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Exploiting multiple modes in a quantum acoustic device could enable applications in quantum information in a hardware-efficient setup, including quantum simulation in a synthetic dimension and continuous-variable quantum computing with cluster states.We develop a multimode surface acoustic wave (SAW) resonator with a superconducting quantum interference device (SQUID) integrated in one of the Bragg reflectors. The interaction with the SQUID-shunted mirror gives rise to coupling between the more than 20 accessible resonator modes. We exploit this coupling to demonstrate two-mode squeezing of SAW phonons, as well as four-mode multipartite entanglement. Our results open avenues for continuous-variable quantum computing in a compact hybrid quantum system.

We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, $k_B T \ll \hbar\omega$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $\omega/2\pi \sim 5\,$GHz, when the resonator was driven by a current at $3\omega$ with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-shifted by $120^\circ$. The downconversion from $3\omega$ to $\omega$ is strongly enhanced by resonant excitation of the second mode of the resonator, and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.

We have observed energy level quantization in an all high critical temperature superconductor d-wave Josephson junction. From the measurements we have also extracted the quality factor Q of the junction which is of the order of 40. These results indicate that the role of dissipation mechanisms in high temperature superconductors has to be revised, and may also have consequences for the class of solid state “quiet” quantum bit with longer coherence time.

We demonstrate the operation of a differential single Cooper-pair box, a charge qubit consisting of two aluminum islands, isolated from ground, coupled by a pair of small-area Josephson junctions. We have tested four devices, all of which show evidence of quasiparticle poisoning. The devices are characterized with microwave spectroscopy and temperature dependence studies.

We propose and demonstrate a new read-out technique for a superconducting qubit by dispersively coupling it to a Josephson parametric oscillator. We employ a tunable quarter-wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with $185\pm15$ photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot readout performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing., Comment: 11 pages, 5 figures

There are several dualities between Josephson and single charge tunneling, being conjugate phenomena, where either the phase (flux) or the number (charge) states are well determined while the complementary entity (number, phase) is undetermined. A zero voltage, phase-dependent current flows in the Josephson junction up to a critical current value while no current flows in the Coulomb blockade region, up to a threshold voltage, in a single charge element having high resistance and small Josephson coupling. The dual of the extremely flux sensitive DC superconducting quantum interference device (SQUID) is the single charge transistor (SET). It has an outstanding charge sensitivity but its high impedance severely limits its bandwidth. A superconducting radio frequency version, RF-SET, is related to the common RF-SQUID and its bandwidth is improved orders of magnitude compared to the usual SET. A charge sensitivity of the order of 3×10 −6 e/√Hz has been demonstrated. It can be used, e.g., as a read out of the charge of a quantum “qu-bit”. The latter is, in this case, based upon the charge state of a small island, being a superposition of a charge or not a charge, which can be compared with a flux based qu-bit where currents go clock- or anti-clockwise in a SQUID loop.

We show that the physics underlying the dynamical Casimir effect may generate multipartite quantum correlations. To achieve it, we propose a circuit quantum electrodynamics (cQED) scenario involving superconducting quantum interference devices (SQUIDs), cavities, and superconducting qubits, also called artificial atoms. Our results predict the generation of highly entangled states for two and three superconducting qubits in different geometric configurations with realistic parameters. This proposal paves the way for a scalable method of multipartite entanglement generation in cavity networks through dynamical Casimir physics., Improved version and references added. Accepted for publication in Physical Review Letters

Two separate research topics are discussed. We discuss noise measurements of single electron transistors and the gain dependence of the noise. We will also describe the fabrication and preliminary measurements on several different superconductor/two-dimensional electron gas/superconductor structures.

We report on the experimental study of the phase periodic resistance oscillations in an Andreev-type interferometer consisting of a mesoscopic normal metal ring (Ag) connected to a superconductor (Al). We observe a spectacular modulation of the oscillations due to an interplay of the phase transfer from the superconducting condensate to quasiparticles and interference phenomena in the normal ring. We discuss the results within the framework of recently developed theory of the long-range proximity effect.

