Narrow Results

We investigate the time evolutions of purity, coherence and entanglement in two superconducting qubits coupled through Josephson junctions. The system is modeled by coupling strength, energy, Josephson energy and phase difference. Meanwhile, the structure is under the action of thermal field and classical Ornstein–Uhlenbeck (OU) noise. According to our findings, quantum correlations are notably developed governed by the system parameters. Purity and entanglement generally increase for the energetic qubit regimes. The state’s entanglement and purity degrade with increased coupling strength and temperature. On the other hand, the optimal preservation of quantum correlations reqires the adjustment to intermediate Josephson energies ($E_j=0.5$) and phase differences ($\varphi =\pi ∕4$). The coherence measurement shows completely opposite traits compared to the entanglement and purity in the system. These results reveal that quantum states need proper parametrization for the considered state while providing optimization for the higher performance of superconducting qubits in quantum information processing.

It has been suggested that dark energy will lead to a frequency cutoff in an experiment involving a Josephson junction. Here we show that were such a cutoff detected, it would have dramatic consequences including the possible demise of the string landscape.

A simple tabletop setup based on a superconductor quantum interference device is proposed to test the gravitational interaction. A D-shaped superconducting loop has the straight segment immersed inside a massive sphere while the half-circle segment is wrapped around the sphere. The superconducting condensate within the straight arm of the loop thus bathes inside a gravitational simple harmonic oscillator potential while the condensate in the half-circle arm bathes in the constant gravitational potential around the sphere. The resulting phase difference at the Josephson junctions on both sides of the straight arm induces a sinusoidal electric current that has a frequency determined by the precise gravitational potential due to the massive sphere.

Based on Feynman's explanation that a Cooper pair is "a bound pair act as a Bose particle", we propose a bosonic phase operator formalism and a bosonic Hamiltonian model for Josephson junction. The Cooper pair number — phase uncertainty relation is thus established. The corresponding minimum uncertainty state is derived which turns out to be a phase state.

Metal (M) doped PrBa₂Cu₃O₇, i.e. PrBa₂(Cu_1-xM_x)₃O₇ for M=Al, Co, Fe, Ga, Ni and Zn, and x=0.05, 0.10, 0.15, and 0.20 were fabricated. No significant second phase was found for the Al, Co, Fe and Ga doped samples up to 20% doping level. Impurity phases, however, were detected for Ni and Zn doped samples when doping concentration reached 15% and higher. At 77 K the electrical resistivity for most of these compounds is several orders in magnitude higher than that of the PrBa₂Cu₃O_7-δ. Although the lattice parameters in the doped samples changes toward tetragonal structure, all sample remained in orthorhombic structure and the parameters remain very close to those of the undoped one and YBa₂Cu₃O_7-δ. For this reason these compounds may serve as improved I-layer materials for making YBa₂Cu₃O_7-δ SIS Josephson junction.

Ramp junctions have been successfully synthesized utilizing an Y_1-xPr_xBa₂Cu₃O_y barrier with a continually graded concentration of Pr. The properties of these junctions are dominated by the barrier material rather than the boundary. Also, the damaged ramp surface is excluded from the weak link region so its influence is minimized. The Josephson coupling occurs at the naturally formed S/N interfaces within the Y_1-xPr_xBa₂Cu₃O_y layer. Thus it leads to a highly transparent S/N boundary and greatly enhances the performance of the junctions. The effective thickness of the barrier can be varied even post fabrication, depending on the measuring temperature and the concentration gradient. The temperature dependence of the barrier thickness and Josephson properties were investigated and compared with those junctions with a conventional single barrier. These unique features should motivate further studies on the nature of these junctions.

First, we show through a numerical simulation that the massive Schwinger model used to formulate solutions to CDW transport in itself is insufficient for the transport of soliton–antisoliton (S–S′) pairs through a pinning gap model of CDW transport. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits the formation of S–S′ pairs which could be used to transport CDW through a potential barrier. Previously, we have argued that there are analogies between this construction and the false vacuum hypothesis used for showing a necessary and sufficient condition for formation of CDW S–S′ pairs in wavefunctionals. Here we note that this can be established via either the use of the Bogomil'nyi inequality or an experimental artifact which is due to the use of the false vacuum hypothesis to obtain a proportional "distance" between the S–S′ charge centers.

Based on Feynman's explanation about Cooper pair that "a bound pair acts as a Bose particle" and the bosonic operator Hamiltonian of the Josephson junction, we realize that the quantum state of the Josephson junction is a Cooper pair number-phase entangled state constructed by the phase operator across the junction. Its Schmidt decomposition is derived. The Cooper pair number-phase squeezed state's projection onto this entangled state leads to a geometric distribution.

We investigate critical current (I_c) modulation of stacked Josephson junctions (SJJs) dc superconducting quantum interference device (dc SQUID) on a Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) whisker. A coupled SJJs with a completely perforated hole of 0.1 μm × 0.2 μm were fabricated by using a 3-D focused-ion-beam (FIB) etching method. Those dc SQUIDs exhibited uniform multi-branch structures and clearly oscillated critical current under external magnetic fields (H_e). With applying H_e, the clear periodic modulation patterns of I_c are obtained and well fitted to the calculated value from the loop area of 0.02 μm².

