Small-capacitance Josephson Junctions Research Articles

Current dependence of the low bias resistance of small capacitance Josephson junctions

The dc current-voltage characteristics of small Josephson junctions reveal features that are not observed in larger junctions, in particular, a switch to the finite voltage state at current values much less than the expected critical current of the junction and a finite resistance in the nominally superconducting regime. Both phenomena are due to the increased sensitivity to noise associated with the small capacitance of the Josephson junction and have been extensively studied a few decades ago. Here I focus on the current bias dependence of the differential resistance of the junction at low current bias in the nominally superconducting regime, using a quantum Langevin equation approach that enables a physically transparent incorporation of the noise environment of the junction. A similar approach might be useful in modeling the sensitivity of superconducting qubits to noise in the microwave regime.

Джозефсоновский контакт малой емкости в зашумленной среде

Джозефсоновский контакт малой емкости в зашумленной среде

Quantum Brownian Motion at Strong Dissipation Probed by Superconducting Tunnel Junctions.

We have investigated the phase dynamics of a superconducting tunnel junction at ultralow temperatures in the presence of high damping, where the interaction with environmental degrees of freedom represents the leading energy scale. In this regime, theory predicts the dynamics to follow a generalization of the classical Smoluchowski description, the quantum Smoluchowski equation, thus, exhibiting overdamped quantum Brownian motion characteristics. For this purpose, we have performed current-biased measurements on the small-capacitance Josephson junction of a scanning tunneling microscope placed in a low impedance environment at milli-Kelvin temperatures. We can describe our experimental findings with high accuracy by using a quantum phase diffusion model based on the quantum Smoluchowski equation. In this way we experimentally demonstrate that overdamped quantum systems follow quasiclassical dynamics with significant quantum effects as the leading corrections.

Superconductor-insulator crossover in Josephson junction arrays due to reduction from two to one dimension

We investigated the dimensionality effect on electrical properties of small-capacitance Josephson junction arrays (JJAs). A one-dimensional JJA and several two-dimensional JJAs with different array widths were fabricated on a substrate simultaneously so that they would have nominally the same junction parameters. As the array width decreases, the current-voltage characteristics show a crossover from a superconducting behavior with a dc Josephson-current-like branch to an insulating one with a Coulomb blockade gap of Cooper pairs. The superconductor-insulator crossover is explained in terms of enhanced quantum fluctuations of superconducting phase variables due to a dimensional reduction.

Phase space topology of a switching current detector

We examine in theory and by numerical simulation, the dynamic process of switching from a zero voltage to a finite voltage state in a Josephson junction circuit. The theoretical model describes small capacitance Josephson junctions which are overdamped at high frequencies, and can be applied to detection of the quantum state of a qubit circuit. We show that the speed and fidelity of the readout are strongly influenced by the topology of the phase space attractors. The readout will be close to optimal when choosing the circuit parameters so as to avoid having an unstable limiting cycle which separates the two basins of attraction.

Bloch Inductance in Small-Capacitance Josephson Junctions

We show that the electrical impedance of a small-capacitance Josephson junction also includes, in addition to the capacitive term -i/(omega)CB, an inductive term i(omega)LB. Similar to the known Bloch capacitance CB(q), the Bloch inductance LB(q) also depends periodically on the quasicharge, q, and its maximum value achieved at q=e(mod 2e) always exceeds the value of the Josephson inductance of this junction LJ(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.

Current–voltage characteristics of a mesoscopic Josephson junction in a low-impedance environment

We have studied current–voltage ( I – V ) characteristics in a single small-capacitance Josephson junction with a parallel shunt resistor and high-resistive leads placed near the junctions. We observe a supercurrent peak without Coulomb blockade in the I – V curves of junctions having the shunt resistance below the quantum resistance R Q ( ≡ h / 4 e 2 = 6.45 k Ω ) .

