Search

This Letter reports results from a haloscope search for dark matter axions with masses between 2.66 and 2.81 $\mu$eV. The search excludes the range of axion-photon couplings predicted by plausible models of the invisible axion. This unprecedented sensitivity is achieved by operating a large-volume haloscope at sub-kelvin temperatures, thereby reducing thermal noise as well as the excess noise from the ultra-low-noise SQUID amplifier used for the signal power readout. Ongoing searches will provide nearly definitive tests of the invisible axion model over a wide range of axion masses., Comment: 5 pages, 4 figures

Non-virialized dark-matter axions may be present in the Milky Way halo in the form of low-velocity-dispersion flows. The Axion Dark Matter eXperiment performed a search for the conversion of these axions into microwave photons using a resonant cavity immersed in a strong, static magnetic field. The spread of photon energy in these measurements was measured at spectral resolutions of the order of 1 Hz and below. If the energy variation were this small, the frequency modulation of any real axion signal due to the orbital and rotational motion of the Earth would become non-negligible. Conservative estimates of the expected signal modulation were made and used as a guide for the search procedure. The photon frequencies covered by this search are 812$-$852 and 858$-$892 MHz, which correspond to an axion mass of 3.36$-$3.52 and 3.55$-$3.69 {\mu}eV. No axion signal was found, and limits were placed on the maximum local density of non-virialized axions of these masses., Comment: 12 pages, 12 figures

Recent determinations of cosmological parameters point to a flat Universe, whose total energy density is composed of about two-thirds vacuum energy and one-third matter. Ordinary baryonic matter is relegated to a small fraction of the latter, within which the luminous part is an order of magnitude smaller yet. Particle dark matter, i.e., one or more relic particle species from the big bang, is thus strongly suggested as the dominant component of matter in the Universe. The axion, a hypothetical elementary pseudoscalar arising from the Peccei-Quinn solution to the strong-$\mathrm{CP}$ problem, is a well-motivated candidate. If the axion exists, it must be extremely light, in the mass range of ${10}^{\ensuremath{-}6}--{10}^{\ensuremath{-}3}\mathrm{eV},$ and possess extraordinarily feeble couplings to matter and radiation. Nevertheless, as proposed by Sikivie in 1983, the axion's two-photon coupling lends itself to a feasible search strategy with currently available technology. In this scheme, axions resonantly convert to single microwave photons by a Primakoff interaction, in a tunable microwave cavity permeated by a strong magnetic field. Present experiments utilizing heterostructure transistor microwave amplifiers have achieved total system noise temperatures of $\ensuremath{\sim}3\mathrm{K}$ and represent the world's quietest spectral radio receivers. Exclusion regions have already been published well into the band of realistic axion model couplings, within the lowest decade of mass range. Recent breakthroughs in the development of near-quantum-limited superconducting quantum interference device amplifiers should reduce the system noise temperature to $\ensuremath{\sim}100\mathrm{mK}$ or less. Ongoing research into using Rydberg-atom single-quantum detectors as the detector in a microwave cavity experiment could further reduce the effective noise temperature. In parallel with improvements in amplifier technology, promising concepts for higher-frequency cavity resonators are being explored to open up the higher decades in mass range. Definitive experiments to find or exclude the axion may therefore be at hand in the next few years. As the microwave cavity technique measures the total energy of the axion, a positive discovery could well reveal fine structure of the signal due to flows of nonthermalized axions. Manifesting diurnal and sidereal modulation, such detailed features would contain a wealth of information about the history, structure, and dynamics of our Milky Way galaxy.

We study the dynamics of a two-dimensional ensemble of randomly distributed classical Heisenberg spins with isotropic RKKY and weaker anisotropic dipole-dipole couplings. Such ensembles may give rise to the flux noise observed in SQUIDs with a $1/{f}^{\ensuremath{\alpha}}$ power spectrum with $\ensuremath{\alpha}\ensuremath{\lesssim}1$. We solve numerically the Landau-Lifshitz-Gilbert equations of motion in the dissipationless limit. We find that Ising-type fluctuators, which arise from spin clustering close to a spin-glass critical behavior with ${T}_{c}=0$, give rise to $1/{f}^{\ensuremath{\alpha}}$ noise. Even weak anisotropic interactions lead to a crossover from the Heisenberg-type criticality to the much stronger Ising-type criticality. The temperature-dependent exponent $\ensuremath{\alpha}(T)\ensuremath{\lesssim}1$ increases and approaches unity when the temperature is lowered. This mechanism acts in parallel to the spin diffusion mechanism. Whereas the latter is sensitive to the device geometry, the spin-clustering mechanism is largely geometry independent.

