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...

Scanning tunneling microscopy and spectroscopy (STM/S) measurements in the superconducting dichalcogenide 2H-NbS2 show a peculiar superconducting density of states with two well defined features at 0.97 meV and 0.53 meV, located respectively above and below the value for the superconducting gap expected from single band s-wave BCS model (∆=1.76kBTc=0.9 meV). Both features have a continuous temperature evolution and disappear at Tc = 5.7 K. Moreover, we observe the hexagonal vortex lattice with radially symmetric vortices and a well developed localized state at the vortex cores. The sixfold star shape characteristic of the vortex lattice of the compound 2H-NbSe2 is, together with the charge density wave order (CDW), absent in 2H-NbS2.PACS numbers: 71.45. Lr, 74.25.Jb,74.50.+r,74.70.Ad The study of the coexistence of superconductivity with competing physical phenomena such as magnetic or charge order has historically produced great interest on the scientific community. Anisotropies or modulations of the superconducting properties (in real and/or reciprocal space) often appear as a consequence of competing orders within the same system [1,2]. In the compound 2H-NbSe 2 , superconductivity appears within a CDW state (T CDW =33K and T c =7.2 K) [3]. Low lying excitations measured deep in the superconducting state long time ago by specific heat [4,5] have been explained by recent experiments and theoretical calculations with a multiband superconductivity and a peculiar anisotropy of the superconducting gap [6,7]. Recent angular resolved photoemission spectroscopy measurements demonstrate that the superconducting gap has, close to T c (at 5.7 K), largest values at k-space positions connected with CDW wavevectors [8,9]. Hess et al. [10,11,12] found that the local superconducting density of states (LDOS) at the center of the vortex core shows a high peak close to the Fermi level highlighting the lowest quasiparticle state bound within the vortex core well [13]. Around the vortex core, the LDOS is far from respecting in-plane symmetry and intriguing vortex lattice images with patterns showing strong in-plane LDOS modulations are obtained [10,11,12]. 2H-NbSe 2 belongs to the transition-metal dichalcogenides (2H-MX 2 with M = Ta, Nb and X = Se, S), a family of systems which is unique to study the interplay between CDW order and superconductivity. The 2H-MX 2 compounds share a double layered structure made of two hexagonal X sheets with an intercalated M sheet (X-M-X), connected through very weak van der Waals bonds [14]. This produces highly anisotropic, quasi two dimensional electronic properties. The features of the Fermi Surface (FS) expected to be common in all systems of the series are two concentric cylindrical FS sheets centered on both Γ and K points, derived from the transition-metal d bands [15,16,17,18]. When going over the series from 2H-TaSe 2 and 2H-TaS 2 to 2H-NbSe 2 and 2H-NbS 2 , the ratio of the intralayer lattice constant with the interlayer distance a/c increases, as well as T c , whereas T CDW decreas...

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...

Single photon level quality factors of 500x10^3 are shown in NbTiN superconducting resonators at millikelvin temperatures. This result originates from the intrinsic low dielectric loss of NbTiN, as demonstrated by comparison with Ta, and by removing unnecessary parts of the dielectric substrate.Comment: 4 pages, 3 figure

We report measurements of the temperature dependence of both in-plane and out-of-plane penetration depths (lambda(a) and lambda(c), respectively) in 2H-NbSe2. Measurements were made with a radio-frequency tunnel diode oscillator circuit at temperatures down to 100 mK. Analysis of the anisotropic superfluid density shows that a reduced energy gap is located on one or more of the quasi-two-dimensional Nb Fermi surface sheets rather than on the Se sheet, in contrast with some previous reports. This result suggests that the gap structure is not simply related to the weak electron-phonon coupling on the Se sheet and is therefore important for microscopic models of anisotropic superconductivity in this compound.

The temperature dependence of the phonon spectrum in the superconducting transition-metal dichalcogenide 2H-NbS 2 is measured by diffuse and inelastic x-ray scattering. A deep, wide, and strongly temperature-dependent softening of the two lowest-energy longitudinal phonon bands appears along the M symmetry line in reciprocal space. In sharp contrast to the isoelectronic compound 2H-NbSe 2 , the soft phonons energies are finite, even at very low temperature, and no charge density wave instability occurs, in disagreement with harmonic ab initio calculations. We show that 2H-NbS 2 is at the verge of the charge density wave transition and its occurrence is only suppressed by the large anharmonic effects. Moreover, the anharmonicity and the electron phonon coupling both show a strong in-plane anisotropy.

