Low-field magnetic response of multi-junction superconducting quantum interference devices

The magnetic states of multi-junction superconducting quantum interference device containing 2N identical conventional Josephson junctions are studied by means of a perturbation analysis of the non-linear first-order ordinary differential equations governing the dynamics of the Josephson junctions in these devices. In the zero-voltage state, persistent currents are calculated in terms of the externally applied magnetic flux Φ_ex . The resulting d.c. susceptibility curves show that paramagnetic and diamagnetic states are present, depending on the value of Φ_ex . The stability of these states is qualitatively studied by means of the effective potential notion for the system.     

Controllable π junction in a Josephson quantum-dot device with molecular spin

We consider a model for a single molecule with a large frozen spin sandwiched in between two BCS superconductors at equilibrium, and show that this system has a π junction behavior at low temperature. The π shift can be reversed by varying the other parameters of the system, e.g., temperature or the position of the quantum dot level, implying a controllable π junction with novel application as a Josephson current switch. We show that the mechanism leading to the π shift can be explained simply in terms of the contributions of the Andreev bound states and of the continuum of states above the superconducting gap. The free energy for certain configuration of parameters shows a bistable nature, which is a necessary pre-condition for achievement of a qubit.     

Vortices in Josephson arrays interacting with non-classical microwaves: The effect of dissipation

Vortices circulating in a ring made from a Josephson array in the insulating phase are studied. The ring contains a `dual Josephson junction' through which the vortices tunnel. External non-classical microwaves are coupled to the device. The time evolution of this two-mode fully quantum mechanical system is studied, taking into account the dissipation in the system. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. Entropic calculations quantify the entanglement between the two systems. Quantum phenomena in the system are also studied through Wigner functions. After a certain time (which depends on the dissipation parameters) these quantum phenomena are destroyed due to dissipation. Received 21 October 2002 / Received in final form 11 February 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: a.konstadopoulou@brad.ac.uk     

Double SQUID tunable flux qubit manipulated by fast pulses: operation requirements, dissipation and decoherence

A double SQUID manipulated by fast magnetic flux pulses can be used as a tunable flux qubit. In this paper we study the requirements for the qubit operation and evaluate the dissipation and decoherence due to the manipulation, with particular attention to the contribution related to the applied tuning control, not present in simpler flux qubits. Furthermore, we shortly discuss the possibility to use an integrated Rapid Single Flux Quantum logic for the qubit control.     

Magnetic calorimeter for registration of small energy release

A scheme of magnetic calorimeter for registration of rare events characterized by small energy release (cosmic rays, WIMPs, solitary X-ray quanta) is proposed. The calorimeter is brought to operation by adiabatic demagnetization, and its magnetic response is measured by a quantum interferometer (SQUID, A. Barone and G. Paterno, Physics and applications of Josephson Effect). Special consideration is given to the specific features of calorimeter operation in the ferromagnetic transition region. The trigger registration of ultrasmall energy release by a ferromagnetic system in the metastable state is described.     

Critical current calculations for long 0-π Josephson junctions

A zigzag boundary between a $d_{x^2 - y^2}$ and an s-wave superconductor is believed to behave like a long Josephson junction with alternating sections of 0 and π symmetry. We calculate the field-dependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long 0-π junction. In this form, the equations describe a hybrid ladder of inductively coupled small 0 and π resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density J_c(H_a) is maximum at non-zero applied magnetic field H_a, and depends strongly on the ratio of Josephson penetration depth λ_J to facet length L_f. If λ_J/L_f ≫1 and the number of facets is large, there is a broad range of H_a where J_c(H_a) is less than 2% of the maximum critical current density of a long 0 junction. All of these features are in qualitative agreement with recent experiments. In the limit λ_J/L_f →∞, our model reduces to a previously-obtained analytical superposition result for J_c(H_a). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor Q_J(H_a), finding that . We suggest that measuring the field-dependence of Q_J(H_a) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.     