We have investigated the transport properties of two-dimensional arrays of normal islands interconnected by tunnel junctions fabricated close to a conducting ground plane. For bias voltages $V$ below a threshold voltage ${V}_{\mathrm{th}},$ the current $I$ is thermally activated with an activation energy proportional to ${V}_{\mathrm{th}}\ensuremath{-}V.$ For $Vg{V}_{\mathrm{th}},$ $I$ scales as $(V\ensuremath{-}{V}_{\mathrm{th}}{)}^{\ensuremath{\zeta}},$ where $\ensuremath{\zeta}=2.01\ifmmode\pm\else\textpm\fi{}0.04$ and $1.58\ifmmode\pm\else\textpm\fi{}0.04$ for two samples. For constant $V,$ $I$ exhibits Coulomb-blockade oscillations as a function of the voltage of the ground plane. The amplitude of these oscillations scales as $(V\ensuremath{-}{V}_{\mathrm{th}}{)}^{\ensuremath{\chi}},$ where $\ensuremath{\chi}=0.68\ifmmode\pm\else\textpm\fi{}0.18$ and $0.31\ifmmode\pm\else\textpm\fi{}0.10$ for the same samples, respectively. These values are consistent with our theoretical prediction $\ensuremath{\chi}=(\ensuremath{\zeta}\ensuremath{-}1)/2.$

We report a new class of $c$-axis Josephson tunneling experiments in which a conventional superconductor (Pb) is deposited across a single twin boundary of a $\mathrm{YBa}{}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ (YBCO) crystal. We measure the critical current as a function of the magnitude and angle of a magnetic field applied in the plane of the junction. In all samples, we observe a clear experimental signature of an order parameter phase shift across the twin boundary. These results provide strong evidence for mixed $d$- and $s$-wave pairing in YBCO, with a reversal in the sign of the $s$-wave component across the twin boundary.

We have fabricated a two-dimensional array of Josephson junctions within 100nm of a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. The screening provided by the 2DEG causes the array to show superconducting behavior despite a large junction resistance. Varying the resistance per square of the 2DEG changes the dissipation in the electrodynamic environment of the array independently of any other parameters in the system. As the resistance increases, the current-voltage characteristics of the array change from superconducting to insulating in character. {copyright} {ital 1997} {ital The American Physical Society}

We have used a dc superconducting quantum interference device to measure the spectral density of magnetic flux noise, {ital S}{sub {Phi}}({ital f}), generated by vortex motion in crystals of YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} (YBCO) both before and after irradiation with 3.1-MeV protons and 1-GeV Au ions. In addition, we have studied the effects of irradiation on the critical current {ital J}{sub {ital c}} of the same samples. Both types of irradiation reduced {ital S}{sub {Phi}}({ital f}) at most temperatures and magnetic fields and increased {ital J}{sub {ital c}} at all temperatures and magnetic fields. By measuring {ital S}{sub {Phi}}({ital f}) versus temperature, we extract the distribution of vortex pinning energies, {ital D}({ital U}{sub 0}). Both crystals have peaks in {ital D}({ital U}{sub 0}) near 0.1 eV and 0.2 eV before irradiation, and a much reduced peak near 0.1 eV after irradiation. The noise level after either kind of irradiation was substantially higher than in an unirradiated YBCO film. {copyright} {ital 1996 The American Physical Society.}

In heavily twinned crystals or films of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ (YBCO), ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ pairing symmetry is expected to cause the cancellation of first-order Josephson tunneling through a YBCO-Pb tunnel junction grown on an a-b face; any residual tunneling is thus second order. As a result, microwaves at frequency f are predicted to induce steps on the current-voltage characteristic at voltages that are multiples of $\frac{1}{2}(hf/2e)$. Experimentally, steps are observed only at multiples of $hf/2e$, suggesting that s-wave pairing is present in YBCO; however, the simultaneous presence of d-wave pairing is by no means ruled out.

Phase-sensitive spectroscopy is used to characterize fully the complex resistivity tensor of YBa{sub 2}Cu{sub 3}O{sub {ital x}} films in the mixed state, in the frequency range 100 to 500 GHz and temperature range 10 K to {ital T}{sub {ital c}}. We compare our results with the predictions of a vortex model containing three parameters: viscosity, pinning, and Magnus force. The viscosity and Magnus parameter we measure are in disagreement with theoretically predicted values. We show that the discrepancies can be explained by incorporating the effects of a highly anisotropic or {ital d}-wave gap.

