We have directly measured quasiparticle number fluctuations in a thin film superconducting Al resonator in thermal equilibrium. The spectrum of these fluctuations provides a measure of both the density and the lifetime of the quasiparticles. We observe that the quasiparticle density decreases exponentially with decreasing temperature, as theoretically predicted, but saturates below 160 mK to 25-55=m 3 . We show that this saturation is consistent with the measured saturation in the quasiparticle lifetime, which also explains similar observations in qubit decoherence times. DOI: 10.1103/PhysRevLett.106.167004 PACS numbers: 74.40.Àn, 07.57.Kp, 74.25.Bt, 74.25.NÀ In a superconductor the density of unpaired electrons (quasiparticles) should vanish when approaching zero temperature [1]. This crucial property promises long decoherence times for superconducting qubits [2] and long relaxation times for highly sensitive radiation detectors [3]. However, relaxation times for resonators [4,5] and qubit decoherence times [6][7][8] were shown to saturate at low temperature. Recent modeling [8,9] suggests that nonequilibrium quasiparticles are the main candidate for this saturation, which was tested qualitatively by injecting quasiparticles into a qubit [10]. A direct measurement of the number of quasiparticles and the energy decay rate in equilibrium at low temperatures would provide new insight in superconductivity at low temperatures, crucially needed in the aforementioned fields.At finite temperature, it follows from thermodynamics that the density of quasiparticles fluctuates around an average value that increases exponentially with temperature [11]. Here we report a measurement of the spectrum of these fluctuations in a single aluminum superconducting film (T c ¼ 1:1 K) in equilibrium, for temperatures from 300 to 100 mK. The number fluctuations show up as fluctuations in the complex conductivity of the film, probed with a microwave resonator. The spectrum of these fluctuations provides a direct measure of the number of quasiparticles in the superconductor. We observe that the quasiparticle density decreases exponentially with decreasing temperature until it saturates at 25-55 m À3 below 160 mK. We prove that the measured saturation of the quasiparticle lifetime to 2.2 ms below 160 mK is consistent with the saturation in quasiparticle density. In addition, our experiment shows that it is possible to reach the fundamental generation-recombination noise limit in detectors based on Al resonators.In a superconductor in thermal equilibrium, the density of quasiparticles per unit volume is given byvalid at k B T < Á, with N 0 the single spin density of states at the Fermi level (1:72 Â 10 10 m À3 eV À1 for Al), k B Boltzmann's constant, T the temperature, and Á the energy gap of the superconductor. Two quasiparticles with opposite spins and momenta can be generated from a Cooper pair by a phonon with an energy larger than the energy gap. When two quasiparticles recombine into a Cooper pair, a phonon is emitted. These proce...

In a superconductor, in which electrons are paired, the density of unpaired electrons should become zero when approaching zero temperature. Therefore, radiation detectors based on breaking of pairs promise supreme sensitivity, which we demonstrate using an aluminium superconducting microwave resonator. Here we show that the resonator also enables the study of the response of the electron system of the superconductor to pair-breaking photons, microwave photons and varying temperatures. A large range in radiation power (at 1.54 THz) can be chosen by carefully filtering the radiation from a blackbody source. We identify two regimes. At high radiation power, fluctuations in the electron system caused by the random arrival rate of the photons are resolved, giving a straightforward measure of the optical efficiency (48±8%) and showing an unprecedented detector sensitivity. At low radiation power, fluctuations are dominated by excess quasiparticles, the number of which is measured through their recombination lifetime.

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...