From intrinsic tunneling spectroscopy, superconducting- and pseudo-gaps could be separated within a wide range of temperatures. We have found that the two gaps have different temperature ( T ) and magnetic field ( H ) dependencies. The superconducting gap closes both as T → T c and H → H c2 , while the pseudo-gap does not change neither with T , or H . This would speak in favor of two coexisting phenomena and against the precursor superconductivity scenario of the pseudo-gap.

We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. We fabricate and investigate devices with suspended gate-controlled nanowires and nonsuspended nanowires, with a broad range of lengths and normal-state resistances. We analyze the main features of the current-voltage characteristics: the Josephson current, excess current, and subgap current as functions of length, temperature, magnetic field, and gate voltage, and compare them with theory. The Josephson critical current for a short-length device, L = 30 nm, exhibits a record high magnitude of 800 nA at low temperature that comes close to the theoretically expected value. The critical current in all other devices is typically reduced compared to the theoretical values. The excess current is consistent with the normal resistance data and agrees well with the theory. The subgap current shows a large number of structures; some of them are identified as subharmonic gap structures generated by multiple Andreev reflection. The other structures, detected in both suspended and nonsuspended devices, have the form of voltage steps at voltages that are independent of either the superconducting gap or length of the wire. By varying the gate voltage in suspended devices, we are able to observe a crossover from typical tunneling transport at large negative gate voltage, with suppressed subgap current and negative excess current, to pronounced proximity junction behavior at large positive gate voltage, with enhanced Josephson current and subgap conductance as well as a large positive excess current., 12 pages, 15 figures

We studied a mesoscopic cross-like normal metal structure connected to two superconducting (S) and two normal (N) reservoirs. We observed the Josephson effect under unusual conditions when there is no current through one of the two S/N interfaces. The potential difference between the S reservoirs was zero unless the voltage applied between S and N reservoirs exceeded a critical value although the electric potential in the N wire connecting the superconductors varied in a nonmonotonic way. The observed effects are discussed theoretically., Comment: 5 pages, 4 figures, to be published in PRB Rapid Communication

We discuss the design for a submillimeter-wave photometer, using a combination of superconducting and single-electron devices, which would have high quantum efficiency, very low noise-equivalent powers, and eventually even submicrosecond timing resolution. The absorption of above-gap photons occurs in a small strip of superconducting Al, whose normal-state resistance can be matched efficiently to an antenna of a higher gap (Nb) superconductor. The quasiparticles produced by photon absorption are then confined via Andreev reflection, and forced to tunnel through a small SIS tunnel junction. The tunneling time is much shorter than the known (>10 /spl mu/s) quasiparticle recombination time, so collection efficiency will be high. The device sensitivity would be limited by the small subgap current in the high-quality Al/AlO/sub x//Al tunnel junction at temperatures (100 mK) well below T/sub c/. Scaling based on the larger junctions used in X-ray detector applications suggests that the total dark current can be

One-dimensional (1D) arrays of small-capacitance Josephson junctions demonstrate a sharp transition, from Josephson-like behavior to the Coulomb blockade of Cooper-pair tunneling, as the effective Josephson coupling between nearest neighbors is tuned with an externally applied magnetic field. Comparing the zero-bias resistance of three arrays with 255, 127, and 63 junctions, we observe a critical behavior where the resistance, extrapolated to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, is independent of length at a critical magnetic field. Comparison is made with a theory of this $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ quantum phase transition, which maps to the 2D classical $\mathrm{XY}$ model.

We describe the fabrication and measurement of one‐dimensional series arrays of small capacitance Josephson junctions and superconducting quantum interference devices. These arrays exhibit a Coulomb blockade of Cooper pair tunneling when the Josephson coupling energy is the order of the charging energy. The effectiveness of a resistive coaxial cable (ThermocoaxTM made by Philips) for attenuation of high frequency electromagnetic noise is demonstrated. This noise influences the measured dc current–voltage characteristic of the array, having qualitatively the same effect as raising the temperature.

