Single Josephson Junction Research Articles

Intrinsic Josephson junction arrays containing only a few junctions

After an ordinary mesa is fabricated on a piece of single crystal Bi 2Sr 2CaCu 2O 8+ δ , another ion milling concentrating on the center of the mesa is carried out, resulting in a U-shaped structure with a very thin stack of intrinsic Josephson junctions sitting at its bottom. By using low energy in the milling and reducing the etching rates, we can control the junction number precisely and even a single intrinsic Josephson junction can be fabricated. The I– V characteristics for 4-, 3-, and 1-junction arrays are shown here to support the argument. In the last case (a single junction), some typical structures are believed to be attributable to the behavior of a superconductor–insulator–superconductor (S–I–S) junction with an I c R n product of 7.2 mV at 4.2 K, and a suppressed energy gap structure of Δ=12 meV. Various microwave-induced steps are observed in the frequency range of 1–20 GHz.

Temperature dependence of zero-bias resistances of a single resistance-shunted Josephson junction

Zero-bias resistances of a single resistance-shunted Josephson junction are calculated as a function of the temperature by means of the path-integral Monte Carlo method in case a charging energy $E_{\rm C}$ is comparable with a Josephson energy $E_{\rm J}$. The low-temperature behavior of the zero-bias resistance changes around $\alpha=R_{\rm Q}/R_{\rm S}=1$, where $R_{\rm S}$ is a shunt resistance and $R_{\rm Q}=h/(2e)^2$. The temperature dependence of the zero-bias resistance shows a power-law-like behavior whose exponent depends on $E_{\rm J}/E_{\rm C}$. These results are compared with the experiments on resistance-shunted Josephson junctions.

Capacitively coupled josephson junctions: A two-qubit system

We describe how single Josephson junctions can be connected together capacitively to form a two-qubit system. We discuss the general behavior of this system show the energy level dependence on various junction parameters and choice of coupling strengths. We also discuss measurement techniques for reading out both qubits which are relevant to our ongoing experiments.

Thermal annealing of Nb/Al-AlO/sub x//Nb Josephson junctions

We thermally annealed single un-shunted Josephson junctions at temperatures of 110 to 270/spl deg/C for durations of 2.5 to 90 minutes. We also exposed some junctions for three separate 15-minute periods in order to compare the result with that of a continuous 45-minute exposure. After annealing, we measured the changes in junction properties such as critical current I/sub C/, normal state resistance R/sub N/, and junction quality parameter V/sub M/. I/sub C/ decreases with increased exposure, (starting at approximately 125/spl deg/C) and R/sub N/ increases, such that the I/sub C/R/sub N/ product remains roughly constant up to 200/spl deg/C, at which point I/sub C/R/sub N/ also begins to decrease. V/sub M/ declines slightly with increased exposure, but with a large amount of scatter. Samples with interrupted exposures degraded less than if annealed continuously. Based on our results, we find that junctions can tolerate an exposure of up to 90 minutes at temperatures as high as 200/spl deg/C without significant degradation in performance, though allowances will need to be made for shifts in critical current. Junctions exposed for up to 15 minutes at 225/spl deg/C are degraded further but may still function well enough for some applications.

Feedback-current-injection-type second-order lowpass sigma-delta modulator

In order to establish double-loop feedback design, we have fabricated a prototype superconducting double-loop lowpass sigma-delta modulator. For digital feedback gain, multiple flux quanta are produced by a ladder circuit and carried through Josephson Transmission Lines (JTLs) to the feedback driver. The feedback driver consists of a single Josephson junction or two serially-connected junctions. Direct injection of the pulse current from the JTLs through a low-value resistor drives the feedback driver. The sigma-delta modulator was operated at the sampling frequency of 1.1 GHz and the measured power spectrum showed the noise shaping roughly of 12 dB/octave, which is characteristic of the second-order sigma-delta modulator.

High quality YBa/sub 2/Cu/sub 3/O/sub 7-δ Josephson junctions and junction arrays fabricated by masked proton beam irradiation damage

High quality single Josephson junctions and junction arrays with 10 junctions in series have been fabricated using masked proton beam irradiation damage technology. Monte Carlo simulation of the irradiation damage profile underneath the metal mask has been carried out systematically to guide the metal mask structure design. A high resolution and high aspect ratio metal mask opening was fabricated by focused 30 keV Ga ion beam milling. Various nonconducting oxide buffer layers have been investigated for a Ga contamination free mask fabrication. A contamination free irradiation process and subsequent removal of metal mask after ion irradiation are the keys for the improved properties of junctions fabricated with YBCO.

