Josephson Array Research Articles

Tests of operating conditions for metrological application of HTS Josephson arrays

We report on an experimental study of metrological properties of High Temperature Superconductor arrays, made of shunted bicrystal YBCO Josephson junctions, to assess their accuracy. A detailed analysis of measurement errors is presented, mainly based on a direct comparison of an HTS array against a low temperature array. Owing to the high sensitivity of the comparison, we were able to measure the changes in the HTS array voltage on a step at nanovolt level. A precise estimate of the dependence of the HTS array step width on operating conditions was obtained. Differences were observed with respect to the results provided by the usual, low sensitivity, techniques, confirming that the method we adopted is necessary in the study of HTS arrays for metrology. The high sensitivity analysis was applied in the derivation of the temperature dependence of the critical current as well, providing some insights on the behaviour of the HTS array.

Voltage Ratio Measurements Using Two Digital Voltmeters and Resistive Voltage Divider

This paper presents a method to accurately measure voltage ratios from 1:2 to 1:10 with a calibrated digital voltmeter (DVM) at voltage ranges of 1-10 V using a simple resistive-voltage divider. The divider can be used as an absolute divider or as a Hamon divider. The achieved accuracy is better than 10/sup -7/, comparable to those reported with measurements with Josephson array voltage source (JAVS).

Study and operating conditions of HTS Josephson arrays for metrological application

We report an experimental study of metrological properties of high-temperature superconductor arrays, made of shunted bicrystal YBCO Josephson junctions. The work is mainly based on a direct comparison against a low temperature array. Owing to the high sensitivity of the measurements, we observed at nanovolt level the changes in the HTS array voltage on a step. A precise estimate of the dependence of the HTS array step width on operating conditions was obtained. Differences were observed with respect to the results of low sensitivity techniques, confirming that our method is necessary in the study of HTS arrays for metrology. The high sensitivity analysis was also applied in the derivation of the temperature dependence of the critical current, providing insights on the behavior of the HTS array.

Simulations of collective synchronization in Josephson junction arrays

We developed a virtual model of a Josephson junction series array based on a rigorous dynamic simulation and investigated coupling effect of Josephson oscillations. Our virtual model for a superconductor-insulator-normal metal-insulator-superconductor junction array reveals that a time-lag junction instability should be avoided for global synchronization in a long array with a large number of junctions. We found that the coupling between the self-generated Josephson oscillations through a microwave transmission line plays an important role in the collective synchronization of the Josephson array.

Synchronization of Josephson vortices in multi-junction systems

A largely adopted model for the description of high-temperature superconductors such as BSCCO results in several long Josephson junctions one on the top of the other (“stacked”). The dynamics of the basic nonlinear excitation of the isolated long Josephson junction, the Josephson vortex, is modified by the coupling among the junctions, so the motion of the flux quanta in the various layers is affected by the flux dynamics in all other layers. Two basic states are possible: a synchronous motion, where all junctions are reflected at the edge at the same instant, and an out-of-phase motion, where vortices in each layer are shifted with respect to neighboring vortices. This is of direct interest for applications since flux quanta emit, upon reflection, radiation at frequencies of great interest (above 100GHz). Research has been directed towards the optimal conditions to favor such emission, that is mainly to retrieve the above described synchronous motion. We discuss the physics behind synchronization of nonlinear elements and we review applications to Josephson arrays. We discuss in the framework of a general model for synchronization, the Kuramoto model, a mechanism that can possibly enhance synchronization, such as coupling to a resonant cavity. We present a version of the Kuramoto model that might include the effects of the strong interaction between the oscillators and the cavity.

