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Understanding the interaction between light and matter is very relevant for fundamental studies of quantum electrodynamics and for the development of quantum technologies. The quantum Rabi model captures the physics of a single atom interacting with a single photon at all regimes of coupling strength. We report the spectroscopic observation of a resonant transition that breaks a selection rule in the quantum Rabi model, implemented using an $LC$ resonator and an artificial atom, a superconducting qubit. The eigenstates of the system consist of a superposition of bare qubit-resonator states with a relative sign. When the qubit-resonator coupling strength is negligible compared to their own frequencies, the matrix element between excited eigenstates of different sign is very small in presence of a resonator drive, establishing a sign-preserving selection rule. Here, our qubit-resonator system operates in the ultrastrong coupling regime, where the coupling strength is 10\% of the resonator frequency, allowing sign-changing transitions to be activated and, therefore, detected. This work shows that sign-changing transitions are an unambiguous, distinctive signature of systems operating in the ultrastrong coupling regime of the quantum Rabi model. These results pave the way to further studies of sign-preserving selection rules in multiqubit and multiphoton models., Comment: 14 pages, 7 figures

We investigate thin films of conducting aluminium-oxide, also known as granular aluminium, as a material for superconducting high quality, high kinetic inductance circuits. The films are deposited by an optimised reactive DC magnetron sputter process and characterised using microwave measurement techniques at milli-Kelvin temperatures. We show that, by precise control of the reactive sputter conditions, a high room temperature sheet resistance and therefore high kinetic inductance at low temperatures can be obtained. For a coplanar waveguide resonator with 1.5\,k$\Omega$ sheet resistance and a kinetic inductance fraction close to unity, we measure a quality factor in the order of 700\,000 at 20\,mK. Furthermore, we observe a sheet resistance reduction by gentle heat treatment in air. This behaviour is exploited to study the kinetic inductance change using the microwave response of a coplanar wave guide resonator. We find the correlation between the kinetic inductance and the sheet resistance to be in good agreement with theoretical expectations., Comment: 16 pages, 7 figures

We present a theoretical analysis of the selective darkening method for implementing quantum controlled-NOT (CNOT) gates. This method, which we recently proposed and demonstrated, consists of driving two transversely-coupled quantum bits (qubits) with a driving field that is resonant with one of the two qubits. For specific relative amplitudes and phases of the driving field felt by the two qubits, one of the two transitions in the degenerate pair is darkened, or in other words, becomes forbidden by effective selection rules. At these driving conditions, the evolution of the two-qubit state realizes a CNOT gate. The gate speed is found to be limited only by the coupling energy J, which is the fundamental speed limit for any entangling gate. Numerical simulations show that at gate speeds corresponding to 0.48J and 0.07J, the gate fidelity is 99% and 99.99%, respectively, and increases further for lower gate speeds. In addition, the effect of higher-lying energy levels and weak anharmonicity is studied, as well as the scalability of the method to systems of multiple qubits. We conclude that in all these respects this method is competitive with existing schemes for creating entanglement, with the added advantages of being applicable for qubits operating at fixed frequencies (either by design or for exploitation of coherence sweet-spots) and having the simplicity of microwave-only operation., Comment: 25 pages, 5 figures

The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with basis states having persistent currents of 1$ \mu$A carried by a billion electrons. By tuning the tunnel barrier between these states we see a cross-over from quantum to classical. Released from non-equilibrium, the system exhibits spontaneous coherent oscillations. For high barriers the lifetime of the states increases dramatically while the tunneling period approaches the phase coherence time and the classical regime is reached., Comment: 4 pages, 5 figures

Controlled manipulation of quantum states is central to studying natural and artificial quantum systems. If a quantum system consists of interacting sub-units, the nature of the coupling may lead to quantum levels with degenerate energy differences. This degeneracy makes frequency-selective quantum operations impossible. For the prominent group of transversely coupled two-level systems, i.e. qubits, we introduce a method to selectively suppress one transition of a degenerate pair while coherently exciting the other, effectively creating artificial selection rules. It requires driving two qubits simultaneously with the same frequency and specified relative amplitude and phase. We demonstrate our method on a pair of superconducting flux qubits. It can directly be applied to the other superconducting qubits, and to any other qubit type that allows for individual driving. Our results provide a single-pulse controlled-NOT gate for the class of transversely coupled qubits.