Quantum effects in small-capacitance single Josephson junctions

We have measured the current-voltage $(I\ensuremath{-}V)$ characteristics of small-capacitance single Josephson junctions at low temperatures $(T=0.02--0.6\mathrm{K}),$ where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc superconducting quantum interence devices (SQUIDs). The single-junction $I\ensuremath{-}V$ curve is sensitive to the impedance of the environment, which can be tuned in situ. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, where the zero-bias resistance ${R}_{0}^{\ensuremath{'}}$ of the SQUID arrays is much higher than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega}.$ The negative differential resistance is evidence of the coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on this theory, we have calculated the $I\ensuremath{-}V$ curves numerically in order to compare then with the experimental ones at ${R}_{0}^{\ensuremath{'}}\ensuremath{\gg}{R}_{K}.$ The numerical calculation agrees with the experiments qualitatively. We also discuss the ${R}_{0}^{\ensuremath{'}}$ dependence of the single-Josephson-junction $I\ensuremath{-}V$ curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.

Josephson-junction qubits: entanglement and coherence

We review briefly the problems that are driving the search for a quantum computer. These include, primarily, methods for encryption and decryption based on Shor’s algorithm for factoring large integers and the use of Pell’s equation for encryption. We also outline some of the approaches that have been suggested for implementing a quantum computer and then focus on Josephson-junction systems as qubits. We have been investigating the current-biased Josephson junction for this application, a suggestion we made about 2 years ago. We have studied macroscopic quantum tunneling and energy level spectroscopy, using microwaves, in single junctions and recently we have begun measurements of the two-quantum bit (qubit) system, i.e. two capacitively coupled junctions. Theoretical studies of energy levels and their dynamic evolution are also in progress. In the present report we discuss the basics of single Josephson junctions and compare their potential as qubits with the potentials of other systems. We also discuss our future plans to obtain greater isolation of the junctions from sources of decoherence and to develop realistic qubits. An important first step must be to exhibit quantum entanglement and measure coherence times. Then it must be shown that the states of the qubits can be initialized, that gate operations can be performed, and that the results can be read out.

Theory of superconductor-insulator transition in single Josephson junctions

A non-band theory is developed to describe the superconductor-insulator (SI) transtition in resistively shunted, single Josephson junctions. The $I-V$ characteristic is formulated by a Landauer-like formula and evaluated by the path-integral transfer-matrix method. The result is consistent with the recent experiments at around 80 $mK$. However, the insulator phase shrinks with decreasing temperature indicating that the single Josephson junction becomes all superconducting at absolute zero temperature, as long as dissipation is present.

Superconductor-insulator quantum phase transition in a single Josephson junction

The superconductor-to-insulator quantum phase transition in resistively shunted Josephson junctions is investigated by means of path-integral Monte Carlo simulations. Our numerical technique allows to directly access the regime of the Josephson-to-charging energy ratios ${E}_{J}{/E}_{C}$ of order one. Our results unambiguously support an earlier theoretical conjecture, based on renormalization-group calculations, that at $\stackrel{\ensuremath{\rightarrow}}{T}0$ the dissipative phase transition occurs at a universal value of the shunt resistance ${R}_{S}{=h/4e}^{2}$ for all values ${E}_{J}{/E}_{C}.$ On the other hand, finite-temperature effects are shown to turn this phase transition into a crossover, whose position depends significantly on ${E}_{J}{/E}_{C},$ as well as on the dissipation strength and temperature. The latter effect needs to be taken into account in order to reconcile earlier theoretical predictions with recent experimental results.

Quantum phase transition and Coulomb blockade with one-dimensional SQUID arrays

We report on experiments with one-dimensional (1D) arrays of small-capacitance superconducting quantum interference devices (SQUIDs), where an external magnetic field can be used to tune in situ the Josephson coupling between neighboring superconducting electrodes. We have studied the superconductor–insulator transition in such arrays, and have also used these arrays to bias a single Josephson junction. In the later experiment, we have observed a clear Coulomb blockade of Cooper-pair tunnelling (CBCPT) in the single junction.