The magnetic flux noise generated by films and crystals of B${\mathrm{i}}_{2}$S${\mathrm{r}}_{2}$CaC${\mathrm{u}}_{2}$ ${\mathrm{O}}_{8+y}$ and YB${\mathrm{a}}_{2}$C${\mathrm{u}}_{3}$ ${\mathrm{O}}_{7\ensuremath{-}x}$, up to 30 \ensuremath{\mu}m thick and cooled in nominally zero magnetic field, has been measured at opposing surfaces by two dc superconducting quantum interference devices. For both materials, the noise sources at the two surfaces were highly correlated at specific temperatures in a given cooldown. This result suggests that the observed vortices moved as rigid rods. At other temperatures, the noise was mostly uncorrelated, suggesting that the relevant vortices were pinned at more than one point along their length.

Coherent time-domain spectroscopy was used to measure the complex transmission tensor of several $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin films in magnetic fields up to 6 T at temperatures from 10 to 200 K. The complex conductivity tensor was determined from transmission measurements in the frequency range 150-800 GHz without the need for Kramers-Kronig analysis. Both the real and imaginary parts of ${\ensuremath{\sigma}}_{\mathrm{xy}}$ were found to peak near 40 K, exceeding their normal state values by more than a factor of 10. This behavior is ascribed to the Hall effect of quasiparticles in the superconducting state.

Using scanning tunneling microscopy (STM), we studied 1[ital T]-TaS[sub 2] in all four of its charge-density-wave (CDW) supporting phases over the temperature range 360--143 K. Special attention was given to the search for discommensurate structures and the distinguishing of true CDW discommensurations and domains from apparent discommensurations and domains formed by interference between the CDW and the atomic lattice. In the lowest-temperature commensurate ([ital C]) phase, we find that the CDW is in the commensurate configuration as expected. We use the [ital C] phase to investigate the effects of multiple tips and find that shifts in the apparent registration of the CDW relative to the atomic lattice result. In the nearly commensurate ([ital NC]) phase, the CDW is in a true domain structure as evidenced by satellite spots in the Fourier transforms of the STM images. In the triclinic ([ital T]) phase, the STM data indicate that the CDW is in a striped domain phase, which is significantly different from the domain model previously proposed. Finally, in the high-temperature incommensurate ([ital I]) phase, we find unexpected satellite spots in the STM Fourier transforms, suggesting that a CDW modulation is also present in this phase.

When sufficient electrical power P is dissipated in a thin metal film at millikelvin temperatures, the electrons can be driven far out of thermal equilibrium with the phonons. For uniform power dissipation in a volume \ensuremath{\Omega} we show that the electrons attain a steady-state temperature ${\mathit{T}}_{\mathit{e}}$=(P/\ensuremath{\Sigma}\ensuremath{\Omega}+${\mathit{T}}_{\mathit{p}}^{5}$${)}^{1/5}$, where ${\mathit{T}}_{\mathit{p}}$ is the phonon temperature and \ensuremath{\Sigma} is a parameter involving the electron-phonon coupling. We have used a sensitive ammeter based on a dc superconducting quantum interference device (SQUID) to measure the Nyquist current noise in thin films of AuCu as a function of P, and thus inferred ${\mathit{T}}_{\mathit{e}}$. We fitted our data to the theory with the single parameter \ensuremath{\Sigma}, and found good agreement for \ensuremath{\Sigma}=(2.4\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{9}$ ${\mathrm{Wm}}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{K}}^{\mathrm{\ensuremath{-}}5}$. When we increased the volume of the resistor by attaching a thin-film cooling fin, there was a much smaller increase in ${\mathit{T}}_{\mathit{e}}$ for a given power dissipation in the resistor, in qualitative agreement with a simple model for nonuniform heating. We also measured the flux noise in dc SQUIDs at low temperatures, and found that the white noise was limited by heating of the electrons in the resistive shunts of the Josephson junctions. We were able to reduce these effects substantially by attaching cooling fins to the shunts.

A superconducting flux qubit is inductively coupled to a Superconducting QUantum Interference Device (SQUID) magnetometer, capacitively shunted to form a 1.294-GHz resonator. The qubit-state-dependent resonator frequency is weakly probed with a microwave signal and detected with a Microstrip SQUID Amplifier. At a mean resonator occupation $\bar{n}$ = 1.5 photons, the readout visibility is increased by a factor of 4.5 over that using a cryogenic semiconductor amplifier. As $\bar{n}$ is increased from 0.008 to 0.1, no reduction in $T_1$ is observed, potentially enabling continuous monitoring of the qubit state., Comment: 5 pages, 5 figures

There is currently fundamental and technological interest in measuring and manipulating nanoscale magnets, particularly in the quantum coherent regime. To observe the dynamics of such systems one requires a magnetometer with not only exceptional sensitivity but also high gain, wide bandwidth, and low backaction. We demonstrate a dispersive magnetometer consisting of a two-junction superconducting quantum interference device (SQUID) in parallel with an integrated, lumped-element capacitor. Input flux signals are encoded as a phase modulation of the microwave drive tone applied to the magnetometer, resulting in a single quadrature voltage signal. For strong drive power, the nonlinearity of the resonator results in quantum limited, phase sensitive parametric amplification of this signal, which improves flux sensitivity at the expense of bandwidth. Depending on the drive parameters, the device performance ranges from an effective flux noise of 0.29 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}$Hz${}^{\ensuremath{-}1/2}$ and 20 MHz of signal bandwidth to a noise of 0.14 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}$Hz${}^{\ensuremath{-}1/2}$ and a bandwidth of 0.6 MHz. These results are in excellent agreement with our theoretical model.

