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We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits, in particular, with application to quantum readout. The developed quantitative description demonstrates strong influence of higher harmonics on their characteristics. While this effect is relevant for various circuits, including the conventional Josephson bifurcation amplifier and the parametrically driven circuit, we first focus on the period-doubling bifurcation under a force driving. This kind of bifurcation is due to nominally quadratic nonlinearity, which enables parametric down-conversion of the driving signal at nearly double resonance frequency to the basic mode. We analyze the effect of higher harmonics on the dynamics of the basic mode, inherent in a nonlinear circuit, which in our case is based on a Josephson junction with a sinusoidal current-phase relation as the origin of nonlinearity. We demonstrate that effects beyond the monochromatic approximation significantly modify the bare characteristics and evaluate their contribution. Due to high sensitivity of this circuit to small variations of parameters, it can serve as an efficient detector of the quantum state of superconducting qubits.

We analyze the effect of circuit parameter variation on the performance of Josephson traveling-wave parametric amplifiers (JTWPAs). Specifically, the JTWPA concept we investigate is using flux-biased nonhysteretic rf-SQUIDs in a transmission line configuration, which harnesses the three-wave mixing (3WM) regime. Dispersion engineering enables phasematching to achieve power gain of $\sim$20 dB, while suppressing the generation of unwanted mixing processes. Two dispersion engineering concepts using a 3WM-JTWPA circuit model, i.e., resonant phase-matching (RPM) and periodic capacitance modulation (PCM), are discussed, with results potentially also applicable to four-wave-mixing (4WM) JTWPAs. We propose suitable circuit parameter sets and evaluate amplifier performance with and without circuit parameter variance using transient circuit simulations. This approach inherently takes into account microwave reflections, unwanted mixing products, imperfect phasematching, pump depletion, etc. In the case of RPM the resonance frequency spread is critical, while PCM is much less sensitive to parameter spread. We discuss degrees of freedom to make the JTWPA circuits more tolerant to parameter spread. Finally, our analysis shows that the flux-bias point where rf-SQUIDs exhibit Kerr-free nonlinearity is close to the sweet spot regarding critical current spread., Comment: 6 pages, 3 figures

The recently proposed Josephson traveling-wave parametric amplifier (JTWPA) based on a ladder transmission line consisting of radio-frequency SQUIDs and exploiting three-wave mixing (3WM), has great potential in achieving both a gain of 20 dB and a flat bandwidth of at least 4 GHz. To realize this concept in practical amplifiers we model the advanced JTWPA circuit with periodic modulation of the circuit parameters (engineered dispersion loadings), which allow the basic mixing process, i.e., $\omega_s=\omega_p-\omega_i$, where $\omega_s$, $\omega_p$, and $\omega_i$ are the signal, the pump, and the idler frequencies, respectively, and efficiently suppress propagation of unwanted higher tones including $\omega_{2p}=2\omega_p$, $\omega_{p+s}=\omega_p +\omega_s$, $\omega_{p+i} = \omega_p + \omega_i$, etc. The engineered dispersion loadings allow achieving sufficiently wide $3$ dB-bandwidth from $3$ GHz to $9$ GHz combined with a reasonably small ripple ($\pm2$ dB) in the gain-versus-frequency dependence.

We investigated both theoretically and experimentally open-ended coplanar waveguide resonators with rf SQUIDs embedded in the central conductor at different positions. These rf SQUIDs can be tuned by an external magnetic field and thus may exhibit the non-centrosymmetric nonlinearity of $\chi^{(2)}$ type with suppressed Kerr nonlinearity. We demonstrated that this nonlinearity allows for efficient mixing of $\lambda/2$ and $\lambda$ modes in the cavity and thus enables various parametric effects with three wave mixing. These effects are the second harmonic generation, the half tone generation, the parametric amplification in both degenerate and non-degenerate regimes and deamplification in degenerate regime., Comment: 12 pages incl. 9 figures

We develop the concept of quasi-phasematching (QPM) by implementing it in the recently proposed Josephson traveling-wave parametric amplifier (JTWPA) with three-wave mixing (3WM). The amplifier is based on a ladder transmission line consisting of flux-biased radio-frequency SQUIDs whose nonlinearity is of $\chi^{(2)}$-type. QPM is achieved in the 3WM process, $\omega_p=\omega_s+\omega_i$ (where $\omega_p$, $\omega_s$, and $\omega_i$ are the pump, signal, and idler frequencies, respectively) due to designing the JTWPA to include periodically inverted groups of these SQUIDs that reverse the sign of the nonlinearity. Modeling shows that the JTWPA bandwidth is relatively large (ca. $0.4\omega_p$) and flat, while unwanted modes, including $\omega_{2p}=2\omega_p$, $\omega_+=\omega_p +\omega_s$, $\omega_- = 2\omega_p - \omega_s$, etc., are strongly suppressed with the help of engineered dispersion., Comment: 6 pages, 4 figures