Quantum Complementarity for the Superconducting Condensate and the Resulting Electrodynamic Duality

Experiments with small capacitance Josephson junction arrays are described that demonstrate the quantum behavior of the phase of the superconducting condensate. This quantum behavior is based on the complementarity of phase and number for a condensate state of many bosons. A key factor to observation of this quantum behavior is the coupling of the superconducting condensate state to dissipation in the electrodynamic environment of the Josephson junction. It is shown how one-dimensional Josephson junction arrays can be used to design an environment with very weak coupling to dissipation, allowing for measurement of condensate with well defined number. The well defined number is manifest in the Coulomb blockade of Cooper pair tunneling.

Geometric quantum computation with Josephson qubits

The quest for large scale integrability and flexibility has very recently stimulated an increasing interest in designing quantum computing devices. In this contribution we discuss a proposal based on small-capacitance Josephson junctions in the charge regime in which quantum gates are implemented by means of adiabatic geometric phases.

Quantum phase transition in one-dimensional Josephson junction arrays

We describe experiments on one-dimensional arrays of small capacitance Josephson junctions which show how the Coulomb blockade of Cooper pair tunneling is influenced by changing the Josephson coupling energy in situ with an externally applied magnetic flux. We show how the zero bias resistance of the array is affected by the length of the array, and we use the length scaling of this resistance to infer that a quantum phase transition occurs as the Josephson coupling energy is changed. The data are qualitatively analyzed in terms of a theoretical model of the quantum phase transition which uses a mapping to the two-dimensional XY model.

Hysteretic current–voltage characteristics and Coulomb blockade in 1D-arrays of Josephson junctions

The IV characteristics (IVC) of 1D-arrays of small capacitance Josephson junctions with E C∼ E J have been measured. The IVC show Coulomb blockade of Cooper pair tunneling and exhibit a pronounced hysteresis which appears to be dual to the well-known resistively shunted junction behavior of ordinary Josephson junctions. A dual serially resistive junction model is used to qualitatively explain the measured data.

Superconducting and Insulating Behavior in One-Dimensional Josephson Junction Arrays

Experiments on one-dimensional small capacitance JosephsonJunction arrays are described. The arrays have a junctioncapacitance that is much larger than the stray capacitance ofthe electrodes, which we argue is important for observation ofCoulomb blockade. The Josephson energy can be tuned in situand an evolution from Josephson-like to Coulomb blockadebehavior is observed. This evolution can be described as asuperconducting to insulating, quantum phase transition. Inthe Coulomb blockade state, hysteretic current-voltagecharacteristics are described by a dynamic model which is dualto the resistively shunted junction model of classicalJosephson junctions.

Aspects of Qubit Dynamics in the Presence of Leakage

Nano-electronics devices such as small-capacitance Josephsonjunction circuits appear to be promising systems to implementquantum logic. While the elementary unit of a quantum computeris a two-state system (the qubit) the computational space of aJosephson junction qubit is a subset of a larger Hilbertspace. Therefore quantum leakage may occur, i.e. during theoperation of the device the quantum state may escape partiallyfrom the computational subspace. We study the consequences ofleakage for the fidelity of Josephson qubits and discuss howthe gate design can be optimized.

Length-Scale Dependence of the Superconductor-to-Insulator Quantum Phase Transition in One Dimension

One-dimensional (1D) arrays of small-capacitance Josephson junctions demonstrate a sharp transition, from Josephson-like behavior to the Coulomb blockade of Cooper-pair tunneling, as the effective Josephson coupling between nearest neighbors is tuned with an externally applied magnetic field. Comparing the zero-bias resistance of three arrays with 255, 127, and 63 junctions, we observe a critical behavior where the resistance, extrapolated to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, is independent of length at a critical magnetic field. Comparison is made with a theory of this $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ quantum phase transition, which maps to the 2D classical $\mathrm{XY}$ model.

Cooper-pair charge solitons: The electrodynamics of localized charge in a superconductor.

