Anomalous spin Josephson effect in spin superconductors

The spin superconductor state is the spin-polarized triplet exciton condensate,which can be viewed as a counterpart of the charge superconductor state.As an analogy of the charge Josephson effect,the spin Josephson effect can be generated in the spin superconductor/normal metal/spin superconductor junctions.Here we study the spin supercurrent in the Josephson junctions consisting of two spin superconductors with noncollinear spin polarizations.For the Josephson junctions with out-of-plane spin polarizations,the possibleπ-state spin supercurrent appears due to the Fermi momentum-splitting Andreev-like reflections at the normal metal/spin superconductor interfaces.For the Josephson junctions with in-plane spin polarizations,the anomalous spin supercurrent appears and is driven by the misorientation angle of the in-plane polarizations.The symmetry analysis shows that the appearance of the anomalous spin Josephson current is possible when the combined symmetry of the spin rotation and the time reversal is broken.

New Derivation of Simple Josephson Effect Relation Using New Quantum Mechanical Equation

A relation of the Josephson current density equation is successfully derived;this is done through a new derivation of the equation of quantum by neglecting kinetic Newtonian term in the energy expression.

Anomalous Direct-Current Josephson Effect in Semiconductor Nanowire Junctions

We investigate the dc Josephson effect in one-dimensional junctions where a ring conductor is sandwiched between two semiconductor nanowires with proximity-induced superconductivity. Peculiar features of the Josephson effect arise due to the interplay of spin-orbit interaction and external Zeenmn field. By tuning the Zeeman field orientation, the device can vary from 0 to π junction. Afore importantly, nonzero ,losephson current is possible at zero phase difference across the junction. Although this anomalous Josephson current is not relevant to the topological phase transition, its magnitude can be significantly enhanced whe, n the nanowire, s become topological superconductors where Majorana bound states emerge. Distinct modulation patterns are obtained for the semiconductor nanowires in the topologically trivial and non-trivial phases. These results are useful to probe the topological phase transition in semiconductor nanowire junctions via the dc Josephson effect.

Anomalous Josephson effect between d-wave superconductors through a two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting

Based on the Bogoliubov-de Gennes equation and the extended McMillan’s Green’s function formalism,we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting.We show that due to the interplay of Rashba spin-orbit coupling and Zeeman splitting and d-wave pairing,the current-phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned.In particular,anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken,which can be realized by tuning some relevant parameters of the system,including the relative orientations and the strengths of the Zeeman field and the spin-orbit field in the bridge region,the relative orientations of the a axes in two superconductor leads,or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads.We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.

Ac Josephson effect in Corbino-geometry Josephson junctions constructed on Bi_(2)Te_(3) surface

Recently, a Corbino-geometry type of Josephson junction constructed on the surface of topological insulators has been proposed for hosting and braiding Majorana zero modes. As a first step to test this proposal, we successfully fabricated Corbino-geometry Josephson junctions(JJs) on the surface of Bi_(2)Te_(3) flakes. Ac Josephson effect with fractional Shapiro steps was observed in the Corbino-geometry JJs while the flux in the junction area was quantized. By analyzing the experimental data using the resistively shunted Josephson junction model, we found that the Corbino-geometry JJs exhibit a skewed current-phase relation due to its high transparency. The results suggest that Corbino-geometry JJs constructed on the surface of topological insulators may provide a promising platform for studying Majorana-related physics.

Influence of Rashba spin–orbit coupling on Josephson effect in triplet superconductor/two-dimensional semiconductor/triplet superconductor junctions

We study theoretically Josephson effect in a planar ballistic junction between two triplet superconductors with pwave orbital symmetries and separated by a two-dimensional(2D)semiconductor channel with strong Rashba spin–orbit coupling.In triplet superconductors,three types of orbital symmetries are considered.We use Bogoliubov–de Gennes formalism to describe quasiparticle propagations through the junction and the supercurrents are calculated in terms of Andreev reflection coefficients.The features of the variation of the supercurrents with the change of the strength of Rashba spin–orbit coupling are investigated in some detail.It is found that for the three types of orbital symmetries considered,both the magnitudes of supercurrent and the current-phase relations can be manipulated effectively by tuning the strength of Rashba spin–orbit coupling.The interplay of Rashba spin–orbit coupling and Zeeman magnetic field on supercurrent is also investigated in some detail.