We have developed a concept for a traveling-wave parametric amplifier driven by a magnetic flux wave. The circuit consists of a serial array of symmetric dc SQUIDs coupled inductively to a separate superconducting LC transmission line carrying the pump microwave; thereby the signal and pump are applied to different ports. The proposed three-wave-mixing amplifier includes, firstly, an adjustable phase velocity of the signal (idler) wave and hence good phase matching yielding large gain in a wide frequency range and, secondly, overcoming of the pump depletion problem. The experimental parameters and characteristics of this amplifier have been evaluated and show promise for applications in quantum-information single-photon circuits., Comment: 14 pages incl. 5 figures

We have developed a recently proposed Josephson traveling-wave parametric amplifier with three-wave mixing [A. B. Zorin, Phys. Rev. Applied 6, 034006, 2016]. The amplifier consists of a microwave transmission line formed by a serial array of nonhysteretic one-junction SQUIDs. These SQUIDs are flux-biased in a way that the phase drops across the Josephson junctions are equal to 90 degrees and the persistent currents in the SQUID loops are equal to the Josephson critical current values. Such a one-dimensional metamaterial possesses a maximal quadratic nonlinearity and zero cubic (Kerr) nonlinearity. This property allows phase matching and exponential power gain of traveling microwaves to take place over a wide frequency range. We report the proof-of-principle experiment performed at a temperature of T = 4.2 K on Nb trilayer samples, which has demonstrated that our concept of a practical broadband Josephson parametric amplifier is valid and very promising for achieving quantum-limited operation., Comment: Submitted for presentation at the 16th International Superconductive Electronics Conference, ISEC 2017, 12-16 June 2017, Sorrento, Italy

We develop a concept of the traveling-wave Josephson parametric amplifier exploiting quadratic nonlinearity of a serial array of one-junction SQUIDs embedded in a superconducting transmission line. The external magnetic flux applied to the SQUIDs makes it possible to efficiently control the shape of their current-phase relation and, hence, the balance between quadratic and cubic (Kerr-like) nonlinearities. This property allows us to operate in the favorable three-wave-mixing mode with minimal phase mismatch, an exponential dependence of the power gain on number of sections $N$, a large bandwidth, a high dynamic range, and substantially separated signal ($f_s$) and pump ($f_p$) frequencies obeying relation $f_s+f_i = f_p$, where $f_i$ is the idler frequency. An estimation of the amplifier characteristics with typical experimental parameters, a pump frequency of $12$ GHz, and $N = 300$ yields a flat gain of 20 dB in the bandwidth of 5.6 GHz.

Using a Josephson junction interferometer (DC SQUID) as a microwave source for irradiating a single-electron trap, both devices fabricated on the same chip, we study the process of photon-assisted tunneling as an effective mechanism of single photon detection. High sensitivity down to a very small oscillation amplitude $v_{\rm J} \sim$ 10 nV$\ll E_{\rm act} \lesssim hf_{\rm J}$ and down to low photon absorption rates $\Gamma_{\rm ph} \sim$ (1--50)Hz, as well as a clear threshold type of operation with an activation energy $E_{\rm act} \sim$ 400 $\mu$eV, are demonstrated for the trap with respect to the microwave photons of frequency $f_{\rm J} \sim$ (100--200)GHz. Tunable generation is demonstrated with respect to the power and frequency of the microwave signal produced by the SQUID source biased within the subgap voltage range. A much weaker effect is observed at the higher junction voltages along the quasiparticle branch of the $I-V$ curve; this response mostly appears due to the recombination phonons., Comment: 4 pages, 4 figures

