Large Josephson Junction Research Articles

Entanglement between two charge qubits taking account the Kerr media

Background. The need to implement controlled coupling between qubits, which are the logical elements of quantum devices such as quantum computers and quantum networks, requires, along with the use of traditional methods, the development of new, more effective ways to organize the interaction of qubits with the microwave fields of resonators used to generate and control the entanglement of qubits. As one of these methods, a method based on the influence of frequency-regulated radio frequency signals on a superconducting Josephson qubit connected by a large Josephson junction to a free qubit has been proposed.
 Aim. The influence of the Kerr medium of the resonator, in which one of the two qubits is placed, on their entanglement induced by the coherent or thermal frequency-regulated radio frequency field of the resonator is considered.
 Methods. To analyze the dynamics of the system under consideration, the solution of the quantum Liouville equation for the full density matrix is studied. An exact solution o this equation is found in the case of initial separable and entangled states of qubits. The exact solution of the evolution equation is used to calculate the criterion of qubit-qubit entanglement – cconcurrence. Numerical modeling of the concurrence was carried out for various states of qubits, coherent and thermal fields of the resonator, as well as various values of the intensity of the resonator field and the Kerr nonlinearity parameter.
 Results. It is shown that for separable initial states of qubits, the inclusion of Kerr nonlinearity reduces the maximum degree of entanglement of qubits. For an entangled initial state of qubits, the possibility of creating long-lived entangled states in the presence of Kerr nonlinearity is shown.
 Conclusion. The type of initial states of qubits and the range of values of the intensities of the resonator fields and the Kerr nonlinearity parameters have been established, for which the most effective control and operation of the evolution of qubits, as well as the degree of their entanglement, in the physical system under consideration, is possible.

Direct Visualization of Phase-Locking of Large Josephson Junction Arrays by Surface Electromagnetic Waves

Phase-locking of oscillators leads to superradiant amplification of the emission power. This is particularly important for development of THz sources, which suffer from low emission efficacy. In this work we study large Josephson junction arrays containing several thousands of Nb-based junctions. Using low-temperature scanning laser microscopy we observe that at certain bias conditions two-dimensional standing-wave patterns are formed, manifesting global synchronization of the arrays. Analysis of standing waves indicates that they are formed by surface plasmon type electromagnetic waves propagating at the electrode/substrate interface. Thus we demonstrate that surface waves provide an effective mechanism for long-range coupling and phase-locking of large junction arrays.

Annealed Low Energy States in Frustrated Large Square Josephson Junction Arrays

Numerical simulations were done to find low energy states in frustrated large square Josephson Junction arrays in a perpendicular magnetic field using simulated annealing on the coupled RSJ model. These simulations were made possible by a new algorithm suitable for parallel gpu computing and reduced complexity. Free boundary conditions were used so that values of the frustration factor f that are incommensurate with the array size are permitted. The resulting energy as a function of f is continuous with logarithmic discontinuities in the derivative dE/df at rational frustration factors f=p/q with small q, substantiating the mathematical proof that this curve is continuous and further showing that the staircase state hypothesis is incorrect. The solution shows qualitative similarities with the lowest energy branch of the Hofstadter butterfly, which is a closely related problem. Furthermore, it is found that at the edge of an array there are either extra vortices or missing vortices depending the frustration factor, and the width of this region is independent of the array size.

利用约瑟夫森量子比特计算电流偏置信息总线中的几何相位

量子计算是一种遵循量子力学规律调控量子信息单元进行计算的新型计算模式。本文利用电流偏置信息总线的Josephson量子位，计算了几何相位。发现该几何相位与大电流约瑟夫逊结、量子振荡器频率、对称约瑟夫逊能量耦合器的偏置电流无关，与施加到第k个量子位的栅极电容、磁通量子、外部电流和栅极电压无关。本文结果对利用约瑟夫森量子比特计算具有一定的理论意义。 Quantum computation is a new computational model which follows the rules of quantum mechanics to control the quantum information unit. This paper calculates the geometric phase by using the Josephson qubits of current-biased information bus. The geometric phase has nothing to do with the bias current of the large current-biased Josephson junction, the quantum oscillator frequency, the coupler with symmetric Josephson energies, and also the gate capacitance, flux quantum, external flux, and gate voltage applied to the kth qubit. The results of this paper have a certain theoretical significance to the calculation of the quantum bit of Josephson.