A Josephson Voltage Calibrator

An automatic voltage calibrator for voltages ranging from −1 V to +1 V is described. The device is based on a Josephson array with Nb-AlOx-Al-AlOx-Nb junctions. Being illuminated by microwave radiation with a frequency of 65.2 GHz, the array, in which the operating supply currents of three junction sections are set by a multichannel digital source controlled by a personal computer, generates 21 voltage values quantized with steps of 51.5, 86.6, and 138 mV. The capabilities of this device are demonstrated by studying the deviation from linearity of a seven-digit digital nanovoltmeter with a measurement uncertainty of below 1 × 10−7. By calibrating a precision Zener-diode voltage standard, it is shown that the uncertainty of this calibrator is no more than 20–50 nV at a voltage level of 1 V.

Quantum state transfer in arrays of flux qubits

In this paper, we describe a possible experimental realization of Bose's idea to use spin chains for short-distance quantum communication (Bose 2003 Phys. Rev. Lett. 91 207901). Josephson arrays have been proposed and analysed as transmission channels for systems of superconducting charge qubits. Here, we consider a chain of persistent-current qubits, that is appropriate for state transfer with high fidelity in systems containing flux qubits. We calculate the fidelity of state transfer for this system. In general, the Hamiltonian of this system is not of XXZ-type, and we analyse the magnitude and the effect of the terms that do not conserve the z-component of the total spin.

Microwave nonlinearities of an isolated longYBa2Cu3O7−δbicrystal grain boundary

We measure the local harmonic generation from an YBa_2Cu_3O_(7-d)(YBCO) bi-crystal grain boundary to examine the local Josephson nonlinearities. Spatially resolved images of second and third harmonic signals generated by the grain boundary are shown. The harmonic generation and the vortex dynamics along the grain boundary are modeled with the Extended Resistively Shunted Josephson (ERSJ) array model, which shows reasonable agreement with the experimental data. The model also gives qualitative insight into the vortex dynamics induced in the junction by the probing current distribution. A characteristic nonlinearity scaling current density JNL ~ 1.5 x 10^5 A/cm^2 for the Josephson nonlinearity is also extracted.

Fabrication of Epitaxial NbN Devices With TiN Resistors

To extend the application range of epitaxial NbN devices, we developed epitaxial TiN thin-film resistors. TiN has approximately the same lattice constant and crystalline structure as NbN and MgO. However, high quality TiN thin films show superconductivity at the liquid helium temperature. We attempted to remove this superconductivity using TiO impurity. The ratio of Ar and N/sub 2/ was fixed at 5:1 and the O/sub 2/ flow ratio varied from 0 to 1.6% in relation to the total gas flow. When O/sub 2/ ranged from 0.5 to 1.6%, superconductivity vanished and the resistivity obtained was about 50-145 /spl mu//spl Omega/cm at 4.2 K. X-ray analysis showed that the TiN films grew epitaxially on the MgO substrate as did the NbN films on the TiN films. Using the TiN resistor, a fully epitaxial NbN Josephson array oscillator was fabricated and tested. The oscillator was formed with 10 TiN-shunted NbN/MgO/NbN tunnel junctions and NbN microstrip resonators. At around 1.0THz, Shapiro steps induced by the Josephson oscillation were observed in the detector I-V characteristics.

A Precise Evaluation of NbN-Based 1-V Programmable Josephson Voltage Standard Arrays

A NbN-based programmable Josephson voltage standard arrays (PJVAs) have been investigated. We show that these arrays can be utilized for programmable operation up to /spl plusmn/1 V. The results of direct comparisons between the PJVA and a conventional superconductor-insulator-superconductor Josephson array agree at voltages between 0.1 V and 1 V within an uncertainty of better than 1 nV. An indirect comparison via a Zener voltage reference also shows agreement within a 1/spl sigma/ type A uncertainty of 13 nV.

Solid-state quantum communication with Josephson arrays

Josephson junction arrays can be used as quantum channels to transfer quantum information between distant sites. In this paper we discuss simple protocols to realize state transfer with high fidelity. The channels do not require complicated gating but use the natural dynamics of a properly designed array. We investigate the influence of static disorder both in the Josephson energies and in the coupling to the background gate charges, as well as the effect of dynamical noise. We also analyze the readout process, and its back action on the state transfer.