We investigate the magnetization reversal mechanism in an individual permalloy (Py) nanotube (NT) using a hybrid magnetometer consisting of a nanometer-scale SQUID (nanoSQUID) and a cantilever torque sensor. The Py NT is affixed to the tip of a Si cantilever and positioned in order to optimally couple its stray flux into a Nb nanoSQUID. We are thus able to measure both the NT's volume magnetization by dynamic cantilever magnetometry and its stray flux using the nanoSQUID. We observe a training effect and temperature dependence in the magnetic hysteresis, suggesting an exchange bias. We find a low blocking temperature $T_B = 18 \pm 2$ K, indicating the presence of a thin antiferromagnetic native oxide, as confirmed by X-ray absorption spectroscopy on similar samples. Furthermore, we measure changes in the shape of the magnetic hysteresis as a function of temperature and increased training. These observations show that the presence of a thin exchange-coupled native oxide modifies the magnetization reversal process at low temperatures. Complementary information obtained via cantilever and nanoSQUID magnetometry allows us to conclude that, in the absence of exchange coupling, this reversal process is nucleated at the NT's ends and propagates along its length as predicted by theory., Comment: 8 pages, 4 figures

An application-specific Josephson generator is being developed as an on-chip calibration source for single-microwave-photon detectors operating below $T \sim $100 mK in the frequency range from 110 to 170 GHz. The targeted calibration power corresponds to the photon detection rate of 0.01 to 10 counts per second. We analyze the Josephson oscillations within the framework of the tunnel junction microscopic (TJM) model and find the corrections to be made to a standard RSJ model of the junction, operating as a quasi-monochromatic source of microwaves. Experimentally, we implemented a number of aluminium-based two-junction interferometers connected to the leads via microstripline resistors made of partly oxidized titanium films. The $I$-$V$ curves exhibit a behaviour ensuring generation of the microwave signal in the frequency range required. By setting the biasing point $\bar{V}$ and applying the magnetic field, one can tune the generator's frequency and power, respectively. A small oscillation linewidth, down to a few GHz, and a low level of black-body radiation emitted by hot parts of the circuit are predicted, using the experimental parameters., Comment: 19 pages

Using an optimally coupled nanometer-scale superconducting quantum interference device, we measure the magnetic flux originating from an individual ferromagnetic Ni nanotube attached to a Si cantilever. At the same time, we detect the nanotube's volume magnetization using torque magnetometry. We observe both the predicted reversible and irreversible reversal processes. A detailed comparison with micromagnetic simulations suggests that vortex-like states are formed in different segments of the individual nanotube. Such stray-field free states are interesting for memory applications and non-invasive sensing., Comment: 12 pages, 4 figures

Nanoscale magnets might form the building blocks of next generation memories. To explore their functionality, magnetic sensing at the nanoscale is key. We present a multifunctional combination of a scanning nanometer-sized superconducting quantum interference device (nanoSQUID) and a Ni nanotube attached to an ultrasoft cantilever as a magnetic tip. We map out and analyze the magnetic coupling between the Ni tube and the Nb nanoSQUID, demonstrate imaging of an Abrikosov vortex trapped in the SQUID structure - which is important in ruling out spurious magnetic signals - and reveal the high potential of the nanoSQUID as an ultrasensitive displacement detector. Our results open a new avenue for fundamental studies of nanoscale magnetism and superconductivity., Comment: 7 pages, 5 figures

We present a detailed report of microwave irradiation of ultra-narrow superconducting nanowires. In our nanofabricated circuits containing a superconducting NbSi nanowire, a dc blockade of current flow was observed at low temperatures below a critical voltage Vc, a strong indicator of the existence of quantum phase-slip (QPS) in the nanowire. We describe the results of applying microwaves to these samples, using a range of frequencies and both continuous-wave and pulsed drive, in order to search for dual Shapiro steps which would constitute an unambiguous demonstration of quantum phase-slip. We observed no steps, and our subsequent thermal analysis suggests that the electron temperature in the series CrO resistors was significantly elevated above the substrate temperature, resulting in sufficient Johnson noise to wash out the steps. To understand the system and inform future work, we have constructed a numerical model of the dynamics of the circuit for dc and ac bias (both continuous wave and pulsed drive signals) in the presence of Johnson noise. Using this model, we outline important design considerations for device and measurement parameters which should be used in any future experiment to enable the observation of dual Shapiro steps at experimentally accessible temperatures and thus lead to the development of a QPS-based quantum current standard., Comment: 13 pages, 17 figures. Published version (a few minor text changes compared to v1)

