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Models of light–matter interactions in quantum electrodynamics typically invoke the dipole approximation1,2, in which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes with which they interact. However, when the ratio between the size of the atom and the mode wavelength is increased, the dipole approximation no longer holds and the atom is referred to as a ‘giant atom’2,3. So far, experimental studies with solid-state devices in the giant-atom regime have been limited to superconducting qubits that couple to short-wavelength surface acoustic waves4–10, probing the properties of the atom at only a single frequency. Here we use an alternative architecture that realizes a giant atom by coupling small atoms to a waveguide at multiple, but well separated, discrete locations. This system enables tunable atom–waveguide couplings with large on–off ratios3 and a coupling spectrum that can be engineered by the design of the device. We also demonstrate decoherence-free interactions between multiple giant atoms that are mediated by the quasi-continuous spectrum of modes in the waveguide—an effect that is not achievable using small atoms11. These features allow qubits in this architecture to switch between protected and emissive configurations in situ while retaining qubit–qubit interactions, opening up possibilities for high-fidelity quantum simulations and non-classical itinerant photon generation12,13. Superconducting giant atoms are realized in a waveguide by coupling small atoms to the waveguide at multiple discrete locations, producing tunable atom–waveguide coupling and enabling decoherence-free interactions.

High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent and use of coupler elements to tunably control two-qubit interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling and frequency crowding issues. Nonetheless, two-qubit gate errors still limit the capability of near-term quantum applications. The reason, in part, is the existing framework for tunable couplers based on the dispersive approximation does not fully incorporate three-body multi-level dynamics, which is essential for addressing coherent leakage to the coupler and parasitic longitudinal ($ZZ$) interactions during two-qubit gates. Here, we present a systematic approach that goes beyond the dispersive approximation to exploit the engineered level structure of the coupler and optimize its control. Using this approach, we experimentally demonstrate CZ and $ZZ$-free iSWAP gates with two-qubit interaction fidelities of $99.76 \pm 0.07$% and $99.87 \pm 0.23$%, respectively, which are close to their $T_1$ limits., Comment: 34 pages, 39 figures

Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices., 21 pages, 12 figures

We experimentally demonstrate a new method of generating entangled itinerant photons using waveguide quantum electrodynamics., Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we reconstruct the moments and correlations of the photonic modes and demonstrate state preparation fidelities of 84%. Our results provide a path toward realizing quantum communication and teleportation protocols using itinerant photons generated by quantum interference within a waveguide quantum electrodynamics architecture.

The dominant source of decoherence in contemporary frequency-tunable superconducting qubits is 1/$f$ flux noise. To understand its origin and find ways to minimize its impact, we systematically study flux noise amplitudes in more than 50 flux qubits with varied SQUID geometry parameters and compare our results to a microscopic model of magnetic spin defects located at the interfaces surrounding the SQUID loops. Our data are in agreement with an extension of the previously proposed model, based on numerical simulations of the current distribution in the investigated SQUIDs. Our results and detailed model provide a guide for minimizing the flux noise susceptibility in future circuits., 14 pages, 6 figures

Solid-state qubits with transition frequencies in the microwave regime, such as superconducting qubits, are at the forefront of quantum information processing. However, high-fidelity, simultaneous control of superconducting qubits at even a moderate scale remains a challenge, partly due to the complexities of packaging these devices. Here, we present an approach to microwave package design focusing on material choices, signal line engineering, and spurious mode suppression. We describe design guidelines validated using simulations and measurements used to develop a 24-port microwave package. Analyzing the qubit environment reveals no spurious modes up to 11GHz. The material and geometric design choices enable the package to support qubits with lifetimes exceeding 350 {\mu}s. The microwave package design guidelines presented here address many issues relevant for near-term quantum processors., Comment: 15 pages, 9 figures

Extending qubit lifetime through a shaped environment Qubits are the quantum two-level systems that encode and process information in quantum computing. Kept in isolation, qubits can be stable. In a practical setting, however, qubits must be addressed and interact with each other. Such an environment is typically viewed as a source of decoherence and has a detrimental effect on a qubit's ability to retain encoded information. Gustavsson et al. used a sequence of pulses as a source of “environment shaping” that could substantially increase the coherence time of a superconducting qubit. Science , this issue p. 1573

© 2019 IEEE. Over the past two decades, the performance of superconducting quantum circuits has tremendously improved. The progress of superconducting qubits enabled a new industry branch to emerge from global technology enterprises to quantum computing startups. Here, an overview of superconducting quantum circuit microwave control is presented. Furthermore, we discuss one of the persistent engineering challenges in the field - how to control the electromagnetic environment of increasingly complex superconducting circuits such that they are simultaneously protected and efficiently controllable.