Josephson flux-flow oscillator: The microscopic tunneling approach

We elaborate a theoretical description of large Josephson junctions which is based on the Werthamer's microscopic tunneling theory. The model naturally incorporates coupling of electromagnetic radiation to the tunnel currents and, therefore, is particularly suitable for description of the self-coupling effect in Josephson junction. In our numerical calculations we treat the arising integro-differential equation, which describes temporal evolution of the superconducting phase difference coupled to the electromagnetic field, by the Odintsov-Semenov-Zorin algorithm. This allows us to avoid evaluation of the time integrals at each time step while taking into account all the memory effects. To validate the obtained microscopic model of large Josephson junction we focus our attention on the Josephson flux flow oscillator. The proposed microscopic model of flux flow oscillator does not involve the phenomenological damping parameter, rather, the damping is taken into account naturally in the tunnel current amplitudes calculated at a given temperature. The theoretically calculated current-voltage characteristics is compared to our experimental results obtained for a set of fabricated flux flow oscillators of different lengths. Our theoretical calculation agrees well with the obtained experimental results, and, to our knowledge, is the first where theoretical description of Josephson flux flow oscillator is brought beyond the perturbed sine-Gordon equation.

Development of Nb/Al–AlOx/Nb Tunnel Junction for Large-Scale Integrated Digital Circuits

We present the latest development of an Nb/Al-AlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /Nb Josephson junction fabrication process for superconducting integrated circuits at SIMIT. Our fabrication process has four niobium superconducting layers and one Ti/Pd resistor layer with 1.0 Ω/square sheet resistor for junction shunting and circuit biasing. Critical current density J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> of the junctions is controlled from 30 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> to 10 kA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> by exposing aluminum layer to pure or mixed O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> atmosphere. Correlation between measured J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and exposure conditions has been established. Average quality factor (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sg</sub> /R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) of the junctions in our process is larger than 20 with subgap leakage factor (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ) beyond 30 mV. Critical current uniformity is obtained according to the switching current (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) distribution of a 1000-JJ array. Measured standard deviation sigma of I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> is less than 4% over the 100-mm wafer. Plasma resonance in a large Josephson junction is used to measure specific capacitance (C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) of the junction. Sheet inductances of superconducting niobium strip-lines are extracted by a SQUID diagnose circuit and the measured results show good agreement with our design values.

The role of magnetic fields for curvature effects in Josephson junction

The large area Josephson junction is considered. On the basis of Maxwell equations the influence of the magnetic field on fluxion dynamics is considered. The presented studies show that assumptions presumed in the literature do not restrict experimental settings adopted in the considerations of the fluxion movement in the Josephson junction. It is shown that the particular orientation of the magnetic fields is not needed in order to study physical effects of curvature and therefore they do not restrict the experimental arrangements.

Tuning THz emission properties of Bi2Sr2CaCu2O8+δ intrinsic Josephson junction stacks by charge carrier injection

We report on doping and undoping experiments of terahertz (THz) emitting intrinsic Josephson junction stacks, where the change in charge carrier concentration is achieved by heavy current injection. The experiments were performed on stand-alone structures fabricated from a Bi2Sr2CaCu2O single crystal near optimal doping. The stacks contained about 930 intrinsic Josephson junctions. On purpose, the doping and undoping experiments were performed over only a modest range of charge carrier concentrations, changing the critical temperature of the stack by less than 1 K. We show that both undoping and doping is feasible also for the large intrinsic Josephson junction stacks used for THz generation. Even moderate changes in doping introduce large changes in the THz emission properties of the stacks. The highest emission power was achieved after doping a pristine sample.

Quantum correlations in two coupled superconducting charge qubits

Quantum correlations are considered analytically in a model that contains two coupled superconducting charge qubits sharing a large Josephson junction. Dynamical properties for the reduced two-qubit state are addressed in the quantum evolution when the coupling between the field and the qubits is either constant or time-dependent. In the latter case, adiabatic and nonergodic features are present for extremely low and fast evolutions, respectively. Finally, the case where the coupling drops to zero is also considered.

Entanglement of two superconducting charge qubits with transient effects

We study two superconducting charge qubits sharing a large Josephson junction with transient effects considered for the case of the linear sweep model to explore the influence of a time-varying field on the entanglement of the qubits. We show that the fluctuations in the entanglement can be controlled by the transient effects. Moreover, the time-averaged entanglement oscillates smoothly and then fluctuates with the increasing influence of the transient effects.

Radiation emission due to fluxon scattering on an inhomogeneity in a large two-dimensional Josephson junction

Interaction of a fluxon in the two-dimensional large Josephson junction with the finite area inhomogeneity is studied within the sine-Gordon theory. The spectral density of the emitted plane waves is computed exactly for the rectangular and rhombic inhomogeneities. Total emitted energy as a function of the fluxon velocity exhibits at least one local maximum. Connection to the previously studied limiting cases including the point impurity and the one-dimensional limit has been performed. An important feature o f the emitted energy as a function of the fluxon velocity is a clear maximum (or maxima). The dependence of these maxima on the geometric properties of the impurity has been studied in detail.

Properties of high-angle Fe(Se,Te) bicrystal grain boundary junctions

We report on the characterization of Fe(Se,Te) grain boundary junctions fabricated on a 45° tilt symmetric bicrystal substrate. The junctions show critical current densities of the order of 104 A/cm2, showing a decay of about one order of magnitude with respect to the critical current density of the film, which is very promising for applications. The current-voltage characteristics show resistively shunted junction-like behaviors, with very low normal-state resistance values, typical of superconducting/normal-metal/superconducting junctions. The magnetic field dependences of the critical currents show the typical behaviors of large Josephson junctions. Nevertheless, the critical current is uniformly distributed across the barrier. We present a simplified theoretical model accounting for this effect. The small influence of faceting along the grain boundary on the electrical parameters may be consistent with an s-wave symmetry of the order parameter.

