One-dimensional Josephson Junction Arrays Research Articles

Heat Bath in a Quantum Circuit.

We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.

One-dimensional Josephson junction arrays: Lifting the Coulomb blockade by depinning

Experiments with one-dimensional arrays of Josephson junctions in the regime of dominating charging energy show that the Coulomb blockade is lifted at the threshold voltage, which is proportional to the array's length and depends strongly on the Josephson energy. We explain this behavior as depinning of the Cooper-pair-charge-density by the applied voltage. We assume strong charge disorder and argue that physics around the depinning point is governed by a disordered sine-Gordon-like model. This allows us to employ the well-known theory of charge density wave depinning. Our model is in good agreement with the experimental data.

Large microwave response of one-dimensional Josephson junction arrays in charge dominant regime

By using photoresistance measurement, one-dimensional (1D) Josephson junction arrays can be used as primary radio-frequency and microwave detectors. The response can be explained by the microwave-enhanced phase diffusion both in the superconducting phase and charge dominant limits. Free from the screening effect due to mobile charges when the junctions were strongly coupled via the Josephson effect, the 1D array exhibited large microwave response in the charge dominant limit. Used as an in-line detector of guided microwaves, the array produces a negligible change of about in the microwave transmission.

Josephson junction transmission lines as tunable artificial crystals

We investigate one-dimensional Josephson junction arrays with generalized unit cells as a circuit approach to engineer microwave band gaps. An array described by a lattice with a basis can be designed to have a gap in the electromagnetic spectrum, in full analogy to electronic band gaps in diatomic or many-atomic crystals. We derive the dependence of this gap on the array parameters in the linear regime, and suggest experimentally feasible designs to bring the gap below the single junction plasma frequency. The gap can be tuned in a wide frequency range by applying external flux, and it persists in the presence of small imperfections.

Interplay between symmetric exchange anisotropy, uniform Dzyaloshinskii-Moriya interaction, and magnetic fields in the phase diagram of quantum magnets and superconductors

We theoretically study the joint influence of uniform Dzyaloshinskii-Moriya (DM) interactions, symmetric exchange anisotropy (with its axis parallel to the DM vector) and arbitrarily oriented magnetic fields on one-dimensional spin 1/2 antiferromagnets. We show that the zero-temperature phase diagram contains three competing phases: (i) an antiferromagnet with Neel vector in the plane spanned by the DM vector and the magnetic field, (ii) a {\em dimerized} antiferromagnet with Neel vector perpendicular to both the DM vector and the magnetic field, and (iii) a gapless Luttinger liquid. Phase (i) is destroyed by a small magnetic field component along the DM vector and is furthermore unstable beyond a critical value of easy-plane anisotropy, which we estimate using Abelian and non-Abelian bosonization along with perturbative renormalization group. We propose a mathematical equivalent of the spin model in a one-dimensional Josephson junction (JJ) array located in proximity to a bulk superconductor. We discuss the analogues of the magnetic phases in the superconducting context and comment on their experimental viability.

Observation of quantum fluctuation in nano Sr2RuO4 p-wave superconductors

We observed quantum fluctuations of the superconducting phase θ in single domain Sr2RuO4 single crystals using a transport measurement. The temperature dependence of the resistivity of submicron Sr2RuO4 shows that a finite resistivity below the superconducting transition temperature of Tc = 1.69 K. The results may suggest that the finite resistivity is occurred by the flow of vortices due to quantum fluctuations of the superconducting phase θ in the same way as one-dimensional Josephson junction array systems.

Discontinuous Current-Phase Relations in Small One-Dimensional Josephson Junction Arrays

We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase (I-phi) relationships. We present results for a three-junction system in the vicinity of charge-degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I-phi relation at phase pi persist and that, at maximum degeneracy, the problem can be mapped to a tight-binding model providing analytical results for arbitrary system size.

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.

Dissipation, topology, and quantum phase transition in a one-dimensional Josephson junction array

We study the phase diagram and quantum critical properties of a resistively shunted Josephson junction array in one dimension from a strong coupling analysis. After mapping the dissipative quantum phase model to an effective sine-Gordon model we study the renormalization group flow and the phase diagram. We try to bridge the phase diagrams obtained from the weak and the strong coupling renormalization group calculations to extract a more comprehensive picture of the complete phase diagram. The relevance of our theory to experiments in nanowires is discussed.

A Superconductor-Insulator Transition in a One-Dimensional Array of Josephson Junctions

We consider a one-dimensional Josephson junction array, in the regime where the junction charging energy is much greater than the charging energy of the superconducting islands. In this regime we critically reexamine the continuum limit description and establish the relationship between parameters of the array and the ones of the resulting sine-Gordon model. The later model is formulated in terms of quasi-charge. We argue that despite arguments to the contrary in the literature, such quasi-charge sine-Gordon description remains valid in the vicinity of the phase transition between the insulating and the superconducting phases. We also discuss the effects of random background charges, which are always present in experimental realizations of such arrays.