Superconductor–insulator transition in a single Josephson junction

Resistively shunted, single Josephson junctions are studied theoretically. The method complements the band picture and is aimed at the superconductor–insulator transition regime in the E J /E C , R q /R plane, where E J and E C are the Josephson energy and the charging energy E C= e 2/2 C, C being the capacitance of the junction and R q= h/4 e 2 and R are the quantum resistance and the shunt resistance. The I– V characteristic is formulated by a new theory and evaluated by the path-integral transfer matrix method. The obtained result is in accordance with the recent experiments.

Control of the electromagnetic environment for single Josephson junctions using arrays of dc SQUIDs

We have measured the current–voltage characteristics of small-capacitance single Josephson junctions at low temperatures T ≤ 0.04 K, where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. When the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e2 ≈ 26 kΩ, a transition to a clear Coulomb blockade of Cooper-pair tunnelling is induced in the single junction. The measured blockade voltage agrees with the theoretical prediction.

Coulomb blockade and coherent single-cooper-pair tunneling in single Josephson junctions.

We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.

Dissipative quantum effects in small Josephson junctions

Dissipation effects on a single Josephson junction are studied based on a harmonic-oscillator model in the weak coupling region. It is shown that the system is controlled by two characteristic energy scales. The origin of these energy scales is explained in terms of a classical plasma problem. This feature provides a new viewpoint on the superconductor–insulator transition of small Josephson junctions.

Time jitter measurement in a circular Josephson transmission line

A Josephson transmission line closed to form a ring was used to measure the time jitter produced by a single shunted Josephson junction. A toggle flip-flop cell was connected to a sampling oscilloscope, and was used to detect the flux quantum arrival time. Time jitter was determined from the variation of this time. The jitter was measured as a function of the number of cycles the flux quantum made in the ring. The reduced jitter produced by a single junction of 0.2 ps/spl radic/n (n-number of junctions passed by the quantum) was measured using Hypres 1 kA/cm/sup 2/ chip fabrication technology. It was found that jitter varies the distance between the quanta with the same rate of 0.2 ps/spl radic/n.

A general approach for determining the switching probability in rapid single flux quantum logic circuits

A major restriction in the development of a working Rapid Single Flux Quantum (RSFQ) logic circuit with high-Tc superconductors is given by the influence of thermal noise. This gives reason to ask for a general determination of the digital bit error rate. As other approaches, our method of calculating the switching probability is based on the Fokker-Planck equation. In the past few years the bit error rates for a single Josephson junction, SQUIDs and the comparator were calculated by using this theory. We demonstrate numerical solution of the multidimensional Fokker-Planck equation to calculate bit error rates due to thermal noise for a Toggle Flip Flop circuit. In the present work, we combine thermal noise analysis with the effects of process variations in order to derive rules for designing high-Tc RSFQ logic circuits.

Experiments on Dissipative Dynamics of Single Josephson Junctions

The energy band description of resistively shunted single Josephson junctions is studied experimentally. At zero bias and low temperature, the junctions are found to undergo a dissipative phase transition, a crossover between two different types of IV-curves, at which macroscopic quantum tunneling delocalizes the Josephson phase and destroys superconductivity. The transition is washed away by increasing temperature, bias current and magnetic field. At low currents and temperatures, the current dependence of the junction resistance is found to scale with the temperature dependence, pointing out to the existence of a zero temperature quantum transition. At higher currents, Zener tunneling between energy bands is observed and compared with existing theories.

Interpretation of a microwave induced current step in a single intrinsic Josephson junction on a Bi-2223 thin film

Thin stacks consisting of a single intrinsic Josephson junction on (Bi,Pb)SrCaCuO thin films are investigated under the influence of external microwave fields. The I– V-characteristic shows a single resistive branch, a clear superconducting gap edge structure and a pronounced current step in external microwave fields. With increasing irradiation power it shifts to higher voltages, while the height of the step remains practically unchanged. In a numerical simulation including an ac-magnetic field parallel to the superconducting layers the experimental features of the structure can be explained by a collective motion of Josephson fluxons.

PHASE LOCKING AND AC AMPLIFICATION OF SMALL JOSEPHSON JUNCTIONS

We have addressed the problem of the phase-locking mechanism of a single Josephson junction irradiated with microwaves, and have numerically and theoretically explored the possibility to achieve ac gain in this system. By investigating the capability of Josephson junctions to enhance the signal received form an external rf source we obtain useful information of the possibility of mutual phase-locking of large arrays of junctions.