Quantum coherence and control is foundational to the science and engineering of quantum systems. In van der Waals (vdW) materials, the collective coherent behavior of carriers has been probed successfully by transport measurements. However, temporal coherence and control, as exemplified by manipulating a single quantum degree of freedom, remains to be verified. Here we demonstrate such coherence and control of a superconducting circuit incorporating graphene-based Josephson junctions. Furthermore, we show that this device can be operated as a voltage-tunable transmon qubit, whose spectrum reflects the electronic properties of massless Dirac fermions traveling ballistically. In addition to the potential for advancing extensible quantum computing technology, our results represent a new approach to studying vdW materials using microwave photons in coherent quantum circuits.

In the cavity-QED architecture, photon number fluctuations from residual cavity photons cause qubit dephasing due to the ac Stark effect. These unwanted photons originate from a variety of sources, such as thermal radiation, leftover measurement photons, and cross talk. Using a capacitively shunted flux qubit coupled to a transmission line cavity, we demonstrate a method that identifies and distinguishes coherent and thermal photons based on noise-spectral reconstruction from time-domain spin-locking relaxometry. Using these measurements, we attribute the limiting dephasing source in our system to thermal photons rather than coherent photons. By improving the cryogenic attenuation on lines leading to the cavity, we successfully suppress residual thermal photons and achieve T_{1}-limited spin-echo decay time. The spin-locking noise-spectroscopy technique allows broad frequency access and readily applies to other qubit modalities for identifying general asymmetric nonclassical noise spectra.

The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 μs at its flux-insensitive point. Qubit relaxation times T1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f-flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85 μs, approximately the 2T1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2 in contemporary qubits based on transverse qubit–resonator interaction., Scalable quantum information processing requires controllable high-coherence qubits. Here, the authors present superconducting flux qubits with broad frequency tunability, strong anharmonicity and high reproducibility, identifying photon shot noise as the main source of dephasing for further improvements.

Detuning a superconducting qubit from its rotating frame is one means to implement a Z-gate operation. In this work, we implement a Z gate by pulsing a current through the qubit’s readout dc SQUID. While the dc SQUID acts as a magnetic flux sensor for qubit readout, we in turn may use it as a flux actuator with tunable strength to impose a qubit frequency shift. Using this approach, we demonstrate Ramsey-type free-induction experiments with time constants as long as 280 ns and rotation frequencies as high as 1.4 GHz. We experimentally demonstrate an inferred Z-gate fidelity of approximately 90%, limited largely by the bandwidth of our system. In the absence of this limitation, we argue that the inferred fidelity may be improved to as high as 99%.

Gate operations in a quantum information processor are generally realized by tailoring specific periods of free and driven evolution of a quantum system. Unwanted environmental noise, which may in principle be distinct during these two periods, acts to decohere the system and increase the gate error rate. Although there has been significant progress characterizing noise processes during free evolution, the corresponding driven-evolution case is more challenging as the noise being probed is also extant during the characterization protocol. Here we demonstrate the noise spectroscopy (0.1-200 MHz) of a superconducting flux qubit during driven evolution by using a robust spin-locking pulse sequence to measure relaxation (T1ρ) in the rotating frame. In the case of flux noise, we resolve spectral features due to coherent fluctuators, and further identify a signature of the 1 MHz defect in a time-domain spin-echo experiment. The driven-evolution noise spectroscopy complements free-evolution methods, enabling the means to characterize and distinguish various noise processes relevant for universal quantum control. © 2013 Macmillan Publishers Limited. All rights reserved.