Final report on the key comparison EUROMET.BIPM.EM-K10.a: Comparison of Josephson array voltage standards by using a portable Josephson transfer standard

The purpose of this comparison was to compare Josephson voltage standards by using the new VNIIM portable Josephson standard voltage (PJVS) as travelling standard. The comparison was carried out under the auspices of EUROMET (Project 723) from September 2003 to May 2004. It was aimed to link more laboratories organized in EUROMET. In addition, the comparison provides a link between EUROMET, COOMET and the BIPM. Twelve national metrology institutes and the BIPM participated, with the Physikalisch-Technische Bundesanstalt (Braunschweig, Germany) acting as pilot laboratory.The PJVS was accompanied and operated by a VNIIM specialist. The technical protocol requested to measure a 1 V fixed output voltage at an output resistance of 4 Ω, while measurements at 1.2 kΩ output resistance were optional. The comparisons were performed in a similar way to the new so-called 'option B' bilateral comparisons carried out by the BIPM; the NMIs had to use their own null detector, polarity switch and measurement procedure to measure the output voltage of the PJVS. This method of comparison is more closely related to standard electronic voltage reference (e.g. Zener) measurements but without the limitation to their noise. During all comparisons the PJVS was connected to the same time base as that used by the laboratory Josephson voltage standard.The results demonstrate that the idea of using a portable quantum standard based on a programmable Josephson array as a travelling standard is a powerful tool to achieve equivalence between institutes quickly and at a very good level of uncertainty. Several institutes achieved a relative uncertainty clearly better than one part in 109 at a 95% level of confidence.Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCEM, according to the provisions of the Mutual Recognition Arrangement (MRA).

Topology-induced confined superfluidity in inhomogeneous arrays

We report a study of the zero-temperature phase diagram of the Bose-Hubbard model on topologically inhomogeneous arrays. We show that the usual Mott-insulator and superfluid domains, in the paradigmatic case of the comb lattice, are separated by regions where the superfluid behavior of the bosonic system is confined along the comb backbone. The existence of such confined superfluidity, arising from topological inhomogeneity, is proved by different analytical and numerical techniques which we extend to the case of inhomogeneous arrays. We also discuss the relevance of our results to real systems exhibiting macroscopic phase coherence, such as coupled Bose condensates and Josephson arrays.

Phase and charge re-entrant phase transitions in two capacitively coupled Josephson arrays with ultrasmall junctions

We have studied the phase diagram of two capacitively coupled Josephson junction arrays with charging energy, $E_c$, and Josephson coupling energy, $E_J$. Our results are obtained using a path integral Quantum Monte Carlo algorithm. The parameter that quantifies the quantum fluctuations in the i-th array is defined by $\alpha_i\equiv \frac{E_{{c}_i}}{E_{J_i}}$. Depending on the value of $\alpha_i$, each independent array may be in the semiclassical or in the quantum regime: We find that thermal fluctuations are important when $\alpha \lesssim 1.5 $ and the quantum fluctuations dominate when $2.0 \lesssim \alpha $. We have extensively studied the interplay between vortex and charge dominated individual array phases. The two arrays are coupled via the capacitance $C_{{\rm inter}}$ at each site of the lattices. We find a {\it reentrant transition} in $\Upsilon(T,\alpha)$, at low temperatures, when one of the arrays is in the semiclassical limit (i.e. $\alpha_{1}=0.5 $) and the quantum array has $2.0 \leq\alpha_{2} \leq 2.5$, for the values considered for the interlayer capacitance. In addition, when $3.0 \leq \alpha_{2} < 4.0$, and for all the inter-layer couplings considered above, a {\it novel} reentrant phase transition occurs in the charge degrees of freedom, i.e. there is a reentrant insulating-conducting transition at low temperatures. We obtain the corresponding phase diagrams and found some features that resemble those seen in experiments with 2D JJA.

