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

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 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...

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

“…We also find that this optically-induced loss decreases with increasing microwave drive within the range of rf powers and optical intensities that we used in our experiments. The reason for this behavior is similar to the higher temperature case described by de Visser et al 13 . In this regime the rf drive causes a redistribution of the quasiparticles such that f (E) increases for E ≥ ∆ + hf r and decreases for ∆ ≤ E ≤ ∆ + hf r .…”

“…The phonon escape time τ e = 8.96 ns = 34τ φ was set to maintain power balance for the absorbed optical power for ≈ 15%. This value is about an order of magnitude larger than the equivalent value used by Goldie and Withington 31 and de Visser et al 13 , however it is within the range of reported values for τ e for Al on sapphire 37 . We found that relatively large changes in τ e resulted in relatively small changes in σ 1 and σ 2 .…”

“…We find that this photo-induced loss decreases with increasing rf drive, much as one expects for loss from coupling to an ensemble of TLSs 24 . However, we argue below that the power-dependent loss is actually due to the subtle behavior of nonequilibrium quasiparticles 13 . We discuss modelling of the power-dependent optically-induced loss and resonator frequency shift as a function of temperature, optical power, and rf power.…”

“…Unfortunately P rf and P rf,ab are not equivalent in our apparatus and this complicates the simulation. The power absorbed by quasiparticles P rf,ab is related to the applied rf power P rf by 13 P rf,ab = 2P rf Q 2 Q qp Q e , (A. 5) where Q is the total quality factor of the LC resonator, Q e is the external quality factor, Q qp is the internal quality factor due to quasiparticles only, and 1/Q = 1/Q i + 1/Q e [see Eq.…”

“…TLS loss exhibits a distinct power-dependent saturation behavior 3,7,8 that leads to a characteristic decrease in loss with an increase in temperature or microwave power. Third, dissipation can be caused by quasiparticles which can be created by thermal effects, stray light, radiation, or other mechanisms [9][10][11][12][13][14][15] . Quasiparticle generation from ionizing radiation or photons provides the physical basis for superconducting radiation detectors 5,6,10,14 , and is also relevant to some proposed hybrid quantum systems in which a superconducting device must function in close proximity to optically trapped atoms 16,17 .…”