One-dimensional arrays of small-capacitance Josephson junctions exhibit a current-voltage curve that is characterized by a zero-current state for bias voltage below a threshold voltage ${V}_{t}$. The threshold voltages can be modulated with an external magnetic field $B$, which tunes effective Josephson coupling between adjacent electrodes of the array. The dependence of ${V}_{t}$ on $B$ is well explained by a model where ${V}_{t}$ is the injection voltage for a Cooper-pair charge soliton.

Fabrication and measurement of one-dimensional arrays of small capacitance Josephson junctions

We describe the fabrication and measurement of one-dimensional series arrays of small capacitance Josephson junctions and superconducting quantum interference devices. These arrays exhibit a Coulomb blockade of Cooper pair tunneling when the Josephson coupling energy is the order of the charging energy. The effectiveness of a resistive coaxial cable (ThermocoaxTM made by Philips) for attenuation of high frequency electromagnetic noise is demonstrated. This noise influences the measured dc current–voltage characteristic of the array, having qualitatively the same effect as raising the temperature.

Bloch oscillations in small-capacitance Josephson junctions.

An analytic study of ac-bias-current effects on the Bloch oscillations in small Josephson junctions at the ${\mathit{E}}_{\mathit{c}}$\ensuremath{\gg}${\mathit{E}}_{\mathit{J}}$ limit (${\mathit{E}}_{\mathit{c}}$ is the charging energy and ${\mathit{E}}_{\mathit{J}}$ is the Josephson energy) is presented. By solving the quasicharge differential equation proposed by Likharev et al., solutions for the quasicharge q(t), as well as the I-V curves, are analyzed. It is shown that due to the sudden jump of the Bloch-oscillation period at some value of the dc current I, resistive steps of anomalous differential resistance emerge in the I-V curve. A general relation between the position of the resistive step on the I-V curve and the applied frequency f is derived. The connections and the differences between our formula and the weak-damping-limit formula I=(m/n)2ef are discussed. The results are compared with recent experiments.

Quasiparticle and Cooper pair tenneling in small capacitance Josephson junctions

The tunneling of single electrons in small capacitance tunnel junctions is influenced by charging effects and by the fluctuations of the elecromagnetic environment. We study the effect of an external circuit with arbitrary impedance on the tunneling of quasiparticles and Cooper pairs in voltage driven Josephson junctions. We present results at finite temperatures and also consider an acdriven system.

Resonant tunneling in small current-biased Josephson junctions.

We investigate the theory of resonant tunneling of the phase difference \ensuremath{\varphi} in current-biased, small-capacitance Josephson junctions. Tunneling of \ensuremath{\varphi} occurs between states localized in adjacent wells of the tilted cosine (``washboard'') potential when the states are nearly degenerate, and leads to unique junction behavior. Most notable are the presence of voltage spikes along the supercurrent branch of the current-voltage characteristic, the reduction of the bias current at which the junction switches to the free-running state to a value well below the thermodynamic value, and peaks in the distribution of rates at which this switching occurs as a function of bias current. For a range of junction parameters, we estimate the magnitude and width of the first (lowest bias current) voltage spike and the rate of switching to the free-running state in the zero temperature, low damping limit. Experimentally, the most readily observable signature of resonant tunneling should be the characteristic peaks in the switching distribution.

Single Cooper-pair tunneling in small-capacitance junctions.

We present observations of charging effects for Cooper pairs in short linear arrays of small-capacitance Josephson junctions. Current-voltage characteristics show a Coulomb gap for Cooper-pair tunneling when the charging energy exceeds the Josephson coupling energy. In a double junction a zero-voltage current is observed that is modulated by a gate voltage applied to the metal island between the junctions. For longer arrays a crossover from Coulomb blockade of Cooper-pair tunneling to a supercurrent is observed when the ratio of Josephson coupling to charging energy is increased.