We present experimental results on the crosstalk between two AC-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning of the phase the measured crosstalk is 0.1 % and the correlation between the measurement outcomes is less than 0.05 %. These results show that bifurcative readout provides a reliable and generic approach for multi-partite correlation experiments., Comment: Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Applied Physics Letters and may be found at http://link.aip.org/link/?apl/96/123508

Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong back-action. We show that the back-action of a DC-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum non-demolition character, with a QND fidelity of 75 %., Comment: submitted to PRL

We measure the dispersive energy-level shift of an $LC$ resonator magnetically coupled to a superconducting qubit, which clearly shows that our system operates in the ultrastrong coupling regime. The large mutual kinetic inductance provides a coupling energy of $\approx0.82$~GHz, requiring the addition of counter-rotating-wave terms in the description of the Jaynes-Cummings model. We find a 50~MHz Bloch-Siegert shift when the qubit is in its symmetry point, fully consistent with our analytical model., Comment: Published version (4 pages, 4 figures), including supplementary material (2 pages, 4 figures)

A flux qubit biased at its symmetry point shows a minimum in the energy splitting (the gap), providing protection against flux noise. We have fabricated a qubit whose gap can be tuned fast and have coupled this qubit strongly to an LC oscillator. We show full spectroscopy of the qubit-resonator system and generate vacuum Rabi oscillations. When the gap is made equal to the oscillator frequency $\nu_{osc}$ we find the strongest qubit-resonator coupling ($g/h\sim0.1\nu_{\rm osc}$). Here being at resonance coincides with the optimal coherence of the symmetry point. Significant further increase of the coupling is possible., Comment: 4 pages, updated

We fabricated and tested a squelch circuit consisting of a copper powder filter with an embedded Josephson junction connected to ground. For small signals (squelch-ON), the small junction inductance attenuates strongly from DC to at least 1 GHz, while for higher frequencies dissipation in the copper powder increases the attenuation exponentially with frequency. For large signals (squelch-OFF) the circuit behaves as a regular metal powder filter. The measured ON/OFF ratio is larger than 50dB up to 50 MHz. This squelch can be applied in low temperature measurement and control circuitry for quantum nanostructures such as superconducting qubits and quantum dots., Comment: Corrected and completed references 6,7,8. Updated some minor details in figures

We experimentally demonstrate the in situ tunability of the minimum energy splitting (gap) of a superconducting flux qubit by means of an additional flux loop. Pulses applied via a local control line allow us to tune the gap over a range of several GHz on a nanosecond timescale. The strong flux sensitivity of the gap (up to 0.7 GHz/mPhi_0) opens up the possibility to create different types of tunable couplings that are effective at the degeneracy point of the qubit. We investigate the dependence of the relaxation time and the Rabi frequency on the qubit gap., Comment: submitted to PRL, 4 pages, 5 figures

We observed the dynamics of a superconducting flux qubit coupled to an extrinsic quantum system (EQS). The presence of the EQS is revealed by an anticrossing in the spectroscopy of the qubit. The excitation of a two-photon transition to the third excited state of the qubit-EQS system allows us to extract detailed information about the energy level structure and the coupling of the EQS. We deduce that the EQS is a two-level system, with a transverse coupling to the qubit. The transition frequency and the coupling of the EQS changed during experiments, which supports the idea that the EQS is a two-level system of microscopic origin., Comment: accepted in Physical Review B

We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum non-demolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model to characterize the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator., Comment: 4 pages, 4 figures