A single-electron trap built with two Superconductor (S) - Insulator (I) - Normal (N) metal tunnel junctions and coupled to a readout SINIS-type single-electron transistor A (SET A) was studied in a photon detection regime. As a source of photon irradiation, we used an operating second SINIS-type SET B positioned in the vicinity of the trap. In the experiment, the average hold time of the trap was found to be critically dependent on the voltage across SET B. Starting in a certain voltage range, a photon-assisted electron escape was observed at a rate roughly proportional to the emission rate of the photons with energies exceeding the superconducting gap of S-electrodes in the trap. The discussed mechanism of photon emission and detection is of interest for low-temperature noise spectrometry and it can be of relevance for the ampere standard based on hybrid SINIS turnstiles., Comment: submitted, 3 pages, 3 figures

We propose a transistor-like circuit including two serially connected segments of a narrow superconducting nanowire joint by a wider segment with a capacitively coupled gate in between. This circuit is made of amorphous NbSi film and embedded in a network of on-chip Cr microresistors ensuring a sufficiently high external electromagnetic impedance. Assuming a virtual regime of quantum phase slips (QPS)in two narrow segments of the wire, leading to quantum interference of voltages on these segments, this circuit is dual to the dc SQUID. Our samples demonstrated appreciable Coulomb blockade voltage (analog of critical current of the SQUIDs) and periodic modulation of this blockade by an electrostatic gate (analog of flux modulation in the SQUIDs). The model of this QPS transistor is discussed., Comment: 5 pages including 3 figures; in v2 the title was updated, typos were fixed and 4 references added

The hold time $\tau$ of a single-electron trap is shown to increase significantly due to suppression of environmentally assisted tunneling events. Using two rf-tight radiation shields instead of a single one, we demonstrate increase of $\tau$ by a factor exceeding $10^3$, up to about 10 hours, for a trap with only two superconductor (S) -- normal-metal (N) tunnel junctions and an on-chip resistor $R$ (R-SNS structure). In the normal state, the improved shielding made it possible to observe $\tau\sim$ 100 s, which is in reasonable agreement with the quantum-leakage-limited level expected for the two-electron cotunneling process., Comment: 4 pages, 3 figures

Dissipative properties of the electromagnetic environment as well as on-chip RC filtering are shown to suppress random state switchings in the two-junction superconductor(S) - normal metal(N) electron trap. In our experiments, a local high-ohmic resistor increased the hold time of the trap by up to two orders of magnitude. A strong effect of on-chip noise filtering was observed for different on-chip geometries. The obtained results are promising for realization of the current standard on the basis of the S-N hybrid turnstile., Comment: 4 pages 3 figures LT26

We have designed an experiment and performed extensive simulations and preliminary measurements to identify a set of realistic circuit parameters that should allow the observation of constant-current steps at I=2ef in short arrays of small Josephson junctions under external AC drive of frequency f. Observation of these steps demonstrating phase lock of the Bloch oscillations with the external drive requires a high-impedance environment for the array, which is provided by on-chip resistors close to the junctions. We show that the width and shape of the steps crucially depend on the shape of the drive and the electron temperature in the resistors.

We investigated, at temperature $4.2\,\mathrm{K}$, electric transport, flux noise and resulting spin sensitivity of miniaturized Nb direct current superconducting quantum interference devices (SQUIDs) based on submicron Josephson junctions with HfTi barriers. The SQUIDs are either of the magnetometer-type or gradiometric in layout. In the white noise regime, for the best magnetometer we obtain a flux noise $S_{\Phi}^{1/2}=250\,\mathrm{n}\Phi_0/\mathrm{Hz}^{1/2}$, corresponding to a spin sensitivity $S^{1/2}_\mu\,\ge\,29\,\mu_B/\mathrm{Hz}^{1/2}$. For the gradiometer we find $S_{\Phi}^{1/2}=300\,\mathrm{n}\Phi_0/\mathrm{Hz}^{1/2}$ and $S^{1/2}_\mu\,\ge\,44\,\mu_B/\mathrm{Hz}^{1/2}$. The devices can still be optimized with respect to flux noise and coupling between a magnetic particle and the SQUID, leaving room for further improvement towards single spin resolution., Comment: 4 pages, 3 figures

We propose a threshold detector with an operation principle, based on a parametric period-doubling bifurcation in an externally pumped nonlinear resonance circuit. The ac-driven resonance circuit includes a dc-current-biased Josephson junction ensuring parametric frequency conversion (period-doubling bifurcation) due to its quadratic nonlinearity. A sharp onset of oscillations at the half-frequency of the drive allows for detection of small variations of an effective inductance and, therefore, the read-out of the quantum state of a coupled Josephson qubit. The bifurcation characteristics of this circuit are compared with those of the conventional Josephson bifurcation amplifier, and its possible advantages are discussed., Comment: 6 pages