The observation of magnetic flux noise in superconducting thin-film flux transformers of YBa[sub 2]Cu[sub 3]O[sub 7[minus][ital x]] enables us to measure a very small, frequency-dependent resistance [ital R][sub [ital v]]([ital f]) in the films, caused by vortex motion. In static magnetic fields below 10[sup [minus]6] T and at voltages down to 10[sup [minus]20] V Hz[sup [minus]1/2],[ital R][sub [ital v]] is proportional to the frequency [ital f] at which the measurement is made, is approximately independent of temperature, and decreases with increasing static current in the transformer. This behavior cannot be explained by certain currently accepted models of dissipation arising from vortex motion, but is consistent with a model in which independent vortices hop between two potential wells in a confined region.

Hidden U(1) gauge symmetries are common to many extensions of the standard model proposed to explain dark matter. The hidden gauge vector bosons of such extensions may mix kinetically with standard model photons, providing a means for electromagnetic power to pass through conducting barriers. The axion dark matter experiment detector was used to search for hidden vector bosons originating in an emitter cavity driven with microwave power. We exclude hidden vector bosons with kinetic couplings $\ensuremath{\chi}g3.48\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ for masses less than $3\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}$. This limit represents an improvement of more than 2 orders of magnitude in sensitivity relative to previous cavity experiments.

We have performed scanning tunneling microscopy of the blue bronzes ${\mathrm{K}}_{0.30}$${\mathrm{MoO}}_{3}$ and ${\mathrm{Rb}}_{0.30}$${\mathrm{MoO}}_{3}$ both above and below the charge-density-wave (CDW) transition temperature, ${\mathit{T}}_{\mathit{P}}$=180 K. We were able to image the Mo-O octahedra on the crystal surface at 295, 143, and 77 K. Below ${\mathit{T}}_{\mathit{P}}$, we were not able to image any additional superstructure due to the CDW, suggesting a relatively small CDW amplitude at the sample surface. Furthermore, the lattice images that we obtained below ${\mathit{T}}_{\mathit{P}}$ are unaffected by the sliding of the CDW.

The magnetic-flux noise generated by a patterned film of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$ is reversibly suppressed by the application of a supercurrent. The total noise power decreases by an order of magnitude, in quantitative agreement with a model involving thermally activated vortex hopping between pairs of pinning sites of nearly equal pinning energy. The model yields a force constant of 6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ N/m for a vortex at a typical pinning site, and a hopping distance which increases with temperature from 13 nm at 4.2 K to 64 nm at 60 K. The number density of vortices is at least 0.02 \ensuremath{\mu}${\mathrm{m}}^{\mathrm{\ensuremath{-}}2}$, even in a magnetic field of less than 1 \ensuremath{\mu}T.

The domain structure in the nearly commensurate charge-density-wave phase of 1T-${\mathrm{TaS}}_{2}$ has been experimentally determined. Fourier-transformed scanning-tunneling-microscopy images display fine satellite structure in excellent agreement with that predicted by the amplitude- and phase-domain model of Nakanishi and Shiba. Earlier analyses of scanning-tunneling- and atomic-force-microscopy images of 1T-${\mathrm{TaS}}_{2}$ in the nearly commensurate phase are shown to be inadequate for the unambiguous identification and characterization of domain structure.

We investigate the theory of resonant tunneling of the phase difference {phi} in current-biased, small-capacitance Josephson junctions. Tunneling of {phi} occurs between states localized in adjacent wells of the tilted cosine ( washboard'') potential when the states are nearly degenerate, and leads to unique junction behavior. Most notable are the presence of voltage spikes along the supercurrent branch of the current-voltage characteristic, the reduction of the bias current at which the junction switches to the free-running state to a value well below the thermodynamic value, and peaks in the distribution of rates at which this switching occurs as a function of bias current. For a range of junction parameters, we estimate the magnitude and width of the first (lowest bias current) voltage spike and the rate of switching to the free-running state in the zero temperature, low damping limit. Experimentally, the most readily observable signature of resonant tunneling should be the characteristic peaks in the switching distribution.