We consider a system composed of two qubits and a high-excitation-energy quantum object used to mediate coupling between the qubits. We treat the entire system quantum mechanically and analyze the properties of the eigenvalues and eigenstates of the total Hamiltonian. After reproducing well-known results concerning the leading term in the mediated coupling, we obtain an expression for the residual coupling between the qubits in the off state. We also analyze the entanglement between the three objects, i.e. the two qubits and the coupler, in the eigenstates of the total Hamiltonian. Although we focus on the application of our results to the recently realized parametric-coupling scheme with two qubits, we also discuss extensions of our results to harmonic-oscillator couplers, couplers that are near resonance with the qubits and multi-qubit systems. In particular, we find that certain errors that are absent for a two-qubit system arise when dealing with multi-qubit systems., Comment: 15 pages (two-column)

In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a particular system - detector interaction which preserves the eigenstates of a suitable operator of the quantum system. This leads to an ideal projective measurement. We present experiments in which we perform two consecutive measurements on a quantum two -level system, a superconducting flux qubit, by probing the hysteretic behaviour of a coupled nonlinear resonator. The large correlation between the results of the two measurements demonstrates the QND nature of the readout method. The fact that a QND measurement is possible for superconducting qubits strengthens the notion that these fabricated mesoscopic systems are to be regarded as fundamental quantum objects. Our results are also relevant for quantum information processing, where projective measurements are used for protocols like state preparation and error correction., Comment: 14 pages, 4 figures

We have studied low-frequency resistance fluctuations in shadow-evaporated Al/AlOx/Al tunnel junctions. Between 300 K and 5 K the spectral density follows a 1/f-law. Below 5 K, individual defects distort the 1/f-shape of the spectrum. The spectral density decreases linearly with temperature between 150 K and 1 K and saturates below 0.8 K. At 4.2 K, the spectral density is about two orders of magnitude lower than expected from a recent survey [D. J. Van Harlingen et al., Phys. Rev. B 70, 064510 (2004)]. Due to the saturation below 0.8 K the estimated qubit dephasing times at 100 mK are only about two times longer than calculated by Van Harlingen et al., Comment: Journal ref added, minor changes to match published version

We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87 %; of the missing 13 %, only 3 % is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by the first measurement., Comment: submitted to Phys. Rev. Lett

We have studied the dephasing of a superconducting flux-qubit coupled to a DC-SQUID based oscillator. By varying the bias conditions of both circuits we were able to tune their effective coupling strength. This allowed us to measure the effect of such a controllable and well-characterized environment on the qubit coherence. We can quantitatively account for our data with a simple model in which thermal fluctuations of the photon number in the oscillator are the limiting factor. In particular, we observe a strong reduction of the dephasing rate whenever the coupling is tuned to zero. At the optimal point we find a large spin-echo decay time of $4 \mu s$., Comment: New version of earlier paper arXiv/0507290 after in-depth rewriting

In this paper we demonstrate that, if it exists, coherent quantum phase slip is the exact dual to Josephson tunneling. We use the duality to predict kinetic capacitance and a sharp resonance in narrow wires. Biased resistively and driven at high frequency, quantum phase slip junctions should exhibit current plateaus of interest for a fundamental standard.

We propose a scheme to couple two superconducting charge or flux qubits biased at their symmetry points with unequal energy splittings. Modulating the coupling constant between two qubits at the sum or difference of their two frequencies allows to bring them into resonance in the rotating frame. Switching on and off the modulation amounts to switching on and off the coupling which can be realized at nanosecond speed. We discuss various physical implementations of this idea, and find that our scheme can lead to rapid operation of a two-qubit gate., Comment: 6 pages

In thin superconducting wires, phase-slip by thermal activation near the critical temperature is a well-known effect. It has recently become clear that phase-slip by quantum tunnelling through the energy barrier can also have a significant rate at low temperatures. In this paper it is suggested that quantum phase-slip can be used to realize a superconducting quantum bit without Josephson junctions. A loop containing a nanofabricated very thin wire is biased with an externally applied magnetic flux of half a flux quantum, resulting in two states with opposite circulating current and equal energy. Quantum phase-slip should provide coherent coupling between these two macroscopic states. Numbers are given for a wire of amorphous niobium-silicon that can be fabricated with advanced electron beam lithography., Comment: Submitted to New Journal of Physics, special issue solid state quantum information