Microwave Kinetic Inductance Detectors (MKIDs) have shown great potential for sub-mm instrumentation because of the high scalability of the technology. Here we demonstrate for the first time in the sub-mm band (0.1. . . 2 mm) a photon noise limited performance of a small antenna coupled MKID detector array and we describe the relation between photon noise and MKID intrinsic generation-recombination noise. Additionally we use the observed photon noise to measure the optical efficiency of detectors to be 0.8 ± 0.2. PACS numbers: 07.57.Kp Advances in sub-mm astronomy (100. . . 1000 GHz) have always been driven by advances in radiation detection technology. Current state of the art imaging arrays consist of up to 1000 pixels of cryogenic detectors with a sensitivity approaching the photon noise limit 1 . Significant further advances in observing speed are only possible by increasing the pixel number. Microwave Kinetic Inductance detectors (MKIDs) 2 are very promising to use for very large arrays due to their intrinsic multiplexing capability 3 . Despite the very low reported values 4,5 of the (dark) Noise Equivalent Power (NEP) ∼ 3 × 10 −19 W/Hz 1/2 , MKIDs have yet to demonstrate photon noise limited performance. In this letter we demonstrate photon noise limited performance of a lens-antenna coupled MKID array. The presented device geometry ensures that all radiation to the antenna is converted into quasiparticles in the sensitive part of the MKID, which is made of Al. This design, combined with the recent observation of generation-recombination noise in an Al MKID 5 , enables the demonstration of photon noise limited radiation detection.The fundamental limit of any ideal photon integrating sub-mm detector is the noise associated with the Bose-Einstein fluctuations in photon arrival rate 6 which results in a photon noise limited NEP:where P is the sky power loading the detector at a frequency F from the sub-mm source. B is the photon occupation number per mode and m the efficiency from emission to detection of one mode. The (1 + mB) term is the correction to Poisson statistics due to wave bunching 6 . In the presented experiment m is small to enable low power coupling. a)MKIDs are superconducting pair breaking detectors, in which incident sky radiation changes the equilibrium between Cooper pairs and quasiparticles and hence the microwave conductivity in a planar superconducting resonator 2 . The number fluctuations between quasiparticles and Cooper pairs in the MKID will limit the device sensitivity giving a generation-recombination (g-r) NEP 5,7 :In the limit where the quasiparticle number in the MKID is dominated by the sky power then NEP G−R can be approximated by:where we only consider recombination noise contributions as quasiparticle creation is correlated with the photon arrival. Here N qp is the number of quasiparticles, τ is the quasiparticle recombination lifetime, η pb ∼ 0.6 is the efficiency for conversion of energy into quasiparticles 8 and ∆ is the superconducting gap. Under illumination we therefore...

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 lm À3 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. The promise of a long quasiparticle lifetime and a long coherence time makes superconducting circuits popular for use in radiation detection and quantum computation. At low temperature the number of quasiparticles in a superconductor should decrease exponentially. Excess quasiparticles were recently suggested to limit the coherence time of superconducting qubits 1 and the tunnelling rate in single-electron transistors.2 Recently, the quasiparticle lifetime in a highquality aluminium superconducting resonator 3 was shown to be consistent with an excess quasiparticle population inferred from noise measurements. 4 There is a vivid debate on the question of the origin of those excess quasiparticles, 1,2,4 which mainly focuses on reducing the influence of the environment on the devices under study. Here we show for superconducting aluminium resonators that the environment is well enough under control in our experimental setup to reveal a new source of quasiparticles, namely, the microwave readout power of these devices. We show that the saturation in the number of quasiparticles at low temperature (100-150 mK), as inferred from noise measurements, decreases from 72 to 17lm À3 with a 6 dB decrease of the microwave power. The quasiparticle lifetime increases accordingly from 1.4 to 3.5 ms.Microwave resonators are popular devices in radiation detection 5 and circuit quantum electrodynamics. 6 The two quadratures of the microwave field in such a resonator are proportional to the real and imaginary part of the conductivity of the superconductor r 1 À ir 2 . The real part corresponds to dissipation in the quasiparticle system and the imaginary part to the kinetic inductance of the condensate. 7 We have shown recently that the real part of the conductivity shows quasiparticle number fluctuations. 4 When two quasiparticles recombine, a Cooper pair is formed and when a Cooper pair is broken it leaves two quasiparticles. Therefore, the superconducting condensate fluctuates as well, and one would expect to see these fluctuations in the reactive response of the microwave resonator. However, this reactive response is obscured by the response of two-level fluctuators in the dielectrics surrounding the resonator.8 Therefore, we study here the correlation between the dissipative and reactive part of the conductivity in an aluminium resonator. We observe correlated ...