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A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

We have developed a method for the reproducible fabrication of superconducting scanning tunneling microscope (STM) tips. We use these tips to form superconductor/insulator/superconductor tunnel junctions with the STM tip as one of the electrodes. We show that such junctions exhibit fluctuation dominated Josephson effects, and describe how the Josephson product I_cR_N can be inferred from the junctions' tunneling characteristics in this regime. This is first demonstrated for tunneling into Pb films, and then applied in studies of single crystals of NbSe₂. We find that in NbSe₂, I_cR_N is lower than expected, which could be attributed to the interplay between superconductivity and the coexisting charge density wave in this material.

We consider a single localized spin-1/2 placed between singlet superconducting leads of a Josephson junction inserted in a superconducting ring, subject to a dc magnetic field B || z. Turning on the tunneling or a time-dependent flux in a superconducting ring, induces oscillations of the Josephson current, with an amplitude sensitive to the initial value of the z-component of the spin, S_z = ±1/2, which allows for a measurement of the initial spin state. At low temperatures when effects of quasiparticles are negligible, this procedure realizes a quantum-non-demolition (QND) measurement of S_z.

The spontaneous emergence of enhanced responses and local orders are properties often associated with complex matter where nonlinearities and spatial inhomogeneities dominate. We discuss these phenomena in quantum devices realized with superconducting Josephson junction networks and cold atoms in optical lattices. We evidence how the pertinent engineering of the network's shape induces the enhancement of the zero-voltage Josephson critical currents in superconducting arrays as well as the emergence of spatially localized condensates for cold atoms in inhomogeneous optical lattices.

The overlap of localized wave functions in a two-mode approximation leads to interaction (cross-collision) between ultra-cold atoms trapped in distinct sites of a double-well potential. We show that this interaction can significantly change the atom tunneling rate for special trap configurations resulting in an effective linear Rabi regime of population oscillation between the trap wells. In this sense, we demonstrate that cross-collisional effects can significantly extend the validity of the two-mode model approach allowing it to be alternatively employed to explain the recently observed increase of tunneling rates due to nonlinear interactions. Moreover, we investigate the extension for ultra-cold atoms trapped in an optical lattice. Control over the cross-collisional terms, obtained through manipulation of the optical trapping potential, can be used as an engineering tool to study many-body physics.

This paper puts forward an interpretation of the Josephson effect based on the alternative theory of superconductivity (ATS). A comparison of the ATS- and BCS-based interpretations is provided. It is demonstrated that the ATS-based interpretation, unlike that based on the BCS theory, does not require a revision of fundamentals of quantum physics.

The presence of low-energy Dirac-like quasiparticles is one of the central features responsible for plethora of recent theoretical and experimental studies on graphene. In this review, we focus on the effect of the Dirac nature of these quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness d and arbitrary gate voltages V₀ applied across the barrier region. The second aspect involves study of the presence of localized magnetic impurities in graphene in which we discuss the unconventional nature of Kondo physics in graphene and the tunablity of Kondo effect with a gate voltage. We also chart out the nature of scanning tunneling conductance spectra for both doped and undoped graphene in the presence of impurities and discuss the effect of Dirac nature of graphene quasiparticles on such spectra. In particular, we provide a detailed analysis of the phenomenon that that the position of the impurity in the graphene matrix plays a crucial role in determining the nature of the STM specta.

In this paper, we investigated theoretically the dynamic effect induced by nonlinear tunneling of two weakly linked Bose–Einstein condensates in an extended boson Josephson-junction model, in which the two-body interaction is extended to neighboring lattice sites in strong interaction regime. As a consequence the dynamic properties compared with the usual Josephson-junction model are crucially modified by the atom-pair tunneling, which leads to the macroscopic quantum-states of coherent relative-phase between two condensates seen to be effective Schrödinger cat states. The relative-phase is controllable by system parameters and thus can be used to realize the qubit in quantum computation.

We present an analysis of Josephson effects in one quantum-dot-embedded junction with one s-wave superconductor (SC) and two topological superconductors (TSs). It is found that when superconducting phase difference is applied between the two TSs, the dot-SC coupling can efficiently modulate the fractional Josephson effect, including the changes of the supercurrent oscillation direction and period. Even though the polarization directions of the TSs are opposite, the dot-SC coupling enables to drive the fractional Josephson effect between the TSs. Next, as the superconducting phase difference is introduced between the TSs and SC, only the normal Josephson effect takes place.