Decoherence in superconducting qubits is known to arise because of a variety of environmental degrees of freedom. In this article, we focus on the influence of thermal fluctuations in a weakly damped circuit resonance coupled to the qubit. Because of the coupling, the qubit frequency is shifted by an amount $n \delta \nu_0$ if the resonator contains $n$ energy quanta. Thermal fluctuations induce temporal variations $n(t)$ and thus dephasing. We give an approximate formula for the qubit dephasing time as a function of $\delta \nu_0$. We discuss the specific case of a flux-qubit coupled to the plasma mode of its DC-SQUID detector. We first derive a plasma mode-qubit interaction hamiltonian which, in addition to the usual Jaynes-Cummings term, has a coupling term quadratic in the oscillator variables coming from the flux-dependence of the SQUID Josephson inductance. Our model predicts that $\delta \nu_0$ cancels in certain non-trivial bias conditions for which dephasing due to thermal fluctuations should be suppressed.

We report detailed measurements of the relaxation and dephasing time in a flux-qubit measured by a switching DC SQUID. We studied their dependence on the two important circuit bias parameters: the externally applied magnetic flux and the bias current through the SQUID in two samples. We demonstrate two complementary strategies to protect the qubit from these decoherence sources. One consists in biasing the qubit so that its resonance frequency is stationary with respect to the control parameters ({\it optimal point}) ; the second consists in {\it decoupling} the qubit from current noise by chosing a proper bias current through the SQUID. At the decoupled optimal point, we measured long spin-echo decay times of up to $4 \mu s$., Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letters

We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled DC superconducting quantum interference device (DC-SQUID). We determine the response function of the DC-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the backaction are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible., Comment: 11 pages, 3 figures; submitted to Phys. Rev. B

In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits or qubits. Single-qubit operations, direct coupling between two qubits, and the realization of a quantum gate have been reported. However, complex manipulation of entangled states - such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments or cavity quantum electrodynamics - has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system., Comment: Nature. Received 25 May; accepted 5 July 2004. doi:10.1038/nature02831

Superconducting circuits fabricated using the widely used shadow evaporation technique can contain unintended junctions which change their quantum dynamics. We discuss a superconducting flux qubit design that exploits the symmetries of a circuit to protect the qubit from unwanted coupling to the noisy environment, in which the unintended junctions can spoil the quantum coherence. We present a theoretical model based on a recently developed circuit theory for superconducting qubits and calculate relaxation and decoherence times that can be compared with existing experiments. Furthermore, the coupling of the qubit to a circuit resonance (plasmon mode) is explained in terms of the asymmetry of the circuit. Finally, possibilities for prolonging the relaxation and decoherence times of the studied superconducting qubit are proposed on the basis of the obtained results., Comment: v.2: published version; 8 pages, 12 figures; added comparison with experiment, improved discussion of T_phi

We present the implementation of a new scheme to detect the quantum state of a persistent-current qubit. It relies on the dependency of the measuring Superconducting Quantum Interference Device (SQUID) plasma frequency on the qubit state, which we detect by resonant activation. With a measurement pulse of only 5ns, we observed Rabi oscillations with high visibility (65%)., Comment: 4 pages, 4 figures, submitted to PRB Rapid Com

We present a new readout method for a superconducting flux qubit, based on the measurement of the Josephson inductance of a superconducting quantum interference device that is inductively coupled to the qubit. The intrinsic flux detection efficiency and back-action are suitable for a fast and nondestructive determination of the quantum state of the qubit, as needed for readout of multiple qubits in a quantum computer. We performed spectroscopy of a flux qubit and we measured relaxation times of the order of 80 $\mu s$., Comment: 4 pages, 4 figures; modified content, figures and references; accepted for publication in Phys. Rev. Lett

We have performed spectroscopy measurements on two coupled flux qubits. The qubits are coupled inductively, which results in a $\sigma_1^z\sigma_2^z$ interaction. By applying microwave radiation, we observe resonances due to transitions from the ground state to the first two excited states. From the position of these resonances as a function of the magnetic field applied we observe the coupling of the qubits. The coupling strength agrees well with calculations of the mutual inductance.