We report on a successful attempt to fabricate a Coulomb blockade electrometer consisting of an ultrasmall YBa2Cu3O7−δ (YBCO) island coupled to two gold electrodes through a high-resistance native surface tunnel barrier. A third electrode placed near the island was used as an electrostatic gate. Spectra typical for tunneling into the YBCO superconductor were reproducibly measured. At temperatures below 0.5 K the low-bias conductance was suppressed by the Coulomb blockade. The blockade could be periodically varied by the gate potential. An external magnetic field of up to 5 T strongly influenced the transport via the island but without any change in the period of the Coulomb oscillations.

We have studied the superconductor-insulator (SI) phase transition for two-dimensional (2D) arrays of small Josephson junctions in a weak magnetic field. The data were analyzed within the context of the theory of the magnetic-field-tuned SI transition in 2D superconductors. We show resistance scaling curves over several orders of magnitude for the 2D arrays. The critical exponent ${\mathit{z}}_{\mathit{B}}$ is determined to be 1.05, in good agreement with the theory. Moreover, the transverse (Hall) resistance at the critical field is found to be very small in comparison to the longitudinal resistance.

A quantum coherent interface between optical and microwave photons can be used as a basic building block within a future quantum information network. The interface is envisioned as an ensemble of rare-earth ions coupled to a superconducting resonator, allowing for coherent transfer between optical and microwave photons. Towards this end, we have realized a hybrid device coupling a Er$^{3+}$ doped Y$_2$SiO$_5$ crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewdith of down to 75 MHz., Comment: 5 pages, 4 figures

In highly resistive superconducting tunnel junctions, excess subgap current is usually observed and is often attributed to microscopic "pinholes" in the tunnel barrier. We have studied the subgap current in superconductor-insulator-superconductor (SIS) and superconductor-insulator-normal-metal (SIN) junctions. In Al/AlOx/Al junctions, we observed a decrease of 2 orders of magnitude in the current upon the transition from the SIS to the SIN regime, where it then matched theory. In Al/AlOx/Cu junctions, we also observed generic features of coherent diffusive Andreev transport in a junction with a homogenous barrier. We use the quasiclassical Keldysh-Green function theory to quantify single- and two-particle tunneling and find good agreement over 2 orders of magnitude in transparency. We argue that our observations rule out pinholes as the origin of the excess current., 4 pages, 4 figures

We present measurements on hybrid single-electron turnstiles with superconducting leads contacting a normal island (SINIS). We observe Andreev tunneling of electrons influencing the current plateau characteristics of the turnstiles under radio-frequency pumping. The data is well accounted for by numerical simulations. We verify the dependence of the Andreev tunneling rate on the turnstile's charging energy. Increasing the charging energy effectively suppresses the Andreev current., 6 pages, 4 figures, 1 table Published version with various improvements to figures and text

We report on measurements of the current-voltage characteristics of ultrasmall Josephson junctions. The junctions were made of either Al or Pb alloy, and the leads connecting the junctions to the outside world were high resistance thin film microstrips fabricated on the chip very close to the junction. The high frequency impedance of these leads was sufficiently large to enable the observation in a single Josephson junction of the Coulomb blockade of Cooper pair tunneling, as well as evidence for the time correlation of Cooper pair tunneling (Bloch Oscillations).

Single charge tunnel effects have been seen in ultrasmall tunnel junctions. They include the Coulomb blockade, space and time correlation of tunnel events and the effect of the environment. This paper concentrates upon the newly found single electron (SET) and Cooper pair ('Bloch') oscillations, their implications and the criteria regarding the environment that have to be fulfilled for their observation.

