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...