Josephson junction of two-species Bose-Einstein condensates in a high-finesse optical cavity

The mean-field dynamics of undistinguishable two-species Bose Josephson junction coupled to a single mode high- finesse optical cavity is investigated. From the Hamiltonian, the phase portrait and the stationary points are given. It is shown that the role of the interspecies interaction equals the intraspecies interaction under suitable conditions. As the interspecies interaction increases, the trapped atoms will start tunneling between the two wells unnaturally for some special cases.

Novel 0–π transitions in Josephson junctions between noncentrosymmetric superconductors

We study the Josephson effect between two noncentrosymmetric superconductors（NCSs） with opposite polarization vectors of Rashba spin–orbit coupling（RSOC）.We find a 0–π transition driven by the triplet–singlet ratio of NCSs.Different from conventional 0–π transitions,the Andreev bound states change their energy range instead of phase shift in the 0–π transition found here.This novel property results in a feature that the critical current becomes almost zero at the transition point,not only a minimum.Furthermore,when the directions of RSOC polarization vectors are the same in two NCSs,the similar effect can also be found in the presence of a perpendicular exchange field or a Dresselhause spin–orbit coupling in the interlayer.We find novel oscillations of critical current without 0–π transition.These novel 0–π transitions or oscillations of critical current present new understanding of the Josephson effect and can also serve as a tool to determine the unknown triplet–singlet ratio of NCSs.

Transport properties of Tl_(2)Ba_(2)CaCu_(2)O_(8) microbridges on a low-angle step substrate

Tl-based superconducting devices have been drawn much attention for their high transition temperature(T_c), which allow the high temperature superconductors(HTS) devices to operate at temperature near 100 K. The realization of Tlbased devices will promote the research and application of HTS devices. In this work, we present transport properties of Tl_(2) Ba_(2) CaCu_(2) O_(8)(Tl-2212) microbridges across a low-angle step on LaAlO_(3)(LAO) substrate. We experimentally demonstrate intrinsic Josephson effects(IJEs) in Tl-2212 films by tailoring the geometry, i.e., reducing the width of the microbridges. In the case of a 1 μm width microbridge, in addition to the observation of voltage branches and remarkable hysteresis on the current–voltage(I–V) characteristics, the temperature dependence of differential resistance shows a finite resistance above 60 K when the bias current is below the critical current. For comparison, the wider microbridges are also investigated, exhibiting a highly critical current but do not showing obvious IJEs.

Collapse-Revival and Entanglement in a Single-Cooper-Pair Box with a Single-Mode Cavity Field

A single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field is considered. The degree of entanglement between the quantized field and the single-Cooper-pair box is examined by using the field entropy. It is found that the collapse and revival phenomenon can exist in this system, the entropy reaches its local minimum at one-half of the quiescent period, and the larger the entropy, the greater the entanglement is.

Hot-Electron Effects in InAs Nanowire Josephson Junctions

The controlled tailoring of the energy distribution in an electron system opens the way to interesting new physics and device concepts, as demonstrated by research on metallic nanodevices during recent years. Here we investigate how Josephson coupling in a superconductor-InAs nanowire junction can be tuned by means of hot-electron injection and we show that a complete suppression of superconductive effects can be achieved using a power as low as 100 pW. Nanowires offer a novel design freedom as they allow axial and radial heterostructures to be defined as well as control over doping profiles, which can be crucial in the development of devices--such as nanorefrigerators--where precisely controlled and predictable energy barriers are mandatory. Our work provides estimates for unknown key thermal and electrical parameters, such as the electron-phonon coupling, in our InAs nanostructures.

Localized Asymmetric Atomic Matter Waves in Two-Component Bose-Einstein Condensates Coupled with Two-Photon Microwave Field

We investigate localized atomic matter waves in the two-photon microwave field. Interestingly, the oscillations two-component Bose-Einstein condensates coupled by of localized atomic matter waves will gradually decay and finally become non-oscillating behavior even if existing coupling field. In particular, atom numbers occupied in two different hyperfine spin states will appear asymmetric occupations after some time evolution.