We have investigated the static, charge-trapping properties of a hybrid superconductor---normal metal electron turnstile embedded into a high-ohmic environment. The device includes a local Cr resistor on one side of the turnstile, and a superconducting trapping island on the other side. The electron hold times, t ~ 2-20s, in our two-junction circuit are comparable with those of typical multi-junction, N >= 4, normal-metal single-electron tunneling devices. A semi-phenomenological model of the environmental activation of tunneling is applied for the analysis of the switching statistics. The experimental results are promising for electrical metrology., Comment: Submitted to New Journal of Physics 2010

The difference between the phases of superconducting order parameter plays in superconducting circuits the role similar to that played by the electrostatic potential difference required to drive a current in conventional circuits. This fundamental property can be altered by inserting in a superconducting circuit a particular type of weak link, the so-called Josephson $\pi$-junction having inverted current-phase relation and enabling a shift of the phase by $\pi$. We demonstrate the operation of three superconducting circuits -- two of them are classical and one quantum -- which all utilize such $\pi$-phase shifters realized using superconductor-ferromagnet-superconductor sandwich technology. The classical circuits are based on single-flux-quantum cells, which are shown to be scalable and compatible with conventional niobium-based superconducting electronics. The quantum circuit is a $\pi$-phase biased qubit, for which we observe coherent Rabi oscillations and compare the measured coherence time with that of conventional superconducting phase qubits., Comment: 14 pages, 4 figures

We propose a superconducting phase qubit on the basis of the radio-frequency SQUID with the screening parameter value $\beta_L = (2\pi/\Phi_0)LI_c \approx 1$, biased by a half flux quantum $\Phi_e=\Phi_0/2$. Significant anharmonicity ($> 30%$) can be achieved in this system due to the interplay of the cosine Josephson potential and the parabolic magnetic-energy potential that ultimately leads to the quartic polynomial shape of the well. The two lowest eigenstates in this global minimum perfectly suit for the qubit which is insensitive to the charge variable, biased in the optimal point and allows an efficient dispersive readout. Moreover, the transition frequency in this qubit can be tuned within an appreciable range allowing variable qubit-qubit coupling., Comment: 5 pages incl. 5 figures

Pumping characteristics were studied of the hybrid normal-metal/superconductor single-electron transistor embedded in a high-ohmic environment. Two 3 micrometer-long microstrip resistors of CrOx with a sum resistance R=80kOhm were placed adjacent to this hybrid device. Substantial improvement of pumping and reduction of the subgap leakage were observed in the low-MHz range. At higher frequencies 0.1-1GHz, a slowdown of tunneling due to the enhanced damping and electron heating negatively affected the pumping, as compared to the reference bare devices., Comment: 3 pages 4 figures

Electron counting experiments attempt to provide a current of a known number of electrons per unit time. We propose architectures utilizing a few readily available electron-pumps or turnstiles with the typical error rates of 100 ppm with common sensitive electrometers to achieve the desirable accuracy of 1 part in 10 ppb. This is achieved not by counting all transferred electrons but by counting only the errors of individual devices; these are less frequent and therefore readily recognized and accounted for. We thereby ease the route towards quantum based standards for current and capacitance., Comment: submitted for publication

We investigate the quantum dynamics of a quadratic-quartic anharmonic oscillator formed by a potential well between two potential barriers. We realize this novel potential shape with a superconducting circuit comprised of a loop interrupted by two Josephson junctions, with near-zero current bias and flux bias near half a flux quantum. We investigate escape out of the central well, which can occur via tunneling through either of the two barriers, and find good agreement with a generalized double-path macroscopic quantum tunneling theory. We also demonstrate that this system exhibits an "optimal line" in current and flux bias space along which the oscillator, which can be operated as a phase qubit, is insensitive to decoherence due to low-frequency current fluctuations.

