Ultrasmall Josephson Junctions Research Articles

Interplay of classical and quantum capacitance in a one-dimensional array of Josephson junctions

Even in the absence of Coulomb interactions phase fluctuations induced by quantum size effects become increasingly important in superconducting nano-structures as the mean level spacing becomes comparable with the bulk superconducting gap. Here we study the role of these fluctuations, termed "quantum capacitance", in the phase diagram of a one-dimensional (1D) ring of ultrasmall Josephson junctions (JJ) at zero temperature by using path integral techniques. Our analysis also includes dissipation due to quasiparticle tunneling and Coulomb interactions through a finite mutual and self capacitance. The resulting phase diagram has several interesting features: A finite quantum capacitance can stabilize superconductivity even in the limit of only a finite mutual-capacitance energy which classically leads to breaking of phase coherence. In the case of vanishing charging effects, relevant in cold atom settings where Coulomb interactions are absent, we show analytically that superfluidity is robust to small quantum finite-size fluctuations and identify the minimum grain size for phase coherence to exist in the array. We have also found that the renormalization group results are in some cases very sensitive to relatively small changes of the instanton fugacity. For instance, a certain combination of capacitances could lead to a non-monotonic dependence of the superconductor-insulator transition on the Josephson coupling.

Supercurrent in Nb/InAs-nanowire/Nb Josephson junctions

We report on the fabrication and measurements of planar mesoscopic Josephson junctions formed by InAs nanowires coupled to superconducting Nb terminals. The use of Si-doped InAs-nanowires with different bulk carrier concentrations allowed to tune the properties of the junctions. We have studied the junction characteristics as a function of temperature, gate voltage, and magnetic field. For junctions with high doping concentrations in the nanowire, Josephson supercurrent values up to 100 nA are found. Owing to the use of Nb as superconductor, the Josephson coupling persists at temperatures up to 4 K. In all junctions, the critical current monotonously decreased with the magnetic field, which can be explained by a recently developed theoretical model for the proximity effect in ultra-small Josephson junctions. For the low-doped Josephson junctions, a control of the critical current by varying the gate voltage has been demonstrated. We have studied conductance fluctuations in nanowires coupled to superconducting and normal metal terminals. The conductance fluctuation amplitude is found to be about 6 times larger in superconducting contacted nanowires. The enhancement of the conductance fluctuations is attributed to phase-coherent Andreev reflection as well as to the large number of phase-coherent channels due to the large superconducting gap of the Nb electrodes.

Superconductor-Metal Transition in an Ultrasmall Josephson Junction Biased by a Noisy Voltage Source

Shot noise in a voltage source changes the character of the quantum (dissipative) phase transition in an ultrasmall Josephson junction: The superconductor-insulator transition transforms into the superconductor-metal transition. In the metallic phase, the IV curve probes the voltage distribution generated by shot noise, whereas in the superconducting phase, it probes the counting statistics of electrons traversing the noise junction.

Feasibility studies of ultra-small Josephson junctions for qubits

Most proposed realizations of a high temperature superconductor (HTS) qubit require the use of very small Josephson junctions. The properties of bicrystal junctions are especially interesting since they make it possible to implement several types of flux qubits in a relatively simple way. We have developed a technique that allows us to produce high quality sub-micrometer junctions in a reproducible way using bicrystal technology. We have successfully fabricated and characterized a large number of YBCO junctions and SQUIDs with bridge width as small as 0.2 micrometer on 0/spl deg/-3/spl deg/, 0/spl deg/-40/spl deg/ and 0/spl deg/-45/spl deg/ bicrystal STO substrates. The properties of these junctions have been extensively examined at temperatures down to 20 mK. The effects of external magnetic fields on these structures have been investigated. Figures of merit for the proposed qubits were also extracted from these measurements.

Spectroscopy of mesoscopic Josephson junction using inelastic Cooper-pair tunneling

We have measured the energy levels of a mesoscopic, nearly classical Josephson junction using the method of inelastic Cooper-pair tunneling. The tunneling in an ultrasmall Josephson junction causes transitions in the junction environment and provides a method of doing spectroscopy with a simple DC measurement. A classical Josephson junction can be thought of as an LC-circuit, which quantum mechanically corresponds to the harmonic oscillator. We find that the simple model agrees with the range of E J/ E C ratios down to about 35.

Tunnel spectroscopy of a double superconducting island qubit

We have probed by tunnel spectroscopy a quantum system consisting of two superconducting islands strongly coupled by an ultrasmall Josephson junction. The Josephson junction allows Cooper pair delocalization between the two islands and gate voltages control the state of the system. Tunnel spectroscopy is made possible by means of two other junctions weakly coupling the islands to measurement leads. We have observed different transport regimes depending on the applied bias voltage.