We have fabricated and investigated submicron-size (0.01 and 0.04 μm 2 ) Pb-alloy single Josephson junctions attached to high-resistance thin-film NiCr or Cr leads which providethe necessary conditions for a strong charging erect. When the Josephson coupling energy is less than the charging energy, we find a novel shape of the current-voltage curves, with a Coulomb gap at small voltages, and a current peak at larger voltages. A theory based on the concept of incoherent Cooper-pair tunneling has explained the data well

The time correlation of tunneling events has been predicted to occur in ultrasmall tunnel junctions: a periodic tunneling with a frequency determined by the current f=I/e. To test the predictions, we have fabricated one-dimensional arrays of Al/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{O}}_{\mathit{y}}$/Al tunnel junctions with areas down to 0.006 \ensuremath{\mu}${\mathrm{m}}^{2}$ corresponding to capacitances of \ensuremath{\sim}0.2 fF. Each array contained between 15 and 53 junctions. Current-voltage characteristics were measured at temperatures between 0.05 and 4.2 K. We observed phase locking of single-electron-tunneling oscillations to external microwaves in the frequency range 0.7\char21{}5 GHz. The phase locking manifested itself as peaks in the differential resistance at bias currents I=nef (n=\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2), corresponding to multiples of the microwave frequency. Numerical simulations show good agreement with our experimental results.

We study the influence of dissipation on the switching current statistics of moderately damped Josephson junctions. Different types of both low- and high-${T}_{c}$ junctions with controlled damping are studied. The damping parameter of the junctions is tuned in a wide range by changing temperature, magnetic field, and gate voltage and introducing a ferromagnetic layer or in situ capacitive shunting. A paradoxical collapse of switching current fluctuations with increasing $T$ occurs in all studied junctions. The phenomenon critically depends on dissipation in the junction and is explained by the interplay of two counteracting consequences of thermal fluctuations, which, on one hand, assist in premature switching into the resistive state and, on the other hand, help in retrapping back to the superconducting state. This is one of the rare examples of anticorrelation between temperature and the amplitude of fluctuations of a physically measurable quantity.

The interface between the Al bottom contact layer and Si substrates in Al based Josephson junctions is believed to have a significant effect on the noise observed in Al based superconducting devices. We have studied the atomic structure of it by transmission electron microscopy. An amorphous layer with a thickness of ∼5 nm was found between the bottom Al electrode and HF-treated Si substrate. It results from intermixing between Al, Si, and O. We also studied the chemical bonding states among the different species using energy loss near edge structure. The observations are of importance for the understanding of the origin of decoherence mechanisms in qubits based on these junctions.

Here we present the direct observation of macroscopic quantum properties in an all high-critical-temperature superconductor d-wave Josephson junction. Although dissipation caused by low-energy excitations is expected to strongly suppress macroscopic quantum effects, we demonstrate energy level quantization in our d-wave Josephson junction. The result indicates that the role of dissipation mechanisms in high-temperature superconductors has to be revised, and it may also have consequences for the class of solid-state “quiet” quantum bits with superior coherence time.

We investigate the pheonomenon of quasiparticle poisoning in a single Cooper‐pair box (SCB). We have designed, fabricated, and tested an SCB that demonstrates a transition between poisoned and unpoisoned Coulomb staircases, depending on the speed with which the gate charge is swept. Poisoning is shown to be suppressed at moderately high sweep rates. Coulomb staircases were measured for a variety of sweep rates, and quasiparticle tunneling rates were extracted from this data.

We study thermal fluctuation phenomena in small Bi-2212 intrinsic Josephson junctions. Being able to measure switching currents of a single intrinsic junction, we observe that its statistics can be very well described by thermal activation from a periodic Josephson potential with the sinusoidal current-phase relation. This is a direct evidence for the dc-intrinsic Josephson effect and confirmation of the tunneling nature of interlayer transport in strongly anisotropic high-temperature superconductors. Furthermore, the fluctuation-free critical current, extracted from the analysis of switching current statistics, exhibits a temperature dependence typical for superconductor-insulator-superconductor tunnel junctions.