L'aimantation locale des composes YBa 2 Cu 3 O 7−x et Bi 2 Sr 2 CaCu 2 O 8+y presente des signaux telegraphiques aleatoires sur des intervalles etroits de temperature. On pense que ces signaux viennent des sauts actives thermiquement des vortex magnetiques uniques entre deux sites d'ancrage

The spectral density of the magnetic flux noise measured in high-temperature superconductors in low magnetic fields scales approximately as the inverse of the frequency and increases with temperature. We use the temperature and frequency dependence of the noise to determine the pinning energies of individual flux vortices in thermal equilibrium. The distribution of pinning energies peaks below 0.1 eV in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ and near 0.2 eV in ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$. The noise power is proportional to the ambient magnetic field, indicating that the vortex motion is uncorrelated.

We propose a model for 1/f flux noise in superconducting devices (f is frequency). The noise is generated by the magnetic moments of electrons in defect states which they occupy for a wide distribution of times before escaping. A trapped electron occupies one of the two Kramers-degenerate ground states, between which the transition rate is negligible at low temperature. As a result, the magnetic moment orientation is locked. Simulations of the noise produced by randomly oriented defects with a density of 5x10(17) m(-2) yield 1/f noise magnitudes in good agreement with experiments.

The three-junction flux qubit (quantum bit) consists of three Josephson junctions connected in series on a superconducting loop. We present a numerical treatment of this device for the general case in which the ratio ${\ensuremath{\beta}}_{Q}$ of the geometrical inductance of the loop to the kinetic inductance of the Josephson junctions is not necessarily negligible. Relatively large geometric inductances allow the flux through each qubit to be controlled independently with on-chip bias lines, an essential consideration for scalability. We derive the three-dimensional potential in terms of the macroscopic degrees of freedom, and include the possible effects of asymmetry among the junctions and of stray capacitance associated with them. To find solutions of the Hamiltonian, we use basis functions consisting of the product of two plane wave states and a harmonic oscillator eigenfunction to compute the energy levels and eigenfunctions of the qubit numerically. We present calculated energy levels for the relevant range of ${\ensuremath{\beta}}_{Q}$. As ${\ensuremath{\beta}}_{Q}$ is increased beyond $0.5$, the tunnel splitting between the ground and first excited states decreases rapidly, and the device becomes progressively less useful as a qubit.

We present a theory for a finite-length superconducting nanowire coupled to an environment. We show that in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to explain the "anti-proximity effect" recently seen by Tian et. al. in Zinc nanowires., Comment: 4 pages, 3 figures

We report measurements on two superconducting flux qubits coupled to a readout Superconducting QUantum Interference Device (SQUID). Two on-chip flux bias lines allow independent flux control of any two of the three elements, as illustrated by a two-dimensional qubit flux map. The application of microwaves yields a frequency-flux dispersion curve for 1- and 2-photon driving of the single-qubit excited state, and coherent manipulation of the single-qubit state results in Rabi oscillations and Ramsey fringes. This architecture should be scalable to many qubits and SQUIDs on a single chip., 5 pages, 4 figures, higher quality figures available upon request. Submitted to PRL

Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance ${C}_{s}$ and resistance ${R}_{s}$ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.

We have built and operated a large-scale axion detector, based on a method originally proposed by Sikivie, to search for halo axions. The apparatus consists of a cylindrical tunable high-Q microwave cavity threaded axially by a static high magnetic field. This field stimulates axions that enter the cavity to convert into single microwave photons. The conversion is resonantly enhanced when the cavity resonant frequency is near the axion rest mass energy. The experiment is cooled to 1.5 K and the electromagnetic power spectrum emitted by the cavity is measured by an ultra-low-noise microwave receiver. The axion would be detected as excess power in a narrow line within the cavity resonance. The apparatus has achieved a power sensitivity better than ${10}^{\ensuremath{-}23} \mathrm{W}$ in the mass range $2.9--3.3 \ensuremath{\mu}\mathrm{eV}.$ For the first time the rf cavity technique has explored plausible axion models, assuming axions make up a significant fraction of the local halo density. The experiment continues to operate and will explore a large part of the mass in the range of $1--10 \ensuremath{\mu}\mathrm{eV}$ in the near future. An upgrade of the experiment is planned with dc superconducting quantum interference device microwave amplifiers operating at a lower physical temperature. This next generation detector would be sensitive to even more weakly coupled axions contributing only fractionally to the local halo density.

We measure the effect of dissipation on the minimum zero-bias conductance, G{sup min}{sub 0} , of a superconducting single electron transistor (sSET) capacitively coupled to a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. Depleting the 2DEG with a back gate voltage decreases the dissipation experienced by the sSET in situ. We find that G{sup min}{sub 0} increases as the dissipation is increased or the temperature is reduced; the functional forms of these dependences are compared with the model of Wilhelm etal.in which the leads coupled to the sSET are represented by lossy transmission lines.