We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing., Comment: submitted 2 December 2002; accepted 4 February 2003

On the way to solid-state quantum computing, overcoming decoherence is the central issue. In this contribution, we discuss the modeling of decoherence of a superonducting flux qubit coupled to dissipative electronic circuitry. We discuss its impact on single qubit decoherence rates and on the performance of two-qubit gates. These results can be used for designing decoherence-optimal setups., Comment: 16 pages, 5 figures, to appear in Advances in Solid State Physics, Vol. 43 (2003)

We have measured a quantum ratchet effect for vortices moving in a quasi-one-dimensional Josephson junction array. In this solid-state device the shape of the vortex potential energy, and consequently the band structure, can be accurately designed. This band structure determines the presence or absence of the quantum ratchet effect, as observed in the presented experiments. In particular, asymmetric structures possessing only one band below the barrier do not exhibit current rectification at low temperatures and bias currents. The quantum nature of transport is also revealed in a universal/non-universal power-law dependence of the measured voltage-current characteristics for samples without/with rectification., Comment: Accepted for publication in Physical Review Letters

We discuss the relaxation and dephasing rates that result from the control and the measurement setup itself in experiments on Josephson persistent-current qubits. For control and measurement of the qubit state, the qubit is inductively coupled to electromagnetic circuitry. We show how this system can be mapped on the spin-boson model, and how the spectral density of the bosonic bath can be derived from the electromagnetic impedance that is coupled to the qubit. Part of the electromagnetic environment is a measurement apparatus (DC-SQUID), that is permanently coupled to the single quantum system that is studied. Since there is an obvious conflict between long coherence times and an efficient measurement scheme, the measurement process is analyzed in detail for different measurement schemes. We show, that the coupling of the measurement apparatus to the qubit can be controlled in situ. Parameters that can be realized in experiments today are used for a quantitative evaluation, and it is shown that the relaxation and dephasing rates that are induced by the measurement setup can be made low enough for a time-resolved study of the quantum dynamics of Josephson persistent-current qubits. Our results can be generalized as engineering rules for the read-out of related qubit systems., Comment: 15 pages, 9 figures, accepted for publication in The European Physics Journal B, necessary style files included

A phase-bias tool, based on a trapped fluxoid in a ring, is proposed and demonstrated. It can provide arbitrary phase values and is simple to fabricate. The phase bias has been realized in two superconducting quantum interference devices, where the critical current versus magnetic flux is shown to be shifted by a \pi/2 and \pi., Comment: 5 pages, including 4 figures. Submitted to APL

Several designs of inter-qubit coupling are considered. It is shown that by a combination of Josephson and capacitive coupling one can realize qubit interactions of variable spin content. Qubit arrays are discussed as models of quantum spin chains. In particular, a qubit model of the 1D quantum Ising spin chain is proposed. A realization of unpaired Majorana fermion states in this system is considered. It is shown that Majorana states are represented by spin flip excitations localized on the chain ends. Using unpaired Majorana states in qubit chains for decoherence protected quantum computing is discussed., Comment: 7 pages, 7 figures

We have used a superconducting single-electron transistor as a DC-electrometer that is strongly coupled to the metal island of another transistor. With this set-up, it is possible to directly measure the charge distribution on this island. The strong capacitive coupling was achieved by a multilayer fabrication technique that allowed us to make the coupling capacitance bigger than the junction capacitances. Simulations of this system were done using orthodox theory of single-electron tunnelling and showed excellent agreement with the measurements., Comment: 6 figures, submitted to PRB

A single-electron inverter was fabricated that switches from a high output to a low output when a fraction of an electron is added to the input. For the proper operation of the inverter, the two single-electron transistors that make up the inverter must exhibit voltage gain. Voltage gain was achieved by fabricating a combination of parallel-plate gate capacitors and small tunnel junctions in a two-layer circuit. Voltage gain of 2.6 was attained at 25 mK and remained larger than one for temperatures up to 140 mK. The temperature dependence of the gain agrees with the orthodox theory of single-electron tunneling., Comment: 3 pages, 4 figures (1 color), to be published in Appl. Phys. Lett