Remarkable advancements in coherence and control fidelity have been achieved in recent years with cryogenic solid-state qubits. Nonetheless, thermalizing such devices to their milliKelvin environments has remained a long-standing fundamental and technical challenge. In this context, we present a systematic study of the first-excited-state population in a 3D transmon superconducting qubit mounted in a dilution refrigerator with a variable temperature. Using a modified version of the protocol developed by Geerlings et al., we observe the excited-state population to be consistent with a Maxwell-Boltzmann distribution, i.e., a qubit in thermal equilibrium with the refrigerator, over the temperature range 35-150 mK. Below 35 mK, the excited-state population saturates at approximately 0.1%. We verified this result using a flux qubit with ten times stronger coupling to its readout resonator. We conclude that these qubits have effective temperature T(eff)=35 mK. Assuming T(eff) is due solely to hot quasiparticles, the inferred qubit lifetime is 108 μs and in plausible agreement with the measured 80 μs.

We present two experimental schemes that can be used to implement the Factorized Quantum Lattice-Gas Algorithm for the 1D Diffusion Equation with Persistent-Current (PC) Qubits. One scheme involves biasing the PC Qubit at multiple flux bias points throughout the course of the algorithm. An implementation analogous to that done in Nuclear Magnetic Resonance (NMR) Quantum Computing is also developed. Errors due to a few key approximations utilized are discussed and differences between the PC Qubit and NMR systems are highlighted

We measured the energy relaxation time in a Nb superconducting persistent current qubit using a time-resolved fast measurement scheme. The energy relaxation time is longer than 10/spl mu/s, showing a strong potential of realizing quantum computation with Nb-based superconducting qubits.

Monolithic integration of control electronics with superconducting qubits will facilitate scalability of a superconducting quantum computer by reducing the room temperature electronics necessary for performing quantum state manipulation. We report the experimental results of the monolithic integration of an on-chip radiation source with a persistent-current (PC) qubit and dc SQUID measurement device. The devices were fabricated at MIT Lincoln Laboratory in a Nb/Al/AlOx/Nb trilayer process. The two PC qubit states were detected by measuring the switching current of an underdamped dc SQUID magnetometer inductively coupled to the qubit. The radiation source comprised an overdamped dc SQUID operating in the voltage state and inductively coupled to the qubit and measurement SQUID through a low-Q RLC filter. The oscillator was designed to have tunable amplitude and frequency to satisfy the requirements for coherent quantum manipulation of a superconducting PC qubit. We will discuss the measurements in the millikelvin regime and the effects of the oscillator noise on the state of the qubit.

We present experiments to characterize a Nb persistent-current qubit as a two-state system. The magnetization signal from the qubit is read-out by a DC-SQUID with near single-shot efficiency. Experiments varying SQUID ramp-rate and temperature suggest thermal activation occurs between the two circulating current states. Such data can be used to fit the parameters of the system, in order to characterize its performance as a potential quantum bit.

We design an RSFQ oscillator with a variable duty cycle to drive a superconductive qubit. This design has been optimized to minimize the decoherence when coupled to the superconductive persistent current qubit. A continuous RSFQ ring oscillator reads the contents of a Non-Destructive Read Out memory cell. By using two out-of-phase counters to Set and Reset the cell, we can vary the duty cycle of the pulses read from the memory cell. This train of flux quanta is filtered, then used to drive the persistent current qubit. The precision is sufficient to measure relaxation time and possibly Rabi oscillations.

A fluxon in a Josephson-junction parallel array behaves like a single particle in a periodic pinning potential. Different configurations of critical currents and cell areas result in different profiles for the fluxon potential. We analyze the minimal conditions to achieve an effective potential in which mirror symmetry is absent, namely a fluxon ratchet potential. Following one of the configurations, we designed circular arrays and probed some of the fluxon properties. Theoretical predictions are nicely fulfilled by the experiments.

Superconducting quantum circuits have been proposed as qubits for developing quantum computation. The goal is to use superconducting quantum circuits to model the measurement process, understand the sources of decoherence, and to develop scalable algorithms. A particularly promising feature of using superconducting technology is the potential of developing high-speed, on-chip control circuitry with single-flux quantum (SFQ) electronics. The picosecond time scales of SFQ electronics means that the superconducting qubits can be controlled rapidly on the time scale that the qubits remain phase-coherent. Recent progress and the major challenges are presented.