A reply to the comment on flux pinning energies in high-{ital T}{sub {ital c}} superconductors is given. The extraction of flux-pinning energies from different types of measurements remains a highly contorversial issues. (AIP)

Spontaneous emission from nuclear spins is measured for the first time, we believe. This is possible because of the use of a low-noise SQUID amplifier with noise temperature (~0.2 K) less than that of the 1.5 K helium bath. The spontaneous emission power is ~5-10% of the background circuit Nyquist noise, which corresponds to the ratio of the effective spin resistance Rs (proportional to the nuclear susceptibility) and circuit resistance R. Although only one spin flip occurs per 108 yr due to spontaneous omission, the effect is magnified, because all 1022 spins in the sample contribute independent of the temperature. This technique implies that spectra of spins can be measured without the requirement of a net polarization and might be useful for samples where spin lattice relaxation times are impracticaily long. Radiation damping terms which are added to the Bloch equations allow for spin noise analysis of power flow between the spin system and cavity. The equivalence is obtained of predictions of Nyquist's theorem at all spin temperatures Ts and bath temperatures T in conformity with the predictions of the Einstein detailed balance equation for spontaneous emission. The model of a macroscopic spin pendulum applies where fluctuation through a mean square angle 〈θ2〉 from magnetization alignment along the polarizing field accounts for coupling of the fluctuating spins to the single-cavity mode. Several aspects of the model for spin noise analysis are applicable to inverted two-level systems.

The kinetic equation is used to compute the elastic and inelastic quasiparticle branch mixing rates for a superconducting film into which quasiparticles are injected via a tunnel barrier from a second superconducting film. Representative graphs are presented of the steady-state quasiparticle distribution, the quasiparticle charge imbalance ${Q}^{*}$ versus injection current, the charge relaxation rate ${\ensuremath{\tau}}_{{Q}^{*}}^{\ensuremath{-}1}$ vs $\frac{\ensuremath{\Delta}}{{k}_{B}{T}_{c}}$ for several values of elastic scattering rate, and the quasiparticle branch relaxation rate ${\ensuremath{\tau}}_{Q}^{\ensuremath{-}1}$ as a function of energy. The quasiparticle potential developed in the injection film is related to ${\ensuremath{\tau}}_{Q}^{\ensuremath{-}1}$ and thence to ${\ensuremath{\tau}}_{0}^{\ensuremath{-}1}$ a characteristic electron-phonon scattering time. Detailed measurements of ${\ensuremath{\tau}}_{Q}$ are reported for films of superconducting A1, some of which were doped with oxygen to give a range of transition temperatures from 1.2 to 2.1 K. From the dependence of ${\ensuremath{\tau}}_{{Q}^{*}}^{\ensuremath{-}1}$ on $\frac{\ensuremath{\Delta}}{{k}_{B}{T}_{c}}$, values are deduced for the gap anisotropy of the films. In the cleanest samples, ${\ensuremath{\tau}}_{0}=0.10\ifmmode\pm\else\textpm\fi{}0.02$ \ensuremath{\mu} sec, a value that is in good agreement with energy-gap relaxation and $2\ensuremath{\Delta}$- phonon (phonons of energy $\ensuremath{\gtrsim}2\ensuremath{\Delta}$) mean-free-path measurements, but a factor of about 4 smaller than that obtained from recombination time measurements and theoretical calculations. The value of ${\ensuremath{\tau}}_{0}^{\ensuremath{-}1}$ in the A1 films increases with the transition temperature ${T}_{c}$ as ${T}_{c}^{5}$ or ${T}_{c}^{6}$, instead of ${T}_{c}^{3}$ as predicted by simple theory. It is suggested that the rapid increase of ${\ensuremath{\tau}}_{0}^{\ensuremath{-}1}$ with ${T}_{c}$ may arise from either a strong dependence of ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ on ${T}_{c}$ or from a small concentration of magnetic impurities.