We have analyzed quasiparticle transitions in an Al charge-phase qubit inducing a dynamic change of the qubit states. The time-averaged mixed state is related to the strong coupling of the qubit to an ensemble of non-equilibrium quasiparticles in the leads. Such quasiparticles tunnel stochastically on and off the island and can excite the qubit. Continuous monitoring of the qubit impedance at a frequency of 80 MHz shows the admixture of the excited state. We present a numerical description of these cyclic transitions and compare it with our experimental data., Comment: 13 pages, 3 figures

We introduce a three-junction SQUID that can be effectively used as an optimal tunable element in Josephson quantum computing applications. This device can replace the simple dc SQUID generally used as tunable element in this kind of applications, with a series of advantages for the coherence time and for the tolerance to small errors. We study the device both theoretically and experimentally at 4.2 K, obtaining a good agreement between the results., Comment: 3 pages, 4 figures

We propose and demonstrate the functioning of a special Rapid Single Flux Quantum (RSFQ) circuit with frequency-dependent damping. This damping is achieved by shunting individual Josephson junctions by pieces of open-ended RC transmission lines. Our circuit includes a toggle flip-flop cell, Josephson transmission lines transferring single flux quantum pulses to and from this cell, as well as DC/SFQ and SFQ/DC converters. Due to the desired frequency-dispersion in the RC line shunts which ensures sufficiently low noise at low frequencies, such circuits are well-suited for integrating with the flux/phase Josephson qubit and enable its efficient control., Comment: 6 pages incl. 6 figures

We investigated transitions in Al charge-phase qubits of SQUID-configuration inductively coupled to an rf tank circuit that made it possible to read out the state by measuring the inductance of the qubit. Depending on the flux and charge bias and the amplitude of the rf oscillations we probed either the ground state or a dynamic change of the qubit states which we attributed to stochastic single quasi-particle tunneling onto and off the qubit island and exchange of energy with the qubit. Within this model, a selection rule for quasi-particle-induced transitions in the qubit is discussed., Comment: 7 pages, 4 figures, major changes in the revised manuscript

The dc transport properties of long arrays of small Al Josephson junctions, biased through on-chip Cr resistors, are studied. The IV-characteristics show a large Coulomb threshold for current as well as negative-slope regions indicating the regime of autonomous Bloch oscillations up to rather high frequencies of f = I/2e ~1 GHz, comparable to those reported by other groups for single junctions. On the other hand, a small depth of the back-bending implies a low duty cycle and a broad spectrum of the oscillations, which we attribute to the insufficiently high impedance of the bias resistors. A self-sustained switching process at a small bias current is used to study the statistics of the switching voltages and to determine the effective Bloch capacitance which was found to considerably exceed the geometric junction capacitance., Comment: 13 pages 5 figures

Self-shunted aluminum Josephson junctions with high-transparency barriers were fabricated using the shadow-evaporation technique and measured at low temperatures, T=25 mK. Due to high junction transparency, the IV-characteristics were found to be of only small hysteresis with retrapping-to-switching current ratio of up to 80%. The observed critical currents were close to the Ambegaokar-Baratoff values (up to 80-100%). Good barrier quality was confirmed by the low subgap leakage currents in the quasiparticle branches, which makes the self-shunted Al junctions promising for application in integrated RSFQ-qubit circuitry., Comment: 3 pages; 2 figures

We investigate the current-voltage characteristics of high-transparency superconductor-insulator-normal metal (SIN) junctions with the specific tunnel resistance below 30 kOhm per square micron. The junctions were fabricated from different superconducting and normal conducting materials, including Nb, Al, AuPd and Cu. The subgap leakage currents were found to be appreciably larger than those given by the standard tunnelling model. We explain our results using the model of two-electron tunnelling in the coherent diffusive transport regime. We demonstrate that even in the high-transparency SIN-junctions, a noticeable reduction of the subgap current can be achieved by splitting a junction into several submicron sub-junctions. These structures can be used as nonlinear low-noise shunts in Rapid-Single-Flux-Quantum (RSFQ) circuitry for controlling Josephson qubits., Comment: 6 pages, 5 figures, 1 table

We present investigations of Josephson charge-phase qubits inductively coupled to a radio-frequency driven tank-circuit enabling the readout of the states by measuring the Josephson inductance of the qubit. The circuits including junctions with linear dimensions of 60 nm and 80 nm are fabricated from Nb trilayer and allowing the determination of relevant sample parameters at liquid helium temperature. The observed partial suppression of the circulating supercurrent at 4.2 K is explained in the framework of a quantum statistical model. We have probed the ground-state properties of qubit structures with different ratios of the Josephson coupling to Coulomb charging energy at 20 mK, demonstrating both the magnetic control of phase and the electrostatic control of charge on the qubit island., Comment: 8 pages, 8 figures