We present measurements of coherence and successive decay dynamics of higher energy levels of a superconducting transmon qubit. By applying consecutive $\pi$-pulses for each sequential transition frequency, we excite the qubit from the ground state up to its fourth excited level and characterize the decay and coherence of each state. We find the decay to proceed mainly sequentially, with relaxation times in excess of 20 $\mu$s for all transitions. We also provide a direct measurement of the charge dispersion of these levels by analyzing beating patterns in Ramsey fringes. The results demonstrate the feasibility of using higher levels in transmon qubits for encoding quantum information., Comment: Minor corrections. Added two plots in Figure 2. Added figures of the setup and the Ramsey fits in the supplemental material, as as more details on the device characterization. Rephrased last paragraph on charge dissipation. Added some references

One-dimensional parallel arrays of Josephson junctions have the ability to perform as oscillators tunable by magnetic flux. We have designed and tested an array impedance matched to a detector junction load. The amplitude and frequency of the array are controlled by the independent variables of magnetic field and current bias. We report on the array's characteristics and compare them to the results predicted by nonlinear simulations and a linear circuit model. This confirms the accuracy of the circuit model, both for impedance matching and in describing the dynamics of the array, even in a multiple-frequency regime.

A general method is illustrated to show that the Hamiltonian for circuits of Josephson junctions can be expanded in terms of three Hamiltonians: a Hamiltonian representative of the inductance-free circuit, a Hamiltonian in the form of an harmonic oscillator for the inductance effects of the circulating currents, and a small correction term. This method is used to show that the inductive effects are a small correction to the difference in energy levels in the persistent current qubit.

Parallel arrays of underdamped Josephson junctions are interesting due to their ability to produce coherent radiation. For a broad range of array parameters, we find that these arrays have solutions which can be represented as traveling waves with a small number of harmonics. We develop equivalent circuits for the DC and AC response using a harmonic balance technique. The reflection and transmission properties at the boundaries are studied by adding a passive terminating load to the array. We also develop a load criteria for optimal output power to both passive and nonlinear loads.

We present experimental results and numerical simulations of a new phase-locked state in two-dimensional arrays when nearly fully frustrated and driven by a dc current. In this state, all the rows of the array act coherently and phase-lock at a voltage that depends on the geometric loop inductance and junction capacitance. We also experimentally observe the resonance in one-dimensional ladder arrays, implying that two-dimensional arrays have inter-row phase-locking mechanisms. The horizontal junctions also appear to play a role in the dynamics. Two-dimensional arrays have been proposed as tunable microwave oscillators.

We have measured a novel phase-locked state in discrete parallel arrays of Josephson junctions which can be used for oscillator applications. Previous Josephson junction oscillators have been based on the Eck step, where a large-amplitude wave of nearly a single harmonic travels through the system. Multi-row systems biased on the Eck step could improve the output power, but their in-phase oscillations are difficult to stabilize. A new in-phase state which is very stable has been measured as a step in the dc I-V characteristic of one and two row systems. Simulations show that large-amplitude oscillations of two harmonics characterize the state. The rows are phase-locked and in-phase for the higher harmonic. We present an analytic expression for the oscillation frequencies and their magnetic tunability.

We present a new method for determining pulse imperfections and improving the single-gate fidelity in a superconducting qubit. By applying consecutive positive and negative pi pulses, we amplify the qubit evolution due to microwave pulse distortions, which causes the qubit state to rotate around an axis perpendicular to the intended rotation axis. Measuring these rotations as a function of pulse period allows us to reconstruct the shape of the microwave pulse arriving at the sample. Using the extracted response to predistort the input signal, we are able to reduce the average error per gate by 37%, which enables us to reach an average single-qubit gate fidelity higher than 0.998. DOI: 10.1103/PhysRevLett.110.040502

Measurements and numerical studies of the self-induced magnetic field effects on flux flow in two-dimensional arrays of niobium Josephson junctions have been performed. It was found that the flux-flow resistance becomes larger as the penetration depth of the array decreases. A phenomenological model, which agrees qualitatively with the experiments and simulations, is presented to explain the self-field effects on flux flow. Due to the smaller spatial extent of supercurrents around a vortex when self-fields are important, both the mass of the vortex and the array viscosity decrease. The decreased mass and viscosity lead to an increase in flux-flow resistance. The effects of spin-wave damping are also discussed for underdamped arrays. Measurements and simulations on the spatial dependence of flux flow indicate that more complex dynamics is involved in the flux-flow regime than a simple linear flow of the vortices.

We have measured and modeled the dynamics of inductively coupled discrete arrays of niobium Josephson junctions. We see splitting of the Eck step in the current‐voltage characteristic. Numerical simulations reproduce this splitting and are used to find an approximate solution for the junction phases at resonance. Using the technique of harmonic balance, we find an analytic expression for the resonance frequencies and the voltages that match this splitting. We can also predict the amplitude of these oscillations. The analytical results describe both the experiments and simulations well.