The resistances of superconductor---normal-metal---superconductor sandwiches have been measured in which the mean free path of the superconductor was greater than or comparable with the coherence length. Below about 0.5 ${T}_{c}$, the resistance was nearly independent of temperature and, to within the experimental error, equal to the estimated resistance of the normal layer, indicating that there was relatively little interface contamination. At temperatures above about 0.9 ${T}_{c}$ the resistance rose rapidly as the temperature was increased towards ${T}_{c}$. A theory for this rise, based on the normal metal-insulator-superconductor tunneling theory of Tinkham and Clarke, is used to calculate the quasiparticle charge imbalance, ${Q}^{*}$, injected into the superconductor from the normal layer. The resultant additional boundary voltage per unit current is expressed as a boundary resistance ${R}_{b}=\frac{Z(T){(D{\ensuremath{\tau}}_{{Q}^{*}})}^{\frac{1}{2}}{\ensuremath{\rho}}_{S}}{A}$, where $Z(T)$ is a universal function of temperature, and $D$, ${\ensuremath{\tau}}_{{Q}^{*}}$, ${\ensuremath{\rho}}_{S}$, and $A$ are the electron diffusion coefficient, the charge relaxation time, the normal-state resistivity, and the cross-section area of the superconductor. Above 0.9 ${T}_{c}$, the data are an excellent fit to the theory if one takes ${\ensuremath{\tau}}_{{Q}^{*}}=\frac{4{k}_{B}T{\ensuremath{\tau}}_{E=0}({T}_{c})}{\ensuremath{\pi}{\ensuremath{\Delta}}_{\ensuremath{\infty}}(T)}$, where ${\ensuremath{\tau}}_{E=0}({T}_{c})$ is the inelastic-scattering time at the Fermi surface at ${T}_{c}$, and ${\ensuremath{\Delta}}_{\ensuremath{\infty}}(T)$ is the energy gap far from the interface. The inferred values of ${\ensuremath{\tau}}_{E=0}({T}_{c})$ in ${\mathrm{Pb}}_{0.99}$${\mathrm{Bi}}_{0.01}$, Sn, ${\mathrm{Sn}}_{0.99}$${\mathrm{In}}_{0.01}$, and In, 0.25 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ s, 2.6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ s, 1.1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ s, and 1.1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ s, respectively, are generally in good agreement with the computed values of Kaplan et al.

The interrelationship of ${\ensuremath{\tau}}_{Q}$,${\ensuremath{\tau}}_{Q}^{*}$, and ${\ensuremath{\tau}}_{R}$, all of which have been used by various authors to describe the relaxation of branch imbalance, is critically reviewed with emphasis on the tractable case of disequilibrium generated by low-voltage tunnel injection and on the physical basis for the differences among the various times.

A pair-quasiparticle potential difference arising from a quasiparticle charge imbalance has been observed in superconducting tin films along which there exist both a supercurrent, $I$, and a temperature gradient, $\ensuremath{\nabla}T$. The voltage is proportional to $I\ensuremath{\nabla}T$ at a given temperature, in agreement with the prediction of Pethick and Smith, and diverges as ${(1\ensuremath{-}\frac{T}{{T}_{c}})}^{\ensuremath{-}1}$ for given values of $I$ and $\ensuremath{\nabla}T$.

We demonstrate that surface deformation mediated by contamination plays a major role in images of graphite obtained by a scanning tunneling microscope in air. Atomic resolution has been obtained with the surface compressed by as much as 100 \AA{}, where abnormally high atomic corrugations, up to 24 \AA{}, are observed. Calculation of the deformation profile reveals that the force necessary to deform the surface must be spread over several thousand square angstroms. The measured deformation is negligible in vacuum with a clean sample and tip, and the corrugation is 0.9 \AA{}.

Nuclear-quadrupole-induced electric signals are measured as a new resonance response mechanism that is the reciprocal of the Stark effect in magnetic resonance. In single crystals that have noncentrosymmetry with respect to the sites of precessing nuclear-quadrupole moments, the electronic polarizability of atoms and chemical bonds on opposite sides of the nuclear-quadrupole moment is not the same. The oscillating electric field produced by the quadrupole moment induces a net electric dipole moment in its neighboring electronic environment. The coherent summation of these dipole moments over the Boltzmann distribution of the nuclear ensemble produces an oscillating macroscopic electric dipole moment. The sample is placed between the plates of a capacitor that is tuned with an inductance to the nuclear precession frequency. Coherent nuclear precession is initiated following a rf magnetic field pulse that tips the nuclear spins into the precession mode. The voltage signal from the capacitor gives rise to an oscillating current in the series circuit and magnetic flux in the inductor. Stray magnetic induction pickup signals are balanced out. The flux is coupled to a dc superconducting quantum interference device (SQUID), which produces a voltage output at the nuclear-quadrupole resonance frequency of \ensuremath{\sim}30 MHz for $^{35}\mathrm{Cl}$ nuclei in ${\mathrm{NaClO}}_{3}$ at 4.2 K. The $^{35}\mathrm{Cl}$ nucleus induces electric dipole moments in nearby oxygen atoms bonded to the Cl atom. Measured free-precession electric signals are compared to the predictions of a point-oxygen-atom polarizability model applied to the Cl---O bond. The technique is sensitive to chirality and to bond angles.