We present a version of acoustic black holes by using the principle of the Josephson effect. We find that in the case where two superconductors A and B are separated by an insulating barrier, an acoustic black hole may be created in the middle region between the two superconductors. We discuss in detail how to describe an acoustic black hole in the Josephson junction and write the metric in the language of the superconducting electronics. Our final results infer that for big enough tunneling current and thickness of the junction, experimental verification of the Hawking temperature could be possible.

In this paper, we propose to directly detect Mott lobes, i.e. the order parameter 〈a〉, describing the Mott insulator (MI) to superfluid (SF) quantum phase transition of the Bose–Hubbard (BH) model. By weakly coupling the system to an environment in the SF phase, the U(1) symmetry breaking of the system is simulated, and the order parameter can be read from the AC Josephson current between the system and the environment. The relation between the order parameter and the Josephson current is obtained from both the mean-field theory approach and an exact numerical simulation of a finite-size example. Our numerical simulations show that the profile of the order parameter read from the Josephson current is different from it predicted by the mean-field theory, but similar to it in a system whose U(1) symmetry is broken by a weak field proportional to a + a^†. This proposal is feasible in optical lattices.

We consider a single localized spin-1/2 placed between singlet superconducting leads of a Josephson junction inserted in a superconducting ring, subject to a dc magnetic field B‖z. Turning on the tunneling or a time-dependent flux in a superconducting ring, induces oscillations of the Josephson current, with an amplitude sensitive to the initial value of the z-component of the spin, S_z = ±1/2, which allows for a measurement of the initial spin state. At low temperatures when effects of quasiparticles are negligible, this procedure realizes a quantum-non-demolition (QND) measurement of S_z.

We propose a new qubit consisting of a superconducting ring with an ordinary Josephson junction and a ferromagnetic π-junction. In the system, two degenerate stable states appear in the phase space without an external magnetic field due to a competition between the 0- and π-states. Because of quantum tunneling between the two degenerate states, bonding and antibonding states, which are used as a bit, are formed. For manipulating the states of the qubit, only small external magnetic field around zero is required. This feature leads to a large-scale integration and a construction of the qubit with a smaller size which is robust to decoherence by external noises.

We theoretically investigate generation of the entangled three macroscopic objects, i.e., macroscopic Greenberger-Horne-Zeilinger states, in Josephson systems by using the Cirac-Zoller scheme. We propose a quantum breather in a long Josephson junction as a macroscopic artifical atom and derive the Jaynes-Cummings-type interaction Hamiltonian required in the scheme. Macroscopic Greenberger-Horne-Zeilinger states play a crucial role in fundamental tests of quantum mechanics versus local realism at a macroscopic level.

We investigate the macroscopic quantum tunneling (MQT) in d-wave high-T_c superconductor Josephson junctions. Using the path-integral method, we analytically obtain the MQT rate for the c-axis twist Josephson junctions. In the case of the zero twist angle, the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is largely suppressed compared with the finite twist angle cases. Furthermore, the effect of the zero energy bound states (ZES) on the MQT in the in-plane junctions is theoretically investigated. We obtained the analytical formula of the MQT rate and showed that the presence of the ZES at the insulator/superconductor interface leads to a strong Ohmic quasiparticle dissipation. Therefore, the MQT rate is noticeably inhibited compared with the c-axis junctions in which the ZES are completely absent.

We study the stationary Josephson effect for neutral fermions in the BCS–BEC crossover, by solving self-consistently the Bogoliubov–de Gennes equations at zero temperature. We show that the maximum of the Josephson current is considerably enhanced at about unitarity. For vanishing small barriers the maximum Josephson current approaches the Landau critical current which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations.

We investigate tunneling properties of Bogoliubov phonons in a Bose-Einstein condensate. We find that the quasiparticle current of Bogoliubov phonon is remarkably enhanced near the potential barrier at low energies. This leads to the increase of the transmission probability in the low energy region. We show that the quasiparticle current twists the relative phase of the condensate wavefunctions and induces a Josephson supercurrent through the barrier. The Josephson critical current is estimated by calculating the induced supercurrent and phase difference.

We have theoretically investigated macroscopic quantum tunneling (MQT) and the influence of nodal quasiparticles and zero energy bound states (ZES) on MQT in s-wave/d-wave hybrid Josephson junctions. In contrast to d-wave/d-wave junctions, the low-energy quasiparticle dissipation resulting from nodal quasiparticles and ZES is suppressed due to a quasiparticle-tunneling blockade effect in an isotropic s-wave superconductor. Therefore, the inherent dissipation in these junctions is found to be weak. This result suggests high potential of s-wave/d-wave hybrid junctions for applications in quantum information devices.