absorbed by the quasiparticle from the rf drive as 31,32 .4) where N 0 is the single-spin density of states at the Fermi surface in the normal state. Unfortunately P rf and P rf,ab are not equivalent in our apparatus and this complicates the simulation.…”

Section: Discussionmentioning

confidence: 99%

Effects of nonequilibrium quasiparticles in a thin-film superconducting microwave resonator under optical illumination

et al. 2016

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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.

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“…At the lowest power n qp = 10 µm −3 and τ r = 4 ms, leading to NEP ≈ 1.5 × 10 −19 W/Hz 1/2 . Although this particular set of (preliminary) results might be explained by a simple heating model [16], we emphasise that on a microscopic level a more rigorous treatment will be needed, since the microwave field will significantly alter the quasiparticle distribution function [17,18], which we hope to investigate deeper. Several other groups have shown remnant quasiparticle densities lower than 1 µm −3 in experiments with qubits [19,20] and single-electron islands [21] using aluminium, which would make NEP ≈ 1 × 10 −20 W/Hz 1/2 possible.…”

Section: Microwave Resonator Experimentsmentioning

confidence: 99%

Generation-Recombination Noise: The Fundamental Sensitivity Limit for Kinetic Inductance Detectors

et al. 2012

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We present measurements of quasiparticle generation-recombination noise in aluminium Microwave Kinetic Inductance Detectors, the fundamental noise source for these detectors. Both the quasiparticle lifetime and the number of quasiparticles can be determined from the noise spectra. The number of quasiparticles saturates to 10 µm −3 at temperatures below 160 mK, which is shown to limit the quasiparticle lifetime to 4 ms. These numbers lead to a generation-recombination noise limited noise equivalent power (NEP) of 1.5 × 10 −19 W/Hz 1/2 . Since NEP ∝ N qp , lowering the number of remnant quasiparticles will be crucial to improve the sensitivity of these detectors. We show that the readout power now limits the number of quasiparticles and thereby the sensitivity.

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Kinetic-equation approach to nonequilibrium superconductivity

Cited by 153 publications

References 50 publications

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

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

Effects of nonequilibrium quasiparticles in a thin-film superconducting microwave resonator under optical illumination

Generation-Recombination Noise: The Fundamental Sensitivity Limit for Kinetic Inductance Detectors

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