One-dimensional Josephson Junction 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.

GHz Superconducting Single-Photon Detectors for Dark Matter Search

The composition of dark matter is one of the puzzling topics in astrophysics. To address this issue, several experiments searching for the existence of axions have been designed, built and realized in the last twenty years. Among all the others, light shining through walls experiments promise to push the exclusion limits to lower energies. For this reason, effort is put for the development of single-photon detectors operating at frequencies <100 GHz. Here, we review recent advancements in superconducting single-photon detection. In particular, we present two sensors based on one-dimensional Josephson junctions with the capability to be in situ tuned by simple current bias: the nanoscale transition edge sensor (nano-TES) and the Josephson escape sensor (JES). These two sensors are the ideal candidates for the realization of microwave light shining through walls (LSW) experiments, since they show unprecedented frequency resolutions of about 100 GHz and 2 GHz for the nano-TES and JES, respectively.

Field cooled annular Josephson tunnel junctions

We investigate the physics of planar annular Josephson tunnel junctions quenched through their transition temperature in the presence of an external magnetic field. Experiments carried out with long Nb/Al-AlOx/Nb annular junctions showed that the magnetic flux trapped in the high-quality doubly-connected superconducting electrodes forming the junction generates a persistent current whose associated magnetic field affects the both the static and dynamics properties of the junctions. More specifically, the field trapped in the hole of one electrode combined with a d.c. bias current induces a viscous flow of dense trains of Josephson vortices which manifests itself through the sequential appearance of displaced linear slopes, Fiske step staircases and Eck steps in the junction’s current-voltage characteristic. Furthermore, a field shift is observed in the first lobe of the magnetic diffraction pattern. The effects of the persistent current can be mitigated or even canceled by an external magnetic field perpendicular to the junction plane. The radial field associated with the persistent current can be accurately modeled with the classical phenomenological sine-Gordon model for extended one-dimensional Josephson junctions. Extensive numerical simulations were carried out to disclose the basic flux-flow mechanism responsible for the appearance of the magnetically induced steps and to elucidate the role of geometrical parameters. It was found that the imprint of the field cooling is enhanced in confocal annular junctions which are the natural generalization of the well studied circular annular junctions.

Kerr nonlinearity in a superconducting Josephson metamaterial

We present a detailed experimental and theoretical analysis of the dispersion and non-linear Kerr frequency shifts of plasma modes in a one-dimensional Josephson junction chain containing 500 SQUIDs in the regime of weak nonlinearity. The measured low-power dispersion curve agrees perfectly with the theoretical model if we take into account the Kerr renormalisation of the bare frequencies and the long-range nature of the island charge screening by a remote ground plane. We measured the self- and cross-Kerr shifts for the frequencies of the eight lowest modes in the chain. We compare the measured Kerr coefficients with theory and find good agreement.

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.

Phase sticking in one-dimensional Josephson junction chains

We studied current-voltage characteristics of long one-dimensional Josephson junction chains with Josephson energy much larger than charging energy, ${E}_{J}\ensuremath{\gg}{E}_{C}$. In this regime, typical I-V curves of the samples consist of a supercurrent-like branch at low-bias voltages followed by a voltage-independent chain current branch, ${I}_{\mathrm{chain}}$ at high bias. Our experiments showed that ${I}_{\mathrm{chain}}$ is not only voltage-independent but it is also practically temperature-independent up to $T=0.7{T}_{C}$. We have successfully model the transport properties in these chains using a capacitively shunted junction model with nonlinear damping.

Localizing quantum phase slips in one-dimensional Josephson junction chains

We studied quantum phase-slip (QPS) phenomena in long one-dimensional Josephson junction series arrays with tunable Josephson coupling. These chains were fabricated with as many as 2888 junctions, where one sample had a separately tunable link in the middle of the chain. Measurements were made of the zero-bias resistance, R0, as well as current–voltage characteristics (IVC). The finite R0 is explained by QPS and shows an exponential dependence on with a distinct change in the exponent at R0 = RQ = h/4e2. When R0 > RQ, the IVC clearly shows a remnant of the Coulomb blockade, which evolves to a zero-current state with a sharp critical voltage as EJ is tuned to a smaller value. The zero-current state below the critical voltage is due to coherent QPSs and we show that these are enhanced when the central link is weaker than all other links. Above the critical voltage, a negative, differential resistance is observed, which nearly restores the zero-current state.

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.

Two-Point Phase Correlations of a One-Dimensional Bosonic Josephson Junction

We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows us to measure the coupling strength and temperature and hence a full characterization of the system.

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.

Measurement of the current-phase relation in Josephson junction rhombi chains

We present low-temperature transport measurements in one-dimensional Josephson junctions rhombi chains. We have measured the current-phase relation of a chain of eight rhombi. The junctions are either in the classical phase regime with the Josephson energy much larger than the charging energy, ${E}_{J}⪢{E}_{C}$, or in the quantum phase regime where ${E}_{J}/{E}_{C}\ensuremath{\approx}2$. In the strong Josephson coupling regime (${E}_{J}⪢{E}_{C}⪢{k}_{B}T$) we observe a sawtoothlike supercurrent as a function of the phase difference over the chain. The period of the supercurrent oscillations changes abruptly from one flux quantum ${\ensuremath{\Phi}}_{0}$ to half the flux quantum ${\ensuremath{\Phi}}_{0}/2$ as the rhombi are tuned in the vicinity of full frustration. The main observed features can be understood from the complex energy ground state of the chain. For ${E}_{J}/{E}_{C}\ensuremath{\approx}2$, we do observe a dramatic suppression and rounding of the switching current dependence which we found to be consistent with the model developed by Matveev et al. [Phys. Rev. Lett. 89, 096802 (2002)] for long Josephson junctions chains.

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.

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.

Analysis of zero-bias resistance in overdamped mesoscopic Josephson junction chains

We measured the temperature dependence and Josephson-coupling-energy ( E J) dependence of the zero-bias resistance of one-dimensional Josephson junction chains. Each junction in the chains was shunted by an ohmic resistance of several kΩ, and the charging energy was more than an order of magnitude larger than E J. The results for overdamped junction chains are in agreement with a theory considering phase fluctuation in the presence of dissipation.

Effects of Quantum and Thermal Fluctuations on the Stability of Mutual Phase-Locking in Long Josephson Junction Stacks

We report the effects of quantum and thermal fluctuations on the stability of phase-locking in one-dimensional long Josephson junction (LJJ) devices, involving high temperature superconductors. Accounting for both the magnetic induction effect and the charging effect, we determine the zero temperature (T = 0) stability phase diagram using renormalization group (RG) analysis. This phase diagram shows that the in-phase mode is stable but some out-of-phase modes are unstable against quantum fluctuations. At finite T, all stable phase-locked modes (at T = 0) are unstable, but its stability is maintained within the decoherence length which decreases inversely with T.

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.