Engineering decoherence in Josephson persistent-current qubits

We discuss the relaxation and dephasing rates that result from the control and the measurement setup itself in experiments on Josephson persistent-current qubits. For control and measurement of the qubit state, the qubit is inductively coupled to electromagnetic circuitry. We show how this system can be mapped on the spin-boson model, and how the spectral density of the bosonic bath can be derived from the electromagnetic impedance that is coupled to the qubit. Part of the electromagnetic environment is a measurement apparatus (DC-SQUID), that is permanently coupled to the single quantum system that is studied. Since there is an obvious conflict between long coherence times and an efficient measurement scheme, the measurement process is analyzed in detail for different measurement schemes. We show, that the coupling of the measurement apparatus to the qubit can be controlled in situ. Parameters that can be realized in experiments today are used for a quantitative evaluation, and it is shown that the relaxation and dephasing rates that are induced by the measurement setup can be made low enough for a time-resolved study of the quantum dynamics of Josephson persistent-current qubits. Our results can be generalized as engineering rules for the read-out of related qubit systems. Received 4 September 2002 Published online 27 January 2003 RID="a" ID="a"Present address: Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA RID="b" ID="b"Present address: Sektion Physik and CeNS, Ludwig-Maximilians Universit?t, Theresienstr. 37, 80333 Munich, Germany e-mail: wilhelm@theorie.physik.uni-muenchen.de     

Investigations on phase locking in a two-dimensional Josephson junction array within the Werthamer and the RCSJ model

The synchronization properties of a simple two-dimensional Josephson array consisting of two coupled SQUID cells are studied within the Werthamer as well as the RCSJ model. Special emphasis is placed on the role of inductances arranged perpendicular and parallel to the current bias direction for the phase locking behavior. The general behavior within the Werthamer model is found to be similar to that within the RCSJ model. However, there are quantitative differences, e.g. an enhanced phase shift between the voltage oscillations within one cell and a shift of the parameter range for the in-phase regime between different cells towards lower values of the McCumber parameter in the Werthamer model. Received: 23 March 1998 / Revised: 3 June 1998 / Accepted: 9 June 1998     

Quantum synchronization

Using the methods of quantum trajectories we study numerically a quantum dissipative system with periodic driving which exhibits synchronization phenomenon in the classical limit. The model allows to analyze the effects of quantum fluctuations on synchronization and establish the regimes where the synchronization is preserved in a quantum case (quantum synchronization). Our results show that at small values of Planck constant ħ the classical devil's staircase remains robust with respect to quantum fluctuations while at large ħ values synchronization plateaus are destroyed. Quantum synchronization in our model has close similarities with Shapiro steps in Josephson junctions and it can be also realized in experiments with cold atoms.     

Whole-wafer fabrication process for three-terminal double stacked tunnel junctions

A new fabrication process for three-terminal superconducting devices consisting of two Josephson junctions in a stacked configuration is reported. The process is based on the deposition of the whole Nb/Al_xO_y/Nb-Al/Al_xO_y/Nb multilayer on a Si crystalline wafer without any vacuum breaking. Lift-off techniques, anodization processes and a SiO film deposition have been adopted for patterning and insulating the two tunnel stacked junctions. Devices have been characterized in terms of current-voltage (I-V) curves and Josephson critical current vs. the externally applied magnetic field. They show high quality factors (V _m values up to 65 mV at 4.2 K), and good current uniformity. Received 5 June 2001     

Chaos synchronization in RCL-shunted Josephson junctions via a common chaos driving

We study chaos synchronization in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using a common chaos driving. The numerical simulations confirm that the synchronization of two RCLSJJs can be achieved with a suitable driving intensity when the maximum condition Lyapunov exponent (MCLE) is negative.     

Josephson current through a ferromagnetic semiconductor/semiconductor/ferromagnetic semiconductor structure

We theoretically calculate the Josephson current for two superconductor/ferromagnetic semiconductor (SC/FS) bilayers separated by a semiconductor (SM) layer. It is found that the critical Josephson current I_C in the junction is strongly determined by not only the relative orientations of the effective exchange field of the two bilayers and scattering potential strengths at the interfaces but also the kinds of holes (the heavy or light) in the two FS layers. Furthermore, a robust approach to measuring the spin polarization P for the heavy and light holes is presented.     

0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Two regimes in the magnetic field response of superconducting MgB<Subscript>2</Subscript>

Using Scanning Tunneling Microscope at low temperature we explore the superconducting phase diagram in the π-band of the two-band superconductor MgB₂. In this band the peculiar shape of the local tunneling spectra and their dynamics in the magnetic field reveal the complex character of the quasiparticle density of states (DOS). The gap in the DOS is first rapidly filled with states in raising the magnetic field up to 0.5 T and then slowly approaches the normal state value: the gap is observed up to 2 T. Such a change in the DOS dynamics suggests the existence of two terms in the DOS of the π-band: a first one, reflecting an intrinsic superconductivity in the band and a second one, originating from an inter-band coupling to the σ-band. Our findings allow a deeper understanding of the unique phase diagram of MgB₂.     