Within the framework of the microscopic model of tunneling, we modelled the behavior of the Josephson junction shunted by the Superconductor-Insulator-Normal metal (SIN) tunnel junction. We found that the electromagnetic impedance of the SIN junction yields both the frequency-dependent damping and dynamic reactance which leads to an increase in the effective capacitance of the circuit. We calculated the dc I-V curves and transient characteristics of these circuits and explained their quantitative differences to the curves obtained within the resistively shunted junction model. The correct operation of the basic single-flux-quanta circuits with such SIN-shunted junctions, i.e. the Josephson transmission line and the toggle flip-flop, have also been modelled., Comment: 8 pages incl. 7 figures

We show that the electrical impedance of a small-capacitance Josephson junction includes besides the capacitive term $-i/\omega C_B$ also an inductive term $i\omega L_B$. Similar to the known Bloch capacitance $C_B(q)$, the Bloch inductance $L_B(q)$ also depends periodically on the quasicharge $q$, and its maximum value achieved at $q=e (\textrm{mod} 2e)$ always exceeds the value of the Josephson inductance of this junction $L_J(\phi)$ at fixed $\phi=0$. The effect of the Bloch inductance on the dynamics of a single junction and a one-dimensional array is described., Comment: 5 pages incl. 3 figs

A capacitance standard based on the definition of capacitance C = Ne/U is realized when a capacitor is charged with a known number N of electrons (e is the elementary charge) and the voltage U across the capacitor is measured. If U is measured by means of a Josephson voltage standard, C is solely determined by quantum numbers and fundamental constants. Presently, PTB is setting up this experiment using a special type of single-electron pump, the so-called r-pump, for transferring electrons one by one onto a cryogenic vacuum capacitor with the decadic capacitance C = 1 pF. We report on the progress in the setup with emphasis on the characterization of the single-electron tunneling elements. We describe the modifications of the single-electron circuit that are necessary to implement the capacitor charging experiment by using a four- or five-junction r-pump., Comment: 11 pages, 5 figures

We demonstrate that shunting of Superconductor-Insulator-Superconductor Josephson junctions by Superconductor-Insulator-Normal metal (S-I-N) structures having pronounced non-linear I-V characteristics can remarkably modify the Josephson dynamics. In the regime of Josephson generation the phase behaves as an overdamped coordinate, while in the superconducting state the damping and current noise are strikingly small, that is vitally important for application of such junctions for readout and control of Josephson qubits. Superconducting Nb/AlO${_x}$/Nb junction shunted by Nb/AlO${_x}$/AuPd junction of S-I-N type was fabricated and, in agreement with our model, exhibited non-hysteretic I-V characteristics at temperatures down to at least 1.4 K., Comment: 4 pages incl. 3 figures

Josephson junction transistors and 50-junction arrays with linear junction dimensions from 200 nm down to 70 nm were fabricated from standard Nb/AlOx/Nb trilayers. The fabrication process includes electron beam lithography, dry etching, anodization, and planarization by chemical-mechanical polishing. The samples were characterized at temperatures down to 25 mK. In general, all junctions are of high quality and their I-U characteristics show low leakage currents and high superconducting energy gap values of 1.35 meV. The characteristics of the transistors and arrays exhibit some features in the subgap area, associated with tunneling of Cooper pairs, quasiparticles and their combinations due to the redistribution of the bias voltage between the junctions. Total island capacitances of the transistor samples ranged from 1.5 fF to 4 fF, depending on the junction sizes. Devices made of junctions with linear dimensions below 100 nm by 100 nm demonstrate a remarkable single-electron behavior in both superconducting and normal state. We also investigated the area dependence of the junction capacitances for transistor and array samples., Comment: 19 pages incl. 2 tables and 11 figures

The Cooper pair box qubit of SQUID configuration enables the readout of the qubit states by probing the effective Josephson inductance of the SQUID. This is realized by coupling the qubit to a tank circuit which induces a small alternating supercurrent in the SQUID loop. The effect of a small (but finite) geometrical inductance of the loop on the eigenstates of the system is figured out. The effect of qubit dephasing due to quadratic coupling to the tank circuit is evaluated. It is shown that the rate of dephasing in the vicinity of the magic points is relatively low unless the Josephson junctions forming the qubit are rather dissimilar. In the vicinity of the avoided level-crossing point such dephasing is always significant., Comment: 10 pages incl. 2 figures

The charge-phase Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the qubit in magic points producing minimum decoherence are given., Comment: 11 pages incl. 6 figs