Implementation of a combined charge-phase quantum bit in a superconducting circuit

We discuss a qubit circuit based on the single Cooper-pair transistor (which consists of two ultrasmall Josephson junctions in series) connected in parallel with a large Josephson junction. The switching of this junction out of its zero-voltage state is used to readout the qubit. We report measurements of the discriminating power of the readout process, and we discuss its back-action on the qubit.

Direct measurement of the Josephson supercurrent in an ultrasmall Josephson junction.

We have measured the supercurrent flowing through a nonhysteretic, ultrasmall, voltage-biased Josephson junction. In contrast with experiments performed so far on hysteretic Josephson junctions, we find a supercurrent peak whose maximum I(s max) increases as the temperature T decreases. The asymptotic T = 0 value of I(s max) agrees with the junction Ambegaokar-Baratoff critical current, as predicted by theory.

Quantum phase expectation values of a mesoscopic Josephson junction from quantum current measurements

A simple way to acquire information on the mean values of the phase operators sinϕ and cosϕ of an ultrasmall Josephson junction prepared in an arbitrary pure or not state is reported. Our proposal exploits the recently predicted occurrence of current spikes in the I-V characteristic of a mesojunction irradiated by a quantum single-mode low-intensity coherent electromagnetic field. A necessary condition for the validity of our treatment is presented and discussed.

Quantum current spikes in theI-Vcharacteristic of a mesojunction coupled to non-classical em fields

The effect of exposing an ultrasmall Josephson junction to a single-mode non-classical far-infrared field is investigated. We prove that on irradiating such a mesodevice with a quantum superposition of two -out-of-phase coherent states, its I-V characteristic exhibits current spikes which may be directly related to quantum interference effects. Moreover, we show that the structure of these current spikes is strongly influenced both by the phase difference between the two coherent states and by their relative quantum phase. The possibility of exploiting such peculiar aspects of the system dynamics to obtain information on the initial state of the field is brought to light.

JOSEPHSON MESOJUNCTIONS AS DETECTORS OF LOW-INTENSITY QUANTIZED COHERENT FAR-INFRARED FIELDS

We show that the quantum nature of a mesoscopic Josephson junction may be exploited for detecting low-intensity electromagnetic quantized fields. In particular we prove that intensity and phase of single-mode quantized coherent field may be reconstructed measuring amplitude and quantum noise of the first quantum Shapiro step occurring in the I-V characteristic of the ultrasmall Josephson junction.

Capacitively coupled Josephson-junction chains: straight versus slanted coupling

We investigate analytically the quantum phase transition in a system of two chains of ultrasmall Josephson junctions, coupled capacitively with each other. Two different schemes of the coupling, straight and slanted, between the two chains are considered. In both coupling schemes, as the coupling capacitance is increased, the transport of particle-hole pairs is found to drive a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type from insulator to superconductor. A substantial discrepancy between the transition points in the two coupling schemes is observed, which reflects the difference between the transport mechanisms.

Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions

We have studied a quantum Hamiltonian that models an array of ultrasmall Josephson junctions with short range Josephson couplings, $E_J$, and charging energies, $E_C$, due to the small capacitance of the junctions. We derive a new effective quantum spherical model for the array Hamiltonian. As an application we start by approximating the capacitance matrix by its self-capacitive limit and in the presence of an external uniform background of charges, $q_x$. In this limit we obtain the zero-temperature superconductor-insulator phase diagram, $E_J^{\rm crit}(E_C,q_x)$, that improves upon previous theoretical results that used a mean field theory approximation. Next we obtain a closed-form expression for the conductivity of a square array, and derive a universal scaling relation valid about the zero--temperature quantum critical point. In the latter regime the energy scale is determined by temperature and we establish universal scaling forms for the frequency dependence of the conductivity.

Temperature-dependent conductivity of ultrasmall Josephson junctions

In this paper we analyse the transport properties of Josephson junctions embedded in an electromagnetic environment caused by pads and leads near to the junctions. At sufficiently low temperatures we find that the conductivity of the Josephson junctions at low bias is strongly suppressed due to the Coulomb blockade of Cooper pair tunnelling. At high enough temperatures, the conductivity of the Josephson junctions is also reduced due to thermal activated phase slip processes. As a consequence, transport of supercurrent with maximal conductivity is reached at an intermediate temperature. The dependence of various transport regimes on the Josephson energy and the charging energy is discussed.

Cotunneling Transport and Quantum Phase Transitions in Coupled Josephson-Junction Chains with Charge Frustration

We investigate the quantum phase transitions in two capacitively coupled chains of ultrasmall Josephson junctions, where the particle-hole symmetry is broken by the gate voltage applied to each superconducting island. Near the maximal-frustration line, cotunneling of the particles along the two chains is shown to play a major role in the transport and to drive a quantum phase transition out of the charge-density-wave insulator, as the Josephson-coupling energy is increased. We also argue briefly that slightly off the symmetry line the universality class of the transition remains the same as that right on the line, being driven by the particle-hole pairs.