Magnetic moment of square SIS Josephson arrays: Self-organized criticality

The temperature-and magnetic-field dependences of the magnetic moment of square Josephson arrays with SIS-type junctions are studied experimentally. Two temperature regions are observed with different types of magnetization curves. Magnetic flux avalanches are detected in the low-temperature region. Statistical analysis of avalanche amplitudes A shows that their size distribution varies in accordance with the power law P∝An with crossover, when exponent n varies from n=−0.7 for small avalanches to n=−6 for large avalanches, while the frequency spectrum varies in accordance with the law 1/fα. Such behavior is interpreted as a manifestation of self-organized criticality.

Topologically protected quantum states and quantum computing in Josephson junctions arrays

We review recent results on a new class of Josephson arrays which have nontrivial topology and exhibit novel quantum states at low temperatures. One of these states is characterized by long-range order in a two-Cooper-pair condensate and by a discrete topological order parameter. The second state is insulating and can be considered as being the result of an evolution of the former state due to Bose-condensation of usual superconductive vortices with a flux quantum Φ0. The quantum phase transition between these two states is controlled by variation of the external magnetic field. Both the superconductive and insulating states are characterized by the presence of 2K-degenerate ground states, with K being the number of topologically different cycles existing in the plane of the array. This degeneracy is “protected” from the external perturbations (and noise) by the topological order parameter and spectral gap. We show that under ideal conditions the low-order effect of the external perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only exponentially small effects of perturbations. We argue that this system provides a physical implementation of an ideal quantum computer with a built-in error correction. A number of relatively simple “echo-like” experiments possible on small-size arrays are discussed.

Accuracy of a Cryocooler-Based Programmable Josephson Voltage Standard

A cryocooler-based programmable Josephson array voltage standard (JAVS) for 4-K operation and a very compact microwave source are described. Both components are crucial for future mobile voltage standards. A direct comparison between two programmable JAVS using these components was performed at 1 V in order to test whether these systems are suitable for metrological application at the highest level of precision. The results of the comparison show that the new components are suitable for mobile JAVS with an uncertainty of less than 1 /spl times/ 10/sup -9/.

Paramagnetism in 1D mixed π/conventional Josephson arrays

One-dimensional mixed π/conventional arrays of Josephson junctions admit paramagnetic solutions besides the standard diamagnetic ones. We analyze the arrays magnetization properties when they show paramagnetism varying the parameters controlling the self-field and the length of the array. We show that paramagnetic solutions are found in all cases independently by the effect of self-field and, moreover, for small length and negligible self-field the paramagnetic solution is the lowest energy stable solution. These arrays can be used to model long grain boundaries (GB) in artificial or intrinsic high- T c junctions made by unconventional d-wave superconductors.

Spontaneous creation of discrete breathers in Josephson arrays

We report on the experimental generation of discrete breather states (intrinsic localized modes) in frustrated Josephson arrays. Our experiments indicate the formation of discrete breathers during the transition from the static to the dynamic (whirling) system state, induced by a uniform external current. Moreover, spatially extended resonant states, driven by a uniform current, are observed to evolve into localized breather states. Experiments were performed on single Josephson plaquettes as well as open-ended Josephson ladders with 10 and 20 cells. We interpret the breather formation as the result of the penetration of vortices into the system.

The bose metal: a commentary

We review the concept of the Bose metal state which arises in 2D superconductors in the quantum limit where vortex loops can grow spontaneously in (2+1) dimensions and, as zero point motions become larger, eventually lead to an insulating state. A nonlocal Coulomb charging term in a Josephson array type model leads to an effective transverse gauge field which can suppress the condensate of vortices in the superinsulating state leading to an intermediate Bose liquid which is not superfluid at T=0, the Bose metal state. We comment on recent work on this state and on other non-superfluid Bose liquids.