Quantum phase transitions and persistent currents in Josephson-junction ladders

In this work we study quantum phase transitions and persistent currents in capacitively coupled one-dimensional Josephson-junction arrays. We will focus particularly on the roles of exciton-like pairs in the strong coupling limit in the presence of external gate charges and magnetic fluxes. We use the numerical density-matrix renormalization group method for the study in the full range of values of gate charge and magnetic flux. To clarify the various effects, we report the pair correlation functions and the exciton densities as welll as the persistent current.

Quantum fluctuations and dissipative phase transition in one-dimensional Josephson junction arrays

We studied superconductor–insulator transition in one-dimensional arrays of small Josephson junctions in which each junction was shunted by ohmic resistor. The I– V characteristics changed from Coulomb-blockade type behavior to Josephson-like one with decreasing shunt resistance R S, even when the Josephson coupling energy E J was much smaller than the charging energy E C (≡e 2/C , C : junction capacitance ) . The critical value of R S was close to R Q (≡6.45 kΩ) for E J/ E C smaller than unity. This agrees with theoretical predictions for dissipation-driven phase transitions in this system.

Andreev reflection off a fluctuating superconductor in the absence of equilibrium

Andreev reflection between a normal metal and a superconductor whose order parameter exhibits quantum phase fluctuations is examined. The approach chosen is nonperturbative in the tunneling Hamiltonian and enables us to probe the whole range of voltage biases up to the gap amplitude. Results are illustrated using the one-dimensional Josephson junction array model previously introduced in the linear response regime. Phase fluctuations are shown to affect the differential conductance and are compared to the result of Blonder, Tinkham, and Klapwijk for a rigid BCS superconductor. The noise spectrum of the Andreev current is also obtained and its second derivative with respect to frequency is proposed as a direct tool to analyze the phase fluctuations.

Boundary effects on Josephson current through one-dimensional Josephson junction arrays

Josephson junctions hybridized with an array of superconducting islands are studied. Assuming large on-site Coulomb interactions, a particle number and a Josephson critical current are calculated as functions of voltages of two leads based on a hard-core boson model, which is equivalent to a spin system with boundary fields. After the Wigner-Jordan transformation, an additional factor depending on the parity of the particle number appears at the boundary. This factor neglected in the previous issues crucially determines properties of the junction. The boundary effects due to this factor are discussed by studying resonant tunneling peaks in critical currents and phase dependence of Josephson currents.

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.

Temperature-dependent resistance of a finite one-dimensional Josephson junction array

We study theoretically the temperature and array-length dependences of the resistance of a finite one-dimensional array of Josephson junctions. We use both analytic approximations and numerical simulations, and conclude that within the self-charging model, all finite arrays are resistive in the low-temperature limit. A heuristic analysis shows qualitative agreement with the resistance obtained from Monte Carlo simulations, establishing a connection between resistance and the occurrence of vortices in the corresponding 1+1D XY model. We compare our results with recent experiments and conclude that while the self-charging model reproduces some of the experimental observations, it underestimates the superconducting tendencies in the experimental structures.

Scaling Analysis of Magnetic-Field-Tuned Phase Transitions in One-Dimensional Josephson Junction Arrays

We have studied experimentally the magnetic field-induced superconductor-insulator quantum phase transition in one-dimensional arrays of small Josephson junctions. The zero bias resistance was found to display a drastic change upon application of a small magnetic field; this result was analyzed in context of the superfluid-insulator transition in one dimension. A scaling analysis suggests a power law dependence of the correlation length instead of an exponential one. The dynamical exponents $z$ were determined to be close to 1, and the correlation length critical exponents were also found to be about 0.3 and 0.6 in the two groups of measured samples.

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.

A general expression for Josephson penetration depth in junction arrays

We have calculated the screening field profiles in a one-dimensional Josephson-junction array of lattice constant a with normalized line density of maximum Josephson-junction current i max. It is shown that the Josephson penetration depth λ J = a/ln[1 + πi max + √(1 + πi max) 2 − 1], whose low and high- i max limits are a/√2 πi max and a/ln(2 + 2 πi max), respectively. The first is used traditionally and consistent with that for uniform long junctions and the second limit should be used for the intergranular properties of granula superconductors. The presence of both limits indicates a transition resulting from the enhancement of the structural discreteness.

Resonant Steps in the Discrete sine-Gordon Chain**The project supported in part by the Research Grant Council RGC, the Hong Kong Baptist University Faculty Research Grant FRG, and National Natural Science Foundation of China

Low-velocity dynamics of a dc-driven discrete sine-Gordon chain is studied in the damped case. It is shown that resonant steps of the average velocity emerge due to the resonant phase locking between the kink motion and its radiated linear modes in its wake. A mean-field description is given, which can predict precisely the numerical results. The mechanism and formula proposed in this paper can be directly applied to the discussion of fluxon dynamics of one-dimensional Josephson junction arrays and Josephson junction ladders.