Decoherence of a solid state based qubit can be caused by coupling to microscopic degrees of freedom in the solid. We lay out a simple theory and use it to estimate decoherence for a recently proposed superconducting persistent current design. All considered sources of decoherence are found to be quite weak, leading to a high quality factor for this qubit., Comment: 10 pages, 1 figure, Latex/revtex.To appear in proceedings of the NATO-ASI on "Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics"; Corrections were made on Oct. 29th, 1999

The Josephson quasiparticle (JQP) cycle in a voltage-biased superconducting single-electron transistor (SSET) combines coherent Cooper pair tunneling with incoherent quasiparticle decay. We have measured the influence of current flow through an independently-biased SSET on the JQP cycle when the two SSET's have a strong mutual capacitive coupling. We find, among other effects, that the JQP current in one SSET is enhanced by the presence of a quasiparticle current in the other SSET. A simplified model of the coupled-SSET system is presented which reproduces the enhancement effect.

Josephson oscillations generated by a SQUID were used to measure photon assisted tunneling in a superconducting single electron tunneling (SET) transistor. The SQUID was fabricated only a few microns from the SET transistor. The close proximity of the generator to the SET transistor allowed for a continuous sweep of the excitation frequency from 10 GHz to 190 GHz. The amplitude of the Josephson oscillations were tuned by adjusting the flux through the SQUID loop while the frequency was independently adjusted by controlling the bias voltage across the SQUID. Current peaks which could be attributed to photon assisted tunneling in the SET transistor were observed for bias voltages less than 4*Delta/e.

We present the multilevel fabrication and measurement of a Coulomb-blockade device displaying tunable negative differential resistance (NDR). Applications for devices displaying NDR include amplification, logic, and memory circuits. Our device consists of two Al/Al$_{x}$O$_{y}$ islands that are strongly coupled by an overlap capacitor. Our measurements agree excellently with a model based on the orthodox theory of single-electron transport., Comment: 3 pages, 3 figures; submitted to APL

We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capacitance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order parameter in the system are considerable, and the vortices behave as quantum particles. Their density may be tuned by an external magnetic field, and therefore one can control the commensurability of the one-dimensional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex, and the long-range interaction between the vortices leads to the existence of a specific commensurate-incommensurate transition in a one-dimensional vortex lattice. In the commensurate phase an elementary excitation is a soliton, with energy separated from the ground state by a finite gap. This gap vanishes in the incommensurate phase. Each soliton carries a fraction of a flux quantum; the propagation of solitons leads to a finite resistance of the array. We find the dependence of the resistance activation energy on the magnetic field and parameters of the Josephson array. This energy consists of the above-mentioned gap, and also of a boundary pinning term, which is different in the commensurate and incommensurate phases. The developed theory allows us to explain quantitatively the available experimental data., Comment: 14 pages, 7 eps figures

A current due to a tunneling event that involves three times the charge of an electron was observed in the current - voltage characteristics of a superconducting single-electron tunneling transistor. In this tunnel event, a Cooper pair tunnels through one tunnel barrier simultaneously with a quasiparticle that tunnels through a second tunnel barrier which is about 0.5 microns distant from the first tunnel barrier. This current was observed in a bias regime where current flow due to sequential quasiparticle tunneling is forbidden due to the Coulomb blockade., Comment: 4 pages, 5 figures

The conductance fluctuations of a metallic wire which is interrupted by a small tunnel junction has been explored experimentally. In this system, the bias voltage V, which drops almost completely inside the tunnel barrier, is used to probe the energy dependence of conductance fluctuations due to disorder in the wire. We find that the variance of the fluctuations is directly proportional to V. The experimental data are consistently described by a theoretical model with two phenomenological parameters: the phase breaking time at low temperatures and the diffusion coefficient., Comment: 9 pages RevTeX and 4 PS figures (accepted for publication in Physical Review Letters)