Free precession and transverse relaxation of hyperpolarized <Superscript>129</Superscript>Xe gas detected by SQUIDs in ultra-low magnetic fields

We studied the free precession of the nuclear magnetization of hyperpolarized ¹²⁹Xe gas in external magnetic fields as low as B₀ = 4.5 nT, using SQUIDs as magnetic flux detectors. The transverse relaxation was mainly caused by the restricted diffusion of ¹²⁹Xe in the presence of ambient magnetic field gradients. Its pressure dependence was measured in the range from 30 mbar to 850 mbar and compared quantitatively to theory. Motional narrowing was observed at low pressure, yielding transverse relaxation times of up to 8000 s.     

Interactions between two solitons with an arbitrary collision direction in two-dimensional Bose-Einstein condensates

We show that there is a link between the Kuramoto paradigm and another system of synchronized oscillators, namely an electrical power distribution grid of generators and consumers. The purpose of this work is to show both the formal analogy and some practical consequences. The mapping can be made quantitative, and under some necessary approximations a class of Kuramoto-like models, those with bimodal distribution of the frequencies, is most appropriate for the power-grid. In fact in the power-grid there are two kinds of oscillators: the “sources" delivering power to the “consumers".     

MO analysis of macroscopic supercurrent flow in MgB 2

We present results from an extended magneto-optical (MO) analysis of two samples cut from high-density pellets of MgB₂. The first sample was studied in order to show that no matter how large the sample is and despite the bulk granularity, the material enters into a critical state in a crystal-like fashion. The second sample was chosen for the quantitative analysis. A numerical approach based on an inverted 2D Biot-Savart model was used to calculate the current paths across the homogeneous polycrystalline bulk, as well as in the vicinity and across some morphological defects. Local current densities in the homogeneous part were estimated as a function of the applied magnetic field at different temperatures, in three regimes: below full penetration, at full penetration and above full penetration, respectively. A hypothesis of interpretation of the apparent absence of magnetic granularity inside the polycrystalline microstructure is presented. It is related to a critical state likely reached by a network of strongly coupled Josephson junctions. Received 31 May 2001 and Received in final form 5 December 2001     

Resonant effects in ballistic Josephson junctions

We study the Josephson effect in ballistic double-barrier SINIS planar junctions, consisting of bulk superconductors (S), a clean normal metal or semiconductor (N), and insulating interfaces (I) modeled as a δ-function potential-energy barriers. We solve the scattering problem based on the Bogoliubov-de Gennes equations and derive a general expression for the dc Josephson current, valid for arbitrary interfacial transparency, the Fermi wave vectors mismatch, and for different effective band masses. The effect of transmission resonances on the Josephson current and on the normal conductance is analyzed for short junctions. Curvature of the temperature dependence of the critical Josephson current is related to the presence of resonances at the Fermi level and to the interfacial transparency. For thin semiconductor layers with negative effective masses of the carriers, finite interfacial transparency and large Fermi wave vectors mismatch we find that an unusual and significant enhancement of both the normal conductance and the critical Josephson current occurs at low temperatures due to the presence of an evanescent mode localized at interfaces.     

Smearing origin of zero-bias conductance peak in Ag-SiO-Bi2Sr2CaCu2O8+δ planar tunnel junctions: influence of diffusive normal metal verified with the circuit theory

We propose a new approach of smearing origins of a zero-bias conductance peak (ZBCP) in high-T_c superconductor tunnel junctions through the analysis based on the circuit theory for a d-wave pairing symmetry. The circuit theory has been recently developed from conventional superconductors to unconventional superconductors. The ZBCP frequently appears in line shapes for this theory, in which the total resistance was constructed by taking account of the effects between a d-wave superconductor and a diffusive normal metal (DN) at a junction interface, including the midgap Andreev resonant states (MARS), the coherent Andreev reflection (CAR) and the proximity effect. Therefore, we have analyzed experimental spectra with the ZBCP of Ag-SiO-Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) planar tunnel junctions for the {110}-oriented direction by using a simplified formula of the circuit theory for d-wave superconductors. The fitting results reveal that the spectral features of the ZBCP are well explained by the circuit theory not only excluding the Dynes's broadening factor but also considering only the MARS and the DN resistance. Thus, the ZBCP behaviors are understood to be consistent with those of recent studies on the circuit theory extended to the systems containing d-wave superconductor tunnel junctions.