We investigate low-temperature and low-voltage-bias charge transport in a superconducting Al single electron transistor in a dissipating environment, realized as on-chip high-ohmic Cr microstrips. In our samples with relatively large charging energy values Ec > EJ, where EJ is the energy of the Josephson coupling, two transport mechanisms were found to be dominating, both based on discrete tunneling of individual Cooper pairs: Depending on the gate voltage Vg, either sequential tunneling of pairs via the transistor island (in the open state of the transistor around the points Qg = CgVg = e mod(2e), where Cg is the gate capacitance) or their cotunneling through the transistor (for Qg away of these points) was found to prevail in the net current. As the open states of our transistors had been found to be unstable with respect to quasiparticle poisoning, high-frequency gate cycling (at f ~ 1 MHz) was applied to study the sequential tunneling mechanism. A simple model based on the master equation was found to be in a good agreement with the experimental data., Comment: 8 pages, 6 figures

We observed current-voltage characteristics of superconducting single charge transistors with on-chip resistors of R about R_Q = h/4e^2 = 6.45 kOhm, which are explained in terms of Cooper-pair cotunneling. Both the effective strength of Josephson coupling and the cotunneling current are modulated by the gate-induced charge on the transistor island. For increasing values of the resistance R we found the Cooper pair current at small transport voltages to be dramatically suppressed., Comment: 4 pages and 2 figures

An all-superconductor charge qubit enabling a radio-frequency readout of its quantum state is described. The core element of the setup is a superconducting loop which includes the single-Cooper-pair (Bloch) transistor. This circuit has two functions: First, it operates as a charge qubit with magnetic control of Josephson coupling and electrostatic control of the charge on the transistor island. Secondly, it acts as the transducer of the rf electrometer, which probes the qubit state by measuring the Josephson inductance of the transistor. The evaluation of the basic parameters of this device shows its superiority over the rf-SET-based qubit setup., Comment: 4 pages incl. 3 figues; the SQUID'2001 paper, to be published in Physica C

Deep submicron Al-AlOx-Nb tunnel junctions and single electron transistors with niobium islands were fabricated by electron beam gun shadow evaporation. Using stencil masks consisting of the thermostable polymer polyethersulfone (PES) and germanium, high quality niobium patterns with good superconducting properties and a gap energy of up to 2Delta = 2.5 meV for the niobium were achieved. The I(U) characteristics of the transistors show special features due to tunneling of single Cooper pairs and significant gate modulation in both the superconducting and the normal state., Comment: 4 pages, 4 figures

The effect of thermal annealing on the properties of Al-AlOx-Al single electron tunneling transistors is reported. After treatment of the devices by annealing processes in forming gas atmosphere at different temperatures and for different times, distinct and reproducible changes of their resistance and capacitance values were found. According to the temperature regime, we observed different behaviors as regards the resistance changes, namely the tendency to decrease the resistance by annealing at T = 200 degree C, but to increase the resistance by annealing at T = 400 degree C. We attribute this behavior to changes in the aluminum oxide barriers of the tunnel junctions. The good reproducibility of these effects with respect to the changes observed allows the proper annealing treatment to be used for post-process tuning of tunnel junction parameters. Also, the influence of the annealing treatment on the noise properties of the transistors at low frequency was investigated. In no case did the noise figures in the 1/f-regime show significant changes., Comment: 6 pages, 7 eps-figures

We report on the effect of the frequency-locked transfer of single Cooper pairs in a superconducting single-electron Al transistor embedded in a dissipative environment (on-chip Cr resistor of R = 40 kOhm). The transistor was dc voltage biased, and the harmonic signal of frequency f of several MHz was applied to the gate. Due to the substantial rate of relaxation, the unidirectional transfer of single pairs occurred in each junction once per clock cycle and the current plateaus at I = 2ef were developed in the transistor's I-V curves. The mechanisms (supercurrent, Landau-Zener tunneling, quasiparticle tunneling, etc.) deteriorating the phase-locking regime are discussed., Comment: 5 pages incl. 3 figures

A quantum-limited electrometer based on charge modulation of the Josephson supercurrent in the Bloch transistor inserted into a superconducting ring is proposed. As this ring is inductive coupled to a high-Q resonance tank circuit, the variations of the charge on the transistor island (input signal) are converted into variations of amplitude and phase of radio-frequency oscillations in the tank. These variations are amplified and then detected. The output noise, the back-action fluctuations and their cross-correlation are computed. It is shown that our device enables measurements of the charge with a sensitivity which is determined by the energy resolution of its amplifier, that can be reduced down to the standard quantum limit of \hbar/2. On the basis of this setup a "back-action-evading" scheme of the charge measurements is proposed., Comment: 5 pages incl. 2 figures