We have fabricated a Cooper-pair transistor (CPT) with parameters such that for appropriate voltage biases, the sub-gap charge transport takes place via slow tunneling of quasiparticles that link two Josephson-coupled charge manifolds. In between the quasiparticle tunneling events, the CPT behaves essentially like a single Cooper-pair box (SCB). The effective capacitance of a SCB can be defined as the derivative of the induced charge with respect to gate voltage. This capacitance has two parts, the geometric capacitance, C_geom, and the quantum capacitance C_Q. The latter is due to the level anti-crossing caused by the Josephson coupling. It depends parametrically on the gate voltage and is dual to the Josephson inductance. Furthermore, it's magnitude may be substantially larger than C_geom. We have been able to detect C_Q in our CPT, by measuring the in-phase and quadrature rf-signal reflected from a resonant circuit in which the CPT is embedded. C_Q can be used as the basis of a charge qubit readout by placing a Cooper-pair box in such a resonant circuit., Comment: 3 figures

The escape rate from the zero voltage state in a superconducting Josephson junction (JJ) is determined by the temperature, but it saturates at low temperature due to macroscopic quantum tunneling (MQT). Complications due to $d$-wave symmetry in a high temperature superconductor, like low energy quasiparticles and an unconventional current-phase relation, may influence the escape rate. We report, for the first time to our knowledge, the observation of MQT in a ${\mathrm{Y}\mathrm{B}\mathrm{a}}_{2}{\mathrm{C}\mathrm{u}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ grain boundary biepitaxial JJ. This proves that dissipation can be significantly reduced by a proper junction configuration, which is of significance for quantum coherence.

Superconductor-Ferromagnet-Superconductor (S-F-S) Josephson junctions were fabricated by making a narrow cut through a S-F double layer using direct writing by Focused Ion Beam (FIB). Due to a high resolution (spot size smaller than 10 nm) of FIB, junctions with a small separation between superconducting electrodes ($\leq$ 30 nm) can be made. Such a short distance is sufficient for achieving a considerable proximity coupling through a diluted CuNi ferromagnet. We have successfully fabricated and studied S-F-S (Nb-CuNi-Nb) and S-S'-S (Nb-Nb/CuNi-Nb) junctions. Junctions exhibit clear Fraunhofer modulation of the critical current as a function of magnetic field, indicating good uniformity of the cut. By changing the depth of the cut, junctions with the $I_c R_n$ product ranging from 0.5 mV to $\sim 1\mu $V were fabricated., Comment: 5 pages, 5 figures, presentation at EUCAS-2003, to be published in Physica C

A new four‐layer resist system was developed to fabricate small capacitance niobium tunnel junctions. Nb/AlOx/Al junctions were used to make a superconducting single electron transistor composed of two dc SQUIDs in series. The current‐voltage characteristics were measured and two types of resonant tunneling of Cooper pairs were observed at different magnetic fields.

We study analytically and numerically a problem of self-heating in small mesa structures. Our results show that the self-heating is proportional to a characteristic in-plane size of the mesa. Experimental data for small high-$T_c$ superconductor Bi2212 mesas are in qualitative agreement with our calculations. We estimate the self-heating in Bi2212 mesas with different sizes and demonstrate that the self-heating can effectively be obviated in small mesa structures., Comment: 3 pages, 2 figures. In the 2-nd version a misprint in the expression for self-heating was correcter

We have studied niobium superconducting thin wires deposited onto a SrTiO$_{3}$ substrate. By measuring the reflection coefficient of the wires, resonances are observed in the superconducting state in the 130 MHz to 4 GHz range. They are interpreted as standing wave resonances of one-dimensional plasma modes propagating along the superconducting wire. The experimental dispersion law, $\omega$ versus $q$, presents a linear dependence over the entire wave vector range. The modes are softened as the temperature increases close the superconducting transition temperature. Very good agreement are observed between our data and the dispersion relation predicted by Kulik and Mooij and Sch\"on., Comment: Submitted to Physical review Letters

We present intrinsic tunneling spectroscopy measurements on small Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ mesas. The tunnel conductance curves show both sharp peaks at the superconducting gap voltage and broad humps representing the $c$-axis pseudo-gap. The superconducting gap vanishes at $T_c$, while the pseudo-gap exists both above and below $T_c$. Our observation implies that the superconducting and pseudo-gaps represent different coexisting phenomena., Comment: 5 pages, 4 figures