We propose and demonstrate the use of underdamped, one-dimensional parallel arrays of Josephson junctions as a tool for circuit diagnostics. By measuring the Fiske modes and the critical current in a magnetic field, we determined the self and nearest neighbor inductances as well as the capacitances of single junctions. We have used this technique to find the capacitance of Nb-Al/sub 2/O/sub x/-Nb junctions for critical current densities of 0.3-20 kA/cm/sup 2/. We find that the specific capacitance increases by about a factor of 2 over this range. This increase has important consequences for the design of single-flux-quantum circuits and SQUIDs. Measurement of the junction capacitance for critical current densities of 100 kA/cm/sup 2/ is possible, but requires submicron junctions with dimensions of the order of 0.3 /spl mu/m. >

We have measured two-dimensional niobium Josephson junction arrays in which self induced fields are important. We find an increase of the depinning current when /spl lambda//sub /spl perp//, the penetration depth in the array, is of the order of one. There is evidence for a destruction of commensurate vortex states in the arrays as the depinning current becomes almost independent of the applied magnetic field. Our data also show that self-field effects change the array flux-flow dynamics and decrease the effective array viscosity. >

Circular arrays of underdamped Josephson junctions exhibit a series of resonant steps in the return path of the subgap region in the current-voltage characteristics. We show that the voltage locations of the steps can be predicted by studying the parametric instabilities of whirling periodic solutions, and experimentally verify the prediction in a ring of 8 underdamped junctions. The whirling modes become unstable in certain voltage intervals, and a branch (a resonant step) of more complicated solutions emerges from the endpoint of each interval. We extend the analysis to open-ended arrays and find that for f=0, the onset of a zero-field step has the same underlying mechanism. For f>0, combinations of lattice eigen-frequencies are excited. >

We analyze the damped driven discrete sine-Gordon equation. For underdamped, highly discrete systems, we show that whirling periodic solutions undergo parametric instabilities at certain drive strengths. The theory predicts novel resonant steps in the current-voltage characteristics of discrete Josephson rings, occurring in the return path of the subgap region. We have observed these steps experimentally in a ring of 8 underdamped junctions. An unusual prediction, verified experimentally, is that such steps occur even if there are no vortices in the ring. Numerical simulations indicate that complex spatiotemporal behavior occurs past the onset of instability.

We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our $1/f$ noise model. The results are applicable to any two-qubit system with transverse coupling, and they highlight the potential of decoupling techniques for improving two-qubit gate fidelities, an essential prerequisite for implementing fault-tolerant quantum computing.

We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.

We report a direct measurement of the low-frequency noise spectrum in a superconducting flux qubit. Our method uses the noise sensitivity of a free-induction Ramsey interference experiment, comprising free evolution in the presence of noise for a fixed period of time followed by single-shot qubit-state measurement. Repeating this procedure enables Fourier-transform noise spectroscopy with access to frequencies up to the achievable repetition rate, a regime relevant to dephasing in ensemble-averaged time-domain measurements such as Ramsey interferometry. Rotating the qubit's quantization axis allows us to measure two types of noise: effective flux noise and effective critical-current or charge noise. For both noise sources, we observe that the very same 1/f-type power laws measured at considerably higher frequencies (0.2-20 MHz) are consistent with the noise in the 0.01-100-Hz range measured here. We find no evidence of temperature dependence of the noises over 65-200 mK, and also no evidence of time-domain correlations between the two noises. These methods and results are pertinent to the dephasing of all superconducting qubits., v2: Modified title and presentation; 11 p. incl. 5 p. appendix

We report the first measurements of current-voltage ( I–V ) characteristics of discrete rings of Josephson junctions. As I is increased, resonant steps appear in the I–V curve, due to phase-locking between a propagating, trapped vortex and the linear waves excited in its wake. Unexpectedly, the phase velocity of the linear waves, not the group velocity, is the physically important quantity and mode numbers outside the Brillouin zone are relevant. Our measurements show that away from the resonant steps, a single vortex can move in an environment with very little damping, making the discrete one-dimensional ring a well-defined model system for the study of ballistic and quantum vortex experiments.