Al - ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ - Al - ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ - Al tunnel junctions have been used to induce and detect enhancements of up to 40% in the energy gap of superconducting aluminum. Quasiparticles are extracted from the middle aluminum film through the first tunnel junction into an aluminum film with a larger energy gap, and the gap enhancement in the middle film is measured from the characteristics of the second tunnel junction. A theory developed for the enhancement is in good agreement with the experimental results for bias voltages below the difference of the energy gaps, but overestimates the enhancement at higher voltages. This discrepancy is believed to arise from the effects of nonequilibrium phonons, which are neglected in the calculation. The low-voltage data are consistent with a value of about 80 ns for the characteristic electron-phonon scattering time, ${\ensuremath{\tau}}_{0}$, in aluminum films with an average transition temperature of 1.34 K.

The charge-imbalance relaxation rate, 1/F*{sub T{sub Q*}}, has been measured in dirty superconducting AlEr films in which Er is a pair-breaking magnetic impurity that induces charge relaxation through elastic exchange scattering. Measurements were made in the range 0.1 {approx}< {Delta}(T)/k{sub B}T{sub c} {approx}< 1.4 for Er concentrations varying from 21 to 1660 at. ppm that produced estimated exchange scattering rates, {tau}{sub S}{sup -1}, from about 10{sup 9} sec{sup -1} to 5 x 10{sup 10} sec{sup -1}. Measured values of 1/F*{sub T{sub Q*}} were in good agreement with the Schmid-Schoen expression, 1/F*{sub T{sub Q*}}=({pi}{Delta}/4k{sub B}T{sub c}{tau}{sub E}) x (1+2{tau}{sub E}/{tau}{sub S}){sup 1/2}, for {Delta}/k{sub B}T{sub c} {approx}< 0.8, where {tau}{sub E}{sup -1} is the electron-phonon scattering rate estimated from the measured transition temperature. For larger values of {Delta}/k{sub B}T{sub c}, the relaxation rate increased less rapidly with {Delta}. The appropriate Boltzmann equation was solved on a computer to obtain values for 1/F*{sub T{sub Q*}} in the range 0.5 {approx}< T/T{sub c} {approx}< 0.999999. The computed values of 1/F*{sub T{sub Q*}} agreed with several analytic expressions valid for {Delta}/k{sub B}T{sub c} << 1, but not with the experimental data: The computed curves increased more rapidly than linearly with {Delta}/k{sub B}T{sub c} nearmore » T{sub c}, and the shape of the 1/F*{sub T{sub Q*}} vs {Delta}/k{sub B}T{sub c} curves was qualitatively different. This discrepancy suggests that either the generally accepted expression for exchange charge relaxation is incorrect, or that the Boltzmann equation is inappropriate for these calculations.« less

We report the first observation of quantized energy levels for a macroscopic variable, namely the phase difference across a current-biased Josephson junction in its zero-voltage state. The position of these energy levels is in quantitative agreement with a quantum mechanical calculation based on parameters of the junction that are measured in the classical regime.

The observed dependence of the $\frac{1}{f}$ noise in metal films on the temperature coefficient of resistance and on sample volume, and the observation of frequency-dependent spatial correlations of the noise, suggest the noise is due to a thermal-diffusion mechanism. The assumption of a spectrum for the intrinsic temperature fluctuations with an explicit $\frac{1}{f}$ region, and the condition $〈{(\ensuremath{\Delta}T)}^{2}〉=\frac{k{T}^{2}}{{C}_{V}}$, yield quantitative predictions of the noise power in excellent agreement with experiment.

The spectral density of the voltage noise has been measured in current-biased resistively shunted Josephson junctions in which quantum corrections to the noise are expected to be important. The experimental data are in excellent agreement with theoretical pretions, demonstrating clearly the contribution of zero-point fluctuations that are generated in the shunt at frequencies near the Josephson frequency and mixed down to the measurement frequency.

Al-Al/sub 2/O/sub 3/-Al tunnel junctions were used to measure large increases in the energy gap of superconducting aluminum films in the presence of 10-GHz microwave radiation. When the microwave power was increased at constant temperature, enchancement occurred only for temperatures at which twice the equilibrium energy only for temperatures at which twice the equilibrium energy gap exceeded the photon energy. When the temperature was increased at constant microwave power, enhancement was observed at higher temperatures.

The quasiparticle transport current induced in a superconducting aluminum film by a temperature gradient has been measured by means of the spatially decaying charge imbalance generated near the end of the sample where the current is divergent. The magnitude and decay length of the charge imbalance are in good agreement with the predictions of a simple model that takes into account the nonuniformity of the temperature gradient. The inferred value of the thermopower in the superconducting state agrees reasonably well with the value measured in the normal state. Measurements of the decay length of charge imbalance induced by current injection yield a value of the inelastic relaxation time ${\ensuremath{\tau}}_{E}$ of about 2 ns. This value is substantially smaller than that obtained from other measurements for reasons that are not known.