We measure the resistance of a normal mesoscopic sample with two Superconducting mirrors and find two regimes with qualitatively different behavior. At temperatures below 90 mK peaks in the conductance were found when the phase difference between the two superconductors is an odd multiple of rr. The peak heights increase with decreasing temperature. Above 100 mK the observed peaks give way to dips in the conductance. While the high-temperature behavior can be explained in terms of the thermal effect [Phys. Rev. Lett, 76, 823 (1996)], we propose that the low-temperature behavior is: a manifestation of resonant transmission of low-energy quasiparticles through Andreev states. [S0163-1829(99)11641-2].

The conductance (G) of mirror-symmetric, disordered normal (N) metal mesoscopic structures with two interfaces to superconductors (S) has been studied experimentally with applied condensate phase differences Delta phi between the N/S interfaces. At Delta phi = 2n pi(n = 0,1,2,3,...) the conductance showed reentrance to the normal state below the temperature corresponding to the Thouless energy. The current-voltage characteristics were found to be: strongly nonlinear even at distances between the N/S interfaces largely exceeding the normal-metal coherence length. An influence of superconductors almost completely disappeared at Delta phi = (2n + 1) pi where the structures showed normal behavior. Calculations based on a quasiclassical theory have been performed offering a quantitative explanation of such a phase-periodic reentrance. The value of the superconducting gap Delta(eff) at the Ag/Al interface has been obtained. We find that Delta(eff)(T,V-->0) = beta .Delta(BCS)(T) with beta = 0.2 independent of temperature in the temperature interval of 0.1 K < T < 1.6 K; Delta(BCS)(T) is the BCS gap vs T function in Al. [S0163-1829(98)01746-9].

The charging energy is important for a mesoscopic body with small capacitance to the environment. Connecting the small island via low capacitance, high resistance tunnel junctions, the current through the resulting structure will depend upon the charge of the island - charge that can be applied via a gate electrode. For a normal metal island, the current varies periodically with the charge; the periodicity is the electron charge e. If the island is superconducting, the period, e or 2e, depends upon whether the superconducting energy gap is less than or larger than the charging energy. This parity effect can be used to study possible nodes in the gap function of a high-Tc superconductor.

An investigation was made of conductance oscillations in normal metal mesoscopic structrures to which superconducting wires were attached. The oscillations were due to phase transfer from the superconducting condensate to normal electrons via Andreev reflections at the normal metal/superconductor interfaces. The phase difference between the interfaces was controlled in a wide range by varying a sub-critical current through the superconductor and, alternatively, by applied magnetic field. This technique may be used to measure phase gradients in superconductors directly, or to control dissipative currents by a non-dissipative supercurrent. Drastic difference was found between the spectra of oscillations in the structures with normal rings and the structures with normal cross-like conductors.

Several of the characteristic and interesting single charge tunneling effects have been observed in ID arrays of tunnel junctions, i. e., in series coupled arrays of many, closely spaced, ultrasmall junctions. For example, the time correlation of tunnel events was first observed in such an array. The interpretation of the results obtained with an array may be complicated as compared to a single junction, but the additional degrees of freedom for an array, like the formation of charge “solitons”, may be of advantage in developing the single charge effects and, in particular, for applications of these effects. One of the advantages of series coupled junctions is that it is easier to fabricate high resistance tunnel junctions closely connected to the junction under study than high resistance conventional resistors.

We have observed very low-energy collective modes in a thin superconducting niobium wire below Tc. The extracted dispersion relation ωp(q) follows a quasi-linear q-dependence which is very well described by the 1D plasma dispersion.