We have measured vortex motion in a long one‐dimensional array of small underdamped niobium tunnel junctions which are coupled in parallel by superconducting wires. In the current‐voltage characteristic, a resonant step occurs similar to the Eck peak in long continuous junctions. Due to the discrete nature of our samples, the voltage of this resonant step follows a sinusoidal dependence on the magnetic field rather than the linear dependence found in long continuous junctions. With a control current applied parallel to the array of junctions, the device can be operated as a vortex‐flow transistor or as a tunable vortex‐flow oscillator. Compared to long continuous junctions, the performance of discrete transistors is better with regard to the threshold current and transresistance, but worse with regard to the output resistance. Discrete oscillators have the advantage over their continuous counterparts in that the output impedance is of the order of 10 Ω. Numerical simulations indicate power levels around 0...

The dynamics of discrete-one-dimensional parallel arrays of Josephson junctions has been studied experimentally and numerically. The energy barriers for vortex motion from cell to cell have been calculated as a function of the discreteness parameter, the ratio of the Josephson inductance to the self-inductance of the cell. The experimental data show resonances in the current-voltage characteristic, analogous to Fiske steps in a single long Josephson junction. These steps provide a novel experimental method for measuring the self-inductance of 1D parallel arrays. >

The static properties of vortices in an array of Josephson junctions are shown to be significantly influenced by magnetic fields induced by the vortex currents. The energy barrier for vortex motion is enhanced, nearly doubling for penetration depths on the order of a cell size. Moreover, we find that correct calculation of the vortex current distribution, the magnetic moment, and the lower critical field require modeling mutual-inductance interactions between all cell pairs in the array. To make numerical simulation of the system feasible, an algorithm is derived that is sufficiently efficient to allow study of large (500×500 cell) arrays

The temperature dependence of the upper critical field reveals that NbN is a paramagnetism limited superconductor with significant electron-electron exchange and correlation potential arising from the Fermi liquid effects, in sharp contrast to the strong spin-orbit scattering effects expected from the relatively high atomic number of Nb and the low electron density of states at the Fermi energy of NbN. The results also indicate that while the normal state resistivity of the films can be altered in a controlled manner, it does not correlate to the spin-orbit scattering rate directly.

We have observed ballistic motion of vortices in arrays of superconducting tunnel junctions. In a special geometry vortices are accelerated in one region, then launched into a second region without driving forces. At low temperatures, where damping is small, the vortices are found to propagate in a beam across the force-free region.

The voltage generated by moving ballistic vortices with a mass ${\mathit{m}}_{\ensuremath{\nu}}$ in a two-dimensional superconducting ring is quantized, and this quantization depends on the amount of charge enclosed by the ring. The quantization of the voltage is the dual to flux quantization in a superconductor, and is a manifestation of the Aharonov-Casher effect. The quantization is obtained by applying the Bohr-Sommerfeld criterion to the canonical momentum of the ballistic vortices. The results of this quantization condition can also be used to understand the persistent voltage predicted by van Wees for an array of Josephson junctions.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY)., The interference between repeated Landau-Zener transitions in a qubit swept through an avoided level crossing results in Stückelberg oscillations in qubit magnetization, a hallmark of the coherent strongly driven regime in two-level systems. The two-dimensional Fourier transforms of the resulting oscillatory patterns are found to exhibit a family of one-dimensional curves in Fourier space, in agreement with recent observations in a superconducting qubit. We interpret these images in terms of time evolution of the quantum phase of the qubit state and show that they can be used to probe dephasing mechanisms., We acknowledge partial support from W. M. Keck Foundation Center for Extreme Quantum Information Theory, and from the United States Government. The work of M. S. R. was supported by DOE CSGF, Grant No. DE-FG02-97ER25308, and the NSF. The work at Lincoln Laboratory was sponsored by the U.S. DOD under Air Force Contract No. FA8721-05-C-0002.

This project has experimentally characterized the coherent quantum nature of the superconducting persistent current qubits which were fabricated in the trilayer niobium technology. The quantum levels of these qubits have been mapped out using both standard microwave frequency spectroscopy as well as a new technique of amplitude spectroscopy. Important to the future implementation of these qubits for quantum computing applications is the demonstration of microwave sideband cooling of the qubits as well as a resonant read-out scheme. In addition to characterizing the quantum nature of a single qubit, this work has also explored the use of Rapid-Single-Flux superconducting circuits to rapidly control the qubit system.