Quantum phase transitions in capacitively coupled two-dimensional Josephson-junction arrays

Quantum phase transitions in two layers of ultrasmall Josephson junctions, coupled capacitively with each other, are investigated. As the inter-layer capacitance is increased, the system at zero temperature is found to exhibit an insulator-to-superconductor transition. It is shown that, unlike in the case for one-dimensional arrays with a similar coupling configuration, the transition cannot be accounted for exclusively by particle-hole pairs.

Charge Glass in Two-Dimensional Arrays of Capacitively Coupled Grains with Random Offset Charges

We study the effect of random offset charges in the insulator to conductor transition in systems of capacitively coupled grains, as realized in two-dimensional arrays of ultrasmall Josephson junctions. In presence of disorder, the conductive transition and charge ordering at nonzero gate voltages are both destroyed for any degree of disorder $\sigma$ at finite temperatures $T$, in the thermodynamic limit, but crossover effects will dominate at length scales smaller than $\xi_{\sigma, T}=T^{-\nu} f(\sigma T^{-\nu})$, where $\nu $ is the thermal critical exponent of the zero-temperature charge glass transition. The conductance is linear and thermally activated but nonlinear behavior sets in at a crossover voltage which decreases as temperature decreases. For large disorder, the results are supported by Monte Carlo dynamics simulations of a Coulomb gas with offset charges and are consistent with the thermally activated behavior found in recent experiments.

Duality in Two Capacitively Coupled Layered Arrays of Ultrasmall Josephson Junctions

We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on their physical parameter values. The former case is dominated by a Cooper-pair superfluid while the quantum one is dominated by dynamic vortices leading to an insulating behavior. We first consider the limit when both arrays are in the semiclassical limit, and next the case when one array is quantum and the other semiclassical. We present WKB and Mean Field theory results for the critical temperature of each array when both are in the semiclassical limit. When one array is in the semiclassical regime and the other one in the quantum fluctuations dominated regimes, we derive a duality transformation between the charged and vortex dominated arrays that involve a gauge vector field, which is proportional to the site coupling capacitance between the arrays. The system considered here has been fabricated and we make some predictions as to possible experimentally measurable quantities that could be compared with theory.

Critical properties of two-dimensional Josephson-junction arrays with zero-point quantum fluctuations.

We present results from an extensive analytic and numerical study of a two-dimensional model of a square array of ultrasmall Josephson junctions. We include the ultrasmall self and mutual capacitances of the junctions, for the same parameter ranges as those produced in the experiments. The model Hamiltonian studied includes the Josephson, $E_J$, as well as the charging, $E_C$, energies between superconducting islands. The corresponding quantum partition function is expressed in different calculationally convenient ways within its path-integral representation. The phase diagram is analytically studied using a WKB renormalization group (WKB-RG) plus a self-consistent harmonic approximation (SCHA) analysis, together with non-perturbative quantum Monte Carlo simulations. Most of the results presented here pertain to the superconductor to normal (S-N) region, although some results for the insulating to normal (I-N) region are also included. We find very good agreement between the WKB-RG and QMC results when compared to the experimental data. To fit the data, we only used the experimentally determined capacitances as fitting parameters. The WKB-RG analysis in the S-N region predicts a low temperature instability i.e. a Quantum Induced Transition (QUIT). We carefully simulations and carry out a finite size analysis of $T_{QUIT}$ as a function of the magnitude of imaginary time axis $L_\tau$. We find that for some relatively large values of $\alpha=E_C/E_J$ ($1\leq \alpha \leq 2.25)$, the $L_\tau\to\infty$ limit does appear to give a {\it non-zero} $T_{QUIT}$, while for $\alpha \ge 2.5$, $T_{QUIT}=0$. We use the SCHA to analytically understand the $L_\tau$ dependence of the QMC results with good agreement between them. Finally, we also carried out a WKB-RG analysis in the I-N region and found no evidence of a low temperature QUIT, up to lowest order in ${\alpha}^{-1}$

Wigner-function approach to a single-electron tunnel junction.

We demonstrate that the Wigner function is suitable to describe single-electron tunneling in ultrasmall tunnel junctions. For a current-biased junction, we derive a master equation for the Wigner function which describes charging effects on Cooper-pair tunneling, quasiparticle-pair tunneling, and normal single-electron tunneling in an unified way. We obtain the current-voltage I-V characteristic for an ultrasmall Josephson junction that recovers those for the Josephson junction with no charging energy in the limit of e/C\ensuremath{\rightarrow}0. It is predicted that, due to charging effect in the ultrasmall Josephson, the position of the Riedel peak and the gap of the quasiparticle-pair interference term are changed from 2\ensuremath{\Delta}/e to 2\ensuremath{\Delta}/e-e/2C, while the quasiparticle current's onset changes from 2\ensuremath{\Delta}/e to 2\ensuremath{\Delta}/e+e/2C. \textcopyright{} 1996 The American Physical Society.