We describe the transport properties of 2d arrays of aluminium–aluminium oxide–aluminium tunnel junctions. The dependence of these properties on temperature and external magnetic field is examined. The arrays have been fabricated on oxidized silicon substrates using e-beam lithography and shadow evaporation. By altering the fabrication parameters used we are able to control the ratio between the charging energy and the Josephson coupling energy and hence the dynamics of the arrays. The various phenomena exhibited by these arrays, such as a magnetic field tuned superconductor–insulator transitions, are discussed.

We have measured the Hall resistance in two-dimensional arrays of ultrasmall aluminium Josephson junctions. We found that the Hall resistance was periodical with respect to an external magnetic fie ...

Excess current peaks in the IV curves of SIS Josephson junctions have been observed by some groups [1–3]. These peaks have the shape of a resonance as a function of voltage. The resonances appear in the subgap regime of the junctions and the subgap current (leakage current) is concealed. The positions of the resonances do not change as a magnetic field is applied to the junctions, but their amplitude decreases when the supercurrent is suppressed. We have measured the subgap current of Al/AlOx/Al junctions and we show that these resonances are due to resonant modes in the chip design which are excited by the ac-Josephson effect. We present a chip design that decreases the amplitude of the resonances to a such degree that the subgap current is quantifiable.

Tunneling of electrons in a macroscopic tunnel junction is a stochastic process governed by several parameters. Of main importance is the tunneling barrier — its width and height, intermediate states in the barrier, dielectric constant, etc — and the applied voltage. Also the density of electron states of the electrodes (including the possible effect of superconductivity) and environmental parameters like the temperature and the bias circuit come into play. However, the number of tunneling electrons per unit time is very large in a usual tunnel junction and we need not care about single tunneling events. Modern micro-electronic fabrication technology makes it possible to realize small tunnel junctions such that the tunneling of a single electron requires a significantly large energy.

We have fabricated and characterized tunable superconducting transmission line resonators. To change the resonance frequency, we modify the boundary condition at one end of the resonator through the tunable Josephson inductance of a superconducting quantum interference device. We demonstrate a large tuning range (several hundred megahertz), high quality factors (104), and that we can change the frequency of a few-photon field on a time scale orders of magnitude faster than the photon lifetime of the resonator. This demonstration has implications in a variety of applications.

We study analytically and numerically a problem of self-heating in small mesa structures. Our results show that the self-heating is proportional to a characteristic in-plane size of the mesa. Experimental data for small high-$T_c$ superconductor Bi2212 mesas are in qualitative agreement with our calculations. We estimate the self-heating in Bi2212 mesas with different sizes and demonstrate that the self-heating can effectively be obviated in small mesa structures.

We have made an experimental study of the tunnelling through a current-biased superconducting single electron transistor at temperatures down to 40 mK. The current-biased transistor consisted of two ultrasmall tunnel junctions connected in series, biased through two high-Ohmic resistors (length 10 μm) located very close to the tunnel junctions. The two-probe measurement of the current-voltage characteristic has shown a periodic modulation with a gate voltage, having two separate fundamental periods in gate charge, ΔQ1=e and ΔQ2=2e, as well as higher harmonics of these two. We have found that the amplitude of the 2e-component was enhanced as superconductivity of the electrodes was suppressed with an external magnetic field. These results are discussed within the context of a parity model.

We have measured the temperature and magnetic field dependencies of the zero bias resistance for several 2D arrays of small aluminum Josephson junctions. The normal state resistances RN of the junctions vary between 2.2 and 7.5 kω whereas the ratio of Josephson coupling energy EJ to the charging energy Ec ranges between 4.3 and 0.6, where Ec=e2/2C, C being the junction capacitance. The vortex mobility is deduced from the frustration ( i.e. the number of flux quantum per unit cell) dependence of zero bias resistance. The mobility decreases when the temperature is lowered, resulting in a decrease of resistance. Fitting the data to a simple exponential form, we find the barrier for the vortex hopping to be - aEJ, with a≈0.3. For all arrays, there exists a crossover temperature Tcr which separates the regime of thermally assisted hopping from that of quantum creep of vortices. For our samples, Tcr is close to the theoretically predicted value of ωp/2π, where ωp=(8EJEc)1/2.