Generation of macroscopic entangled coherent states with large Josephson junctions

Abstract We propose a simple and experimental architecture to generate macroscopic entanglement in a solid system which consists of two large Josephson junctions and a flux qubit. Through quantum measuring of flux qubit, entangled coherent states of two large Josephson junctions are obtained. The concurrence of entangled coherent states can be accommodated by adjusted systematic parameters. We also give a brief discussion on the experimental feasibility of this proposal.

ENTANGLEMENT BETWEEN CHARGE AND FLUX QUBITS

Following the scheme proposed by X. L. He et al. [Phys. Rev. B76 (2007) 024517], we investigate the generation of a maximally entangled state between the charge and flux qubits. It is shown that macroscopic Einstein–Podolsky–Rosen (EPR) pairs can be created and the entanglement can be long-lived. Since the large Josephson junction is only virtually excited, no quantum information will be transferred from the charge and flux qubits to the large Josephson junction. Based on the strong inductive coupling, a fast entanglement operation can be achieved.

Possible curvature effects in the Josephson junction

The large area Josephson junction with one compact dimension is considered. A geometry that increases the velocity of the kink propagating along the junction is considered. The geometry described in this paper can be used in order to increase or decrease the speed of the signal in the transmission elements in electronic devices. Reflection of the kink front from the large curvature areas is also confirmed.

Measurement-induced nonlocality and geometric quantum discord in two SC-charge qubits

By using geometric quantum discord and measurement-induced nonlocality, quantum correlations are investigated for two superconducting (SC) charge qubits that share a large Josephson junction where the field is assumed to be prepared initially in a coherent state. It is found that the difference between measure measurement-induced nonlocality and geometric quantum discord, of the final state of the two SC-charge qubits system which is especial case of X-states, is equal to a constant value. It is found that the quantum correlations and entanglement of the qubits are very sensitive to the mean number of the coherent photons. The entanglement exists in small intervals of death quantum discord and measurement-induced nonlocality. This is further evidence in support of the fact that quantum correlation and entanglement are not synonymous.

Scattering of quasi-one-dimensional solitons on impurities in large Josephson junctions

Fluxon transmission through impurities of different shape in a quasi-one-dimensional long Josephson junction is investigated. The junction width is significantly less than its length but, at the same time, is of the order of the Josephson penetration length λJ or exceeds it. The retrapping current on the impurities of the point, line and rectangular shape is computed as a function of the junction width both numerically and analytically. Good agreement between the analytic formulae and the numerical simulation results for the intermediate (several λJ) junction width is observed.

Microwave Characterization of Josephson Junction Arrays: Implementing a Low Loss Superinductance

We have measured the plasma resonances of an array of Josephson junctions in the regime E(J)>>E(C), up to the ninth harmonic by incorporating it as part of a resonator capacitively coupled to a coplanar waveguide. From the characteristics of the resonances, we infer the successful implementation of a superinductance, an electrical element with a nondissipative impedance greater than the resistance quantum [R(Q)=h/(2e)(2) is approximately equal to 6.5 kΩ] at microwave frequencies. Such an element is crucial for preserving the quantum coherence in circuits exploiting large fluctuations of the superconducting phase. Our results show internal losses less than 20 ppm, self-resonant frequencies greater than 10 GHz, and phase-slip rates less than 1 mHz, enabling direct application of such arrays for quantum information and metrology. Arrays with a loop geometry also demonstrate a new manifestation of flux quantization in a dispersive analog of the Little-Parks effect.

Flux qubit with a large loop size and tunable Josephson junctions

We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ (Josephaon junction) flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.

Effect of charging energy on critical current of dc-SQUID comprising two sub-micron aluminum Josephson junctions

Tiny Al/AlOx/Al tunnel junctions are widely used in single-electron, single-Cooper-pair, and quantum-bit devices. A crucial parameter for such devices is the charging energy of a single electron or a single Cooper-pair in the junctions, and hence, determination of the junction capacitance is quite important. In this paper, we report our experiments to determine the capacitance of sub-micron Al tunnel junctions. We employ a SQUID resonance technique. Differently from the work reported by Deppe et al. [4], the loop inductance is obtained by not only numerical calculation but also experimental results of quantum interference, which eliminates uncertainty about the field penetration depth of Al thin films. The specific capacitance is obtained as 54fF/μm2. We have also found that the critical current of the dc-SQUID is smaller than the value given by the classical theory for large Josephson junctions. Calculation including the charging energy effect provides better fitting to the experiments, where the critical current is assumed to be proportional to the square root of the ratio of the Josephson coupling energy to the charging energy.