Andreev Reflection of Pseudo-Correlated Pairs Electrons in the System ＂Superconductor-Fluctuation Superconductor-Superconductor＂

In the article, the Josephson system ＂Superconductor-Fluctuation Superconductor-Superconductor＂, consisting of a combination of superconductors with a fluctuation superconductor was considered. The possibility of transformation of the superconducting （Cooper） pairs in psevdocorrelated （fluctuation） of a pair of electrons is shown, and vice versa, the fluctuation pairs in the Cooper pairs in such a Josephson system. The characteristic features of the Andreev reflection of the weakly bound electron, which is part of the fluctuation pairs in the interface ＂fluctuation superconductor-superconductor＂ with a probability of forming a pair of ＂Electron-Hole＂ and the generation of psevdocorrelated pair discussed. The probability of formation of two correlated superconducting electron pairs, forming original cluster with a charge 4e, in the interface ＂Fluctuation Superconductor-Superconductor＂ as a result of transmutation of the reflected hole into an electron or subjection Andreev reflection of both electrons of fluctuation pairs is viewed. The above processes may be useful for better understanding the fluctuation effects in superconducting materials which appear at temperatures above the critical value.

The Formation of the Electronic Tornado is the Basis of Superconductivity

The space-time ladder theory reveals that the formation of electronic tornadoes,or the formation of electronic dissipative structures,to be precise,the enhancement of electronic Energy Qi field is the basis of superconductivity.The surrounding area of the electronic tornado is expanding,which is the basis of the Meissner effect,and the center is contracting,which is the basis of the pinning force.When the attractive force of the Energy Qi field is greater than the Coulomb repulsive force,the electrons form a Cooper pair and release dark energy into virtual space-time.When the dark energy increases to a certain extent,the virtual space-time frees the Cooper pair and forms an electron-virtual space-time wave,which fluctuates freely in the superconducting material,which is the basis for the superconducting resistance to be zero.This is similar to the principle of a hot air balloon.The virtual space-time is hot air and the electron pair is a hot air balloon device.Conductor electrons are free and easy to emit dark energy,resulting in insufficient dark energy,and it is not easy to form electron-pair virtual space-time waves,so the superconducting critical temperature is very low.This is because the emission coefficient of the conductor is too high.Insulator electrons are not easy to emit dark energy and easily form electron-pair virtual space-time waves.Therefore,the superconducting critical temperature is slightly higher because of the low emission coefficient of the insulator.The solution of the Qi-space-time wave equation,that is,the coherence coefficient,is an important factor in superconductivity.In addition,the conditions under which tornadoes form are also an important basis for superconductivity.Finally,it is emphasized that the coherence coefficient and prevention of dark energy emission are the two most important elements for preparing superconducting materials.

Reveal the nematic topological superconductivity from the anisotropic unconventional Josephson effect:Theory and application to doped Bi_(2)Se_(3)

We propose a scheme to reveal the possible nematic superconducting order parameter in the doped Bi2Se3 by observing the anisotropic unconventional Josephson effect without an external magnetic field.We find the presence of an intrinsicπ-phase in the spin-triplet channel of Andreev reflection.Its competition with the odd-parity superconducting gap phase can lead to unconventional Josephson effect in the Josephson junction,whose normal region is connected to the same side of the superconductor,called the U-shaped junction according to its geometry.For Josephson junctions with the interfaces perpendicular to the nematic direction,the competition will lead to a Josephsonπ-junctions.In the case where the interface is parallel to the nematic direction,it will lead to a Josephson 0-junction.Thus,this can directly reflect the nematic superconductivity.It is worth noting that Josephson coupling with the 4πperiod appears only in the normal injected channels.Interestingly,if the Josephson junction adopts a conventional geometry,it always exhibits a normal Josephson 0-junction regardless of the gap function taken by the doped Bi2Se3 and therefore cannot distinguish the pairing symmetry.We thus propose a superconducting quantum interference device containing a U-shaped Josephson junction to detect nematic superconductivity.This proposal not only can be applied to detect nematic superconductivity but also provides a feasible platform for topological quantum computation.

Quantum tunneling of ultracold atoms in optical traps

We review our theoretical advances in quantum tunneling of BoseEinstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectivdy, which are tile crucial feature of the non-Abelian Joseptmon effect. When the optical lattices are under gravity, we investigate the quantum tummling in the ＂Wannier-Stark localization＂ regime and ＂Lan（lau Zener tunneling＂ regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At hltermediate temperatures, the results of tile total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantmn tunneling ultimately. And we study the alternating-current and direct-current （ac and de） photonic 3osephson effects in two weakly linked microcavities containing ultracold two-level atones, which allows for direct observation of the effects. This enables new investigations of the effect of maw-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantmn tunneling of Bose- Einstein condensates.

Tunneling and Self-Trapping of Superfluid Fermi Gases in BCS-BEC Crossover

We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer （BCS） superfluid to Bose-Einstein condensates （BEC）. Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the ease of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.