A model for the analytic description of vortices in a system consisting of a long Josephson junction and a waveguide is formulated. For this system all types of elementary vortices and its chains are listed. The allowed range of velocities of an elementary vortex is found. It is established that a free vortex can be a fast one which moves with velocity much greater than the Swihart velocity of Josephson junction. The effect of the waveguide on the induced vortices motion is studied. It is shown that fast vortex can be generated by relatively small values of bias current density. The effect of vortex Cherenkov losses on the bias current is described.

The transport of a spatially periodic system with time delayed feedback driven by coupled noise terms is investigated. A general approximate equation of the current is derived. For the superconduction Josephson junction, it is found that suitable time delay can enhance the current in the system. In the presence of the coupling between noise terms, the current direction is determined by the sign of the coupling. The negative coupling can induce positive current, while the positive coupling can induce negative current. The absolute value of the current is a peaked function of the additive noise but a monotonically increasing function of the multiplicative noise. Numerical simulations are in good agreement with the approximate theoretical results.

A system composed of a single-Cooper-pair box irradiated by a single-mode quantized field has been considered. The entanglement relative to the mixedness μ and the detuning δ is investigated with negative partial transpose. It is found that in the case of initial mixed state, the entanglement is weakened, but increases as time evolves. For a detuned system, the entanglement is further suppressed but more stationary than that for a resonant system.

The quantum theory for a mesoscopic electric circuit including a Josephson junction with charge discreteness is studied. By considering coupling energy of the mesoscopic capacitor in Josephson junction device, a Hamiltonian describing the dynamics of a quantum mesoscopic electric LC-circuit with charge discreteness is introduced. We first calculate the persistent current on a quantum driven ring including Josephson junction. Then we obtain the persistent current and energy spectrum of a quantum mesoscopic electrical circuit which includes capacitor, inductor, time-dependent external source and Josephson junction.

A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.

A method was devised to construct a generalized dual field theory with a quantum field theory named the dual Hamiltonian (DH) method. As a simple example using this method, we examined the duality between coherent quantum phase-slip and Josephson junction (JJ) in single junction systems and nanowires. This method was proved to be reliable within the Villain approximation.

In this paper we calculate the loss of fidelity due to quantum leakage for the Josephson charge qubit (JCQ). In this investigation the characteristic values and characteristic states of the Mathieu equation are used. It is shown that for present typical parameters of JCQ, E_J/E_ch ~ 0.02, the loss of the fidelity per elementary operation is about 10^-4 which satisfies DiVincenzo's low decoherence criterion. By appropriately improving the designs of the Josephson junction, namely, decreasing E_J/E_ch to ~ 0.01, the loss of fidelity per elementary operation can decrease even smaller to 10^-5. The first-order nonadiabatic correction is also obtained by using the approach.

Based on Feynman's explanation about the Cooper pair that "a bound pairs act as a Bose particle" and the bosonic operator Hamiltonian of Josephson junction (H.-Y. Fan, Int. J. Mod. Phys. B17 (2003) 2599) as well as the entangled state representation, we establish a possible number–phase squeezing mechanism for the Cooper-pair and the phase difference between the two sides of the junction. We find that when an extra energy (e.g. microwave radiation) is provided to the junction, then this squeezing mechanism can happen.

We consider a superconductor/double-ferromagnet/superconductor (S/I₁/F/I_C/F'/I₂/S) ballistic junction with thin insulating layers in the interfaces. An extensive investigation is carried out for the possibility of 0- or π-junction and the important phaseshift. The average exchange field for the two ferromagnets has limited use, only for weak exchange fields. Several analytical formulas are obtained for the energy spectrum in simple cases with interface potential (a) absent, (b) between ferromagnets only, (c) double resonance barrier between S and F layers. They give reasonable agreement even outside their range of validity. For the case of strong S/F barriers we find a strong interplay of Andreev bound states and interbarrier resonances.

We present the bosonic operator Hamiltonian models of two Josephson junctions which are connected in series and in parallel, respectively. By introducing the entangled state representations (|η〉 representation and Cooper pairs representation) and projecting the operator Hamiltonian onto the |η〉 representation we obtain the correct Josephson current and phase equations consistent with the classical Hamiltonian cases.

The possibility of high-field Josephson magnetic resonance (HFJMR) in high-T_c superconductors (HTSCs) is theoretically demonstrated. The HFJMR is caused by the penetration of Abrikosov vortices into the grains in fields within H_c1≤H<H_x (where H_c1 is the first critical field and H_x is the field corresponding to vortex separation from pinning centers in the grains). The signals from microwave absorption is dependent on the ratio of grain sizes that produces junction, the anisotropy and the intergrain coupling strength. These properties can be used for investigations of HTSC macrostructures and a vortex matter.