Josephson Phase Research Articles

Tunable ground states in helical p-wave Josephson junctions

We study new types of Josephson junctions composed of helical p-wave superconductors with and -pairing symmetries using quasi-classical Green’s functions with generalized Riccati parametrization. The junctions can host rich ground states: π phase, 0 + π phase, φ0 phase and φ phase. The phase transition can be tuned by rotating the magnetization in the ferromagnetic interface. We present the phase diagrams in the parameter space formed by the orientation of the magnetization or by the magnitude of the interfacial potentials. The selection rules for the lowest order current which are responsible for the formation of the rich phases are summarized from the current-phase relations based on the numerical calculation. We construct a Ginzburg–Landau type of free energy for the junctions with d-vectors and the magnetization, which not only reveals the interaction forms of spin-triplet superconductivity and ferromagnetism, but can also directly lead to the selection rules. In addition, the energies of the Andreev bound states and the novel symmetries in the current-phase relations are also investigated. Our results are helpful both in the prediction of novel Josephson phases and in the design of quantum circuits.

Confocal Annular Josephson Tunnel Junctions

The physics of Josephson tunnel junctions drastically depends on their geometrical configurations and here we show that also tiny geometrical details play a determinant role. More specifically, we develop the theory of short and long confocal annular Josephson tunnel junctions in the presence of an in-plane magnetic field of arbitrary orientations. The behavior of a circular annular Josephson tunnel junction is then seen to be simply a special case of the above result. For junctions having a normalized perimeter less than one the threshold curves are derived and computed even in the case with trapped Josephson vortices. For longer junctions a numerical analysis is carried out after the derivation of the appropriate motion equation for the Josephson phase. We found that the system is modeled by a modified and perturbed sine-Gordon equation with a space dependent effective Josephson penetration length inversely proportional to the local junction width. Both the fluxon statics and dynamics are deeply affected by the non-uniform annulus width. Static zero-field multiple-fluxon solutions exist even in presence of a large bias current. The tangential velocity of a traveling fluxon is not determined by the balance between the driving and drag forces due to the dissipative losses. Furthermore, the fluxon motion is characterized by a strong radial inward acceleration which causes electromagnetic radiation concentrated at the ellipse equatorial points.

Josephson effect in a triple-quantum-dot ring with one dot coupled to superconductors: Numerical renormalization group calculations

We investigate the Josephson effect in a triple-quantum-dot ring in which only one dot is coupled to the superconductors, by performing the numerical renormalization group calculations. As a result, two kinds of Josephson phase transitions arise. One is the phase transition accompanied by the sharp change of the current direction, whereas the other phase transition is only accompanied by the smooth change of the current direction. Our analysis shows that in this structure, the phase transitions are determined by the variation of interdot spin correlations. The geometry of triple-dot ring induces various spin-correlation modes, leading to the complicate phase transitions. What's notable is that a spin singlet can form between the two lateral dots, which is decoupled from the main channel of this structure. It is certain that such a structure provides an alternative proposal to manipulate the spin correlation between the lateral dots.

1D Josephson quantum interference grids: diffraction patterns and dynamics

We investigate the magnetic response of transmission lines with embedded Josephson junctions and thus generating a 1D underdamped array. The measured multi-junction interference patterns are compared with the theoretical predictions for Josephson supercurrent modulations when an external magnetic field couples both to the inter-junction loops and to the junctions themselves. The results provide a striking example of the analogy between Josephson phase modulation and 1D optical diffraction grid. The Fiske resonances in the current-voltage characteristics with voltage spacing , where L is the total physical length of the array, the magnetic flux quantum and the speed of light in the transmission line, demonstrate that the discrete line supports stable dynamic patterns generated by the ac Josephson effect interacting with the cavity modes of the line.

Resonant enhancement of macroscopic quantum tunneling in Josephson junctions: Influence of coherent two-level systems

We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature ${T}_{cr}$ the thermal fluctuations of the Josephson phase induce such a switching, and as $T<{T}_{cr}$ the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.

Tunable±φ,φ0, andφ0±φJosephson junction

We study a 0-$\pi$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation $I_s(\psi)$ and the Josephson energy $U(\psi)$, where $\psi$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\varphi$ JJ with degenerate ground state phases $\psi=\pm\varphi$. The $\varphi$ domain is rather large, so one can easily construct a $\varphi$ JJ experimentally. We derive the current phase relation and show that it can be tuned \emph{in situ} by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\psi=\pm\varphi$, $\psi=\varphi_0$ ($\varphi_0 \neq 0,\pi$) and even $\psi=\varphi_0\pm\varphi$. The dependence of $\varphi_0$ on applied magnetic flux is not $2\pi$ (one flux quantum) periodic.

Diffusion anomalies in ac-driven Brownian ratchets.

We study diffusion in ratchet systems. As a particular experimental realization we consider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux. We analyze mean-square displacement of the Josephson phase and find that within selected parameter regimes it evolves in three distinct stages: initially as superdiffusion, next as subdiffusion, and finally as normal diffusion in the asymptotic long-time limit. We show how crossover times that separates these stages can be controlled by temperature and an external magnetic flux. The first two stages can last many orders longer than characteristic time scales of the system, thus being comfortably detectable experimentally. The origin of abnormal behavior is noticeable related to the ratchet form of the potential revealing an entirely new mechanism of emergence of anomalous diffusion. Moreover, a normal diffusion coefficient exhibits nonmonotonic dependence on temperature leading to an intriguing phenomenon of thermal noise suppressed diffusion. The proposed setup for experimental verification of our findings provides a new and promising testing ground for investigating anomalies in diffusion phenomena.

Josephson phase diffusion in the superconducting quantum interference device ratchet.

We study diffusion of the Josephson phase in the asymmetric superconducting quantum interference device (SQUID) subjected to a time-periodic current and pierced by an external magnetic flux. We analyze a relation between phase diffusion and quality of transport characterized by the dc voltage across the SQUID and efficiency of the device. In doing so, we concentrate on the previously reported regime [J. Spiechowicz and J. Łuczka, New J. Phys. 17, 023054 (2015)] for which efficiency of the SQUID attains a global maximum. For long times, the mean-square displacement of the phase is a linear function of time, meaning that diffusion is normal. Its coefficient is small indicating rather regular phase evolution. However, it can be magnified several times by tailoring experimentally accessible parameters like amplitudes of the ac current or external magnetic flux. Finally, we prove that in the deterministic limit this regime is essentially non-chaotic and possesses an unexpected simplicity of attractors.

Ground-state properties of a triangular triple quantum dot connected to superconducting leads

We study ground-state properties of a triangular triple quantum dot connected to two superconducting (SC) leads. In this system orbital motion along the triangular configuration causes various types of quantum phases, such as the SU(4) Kondo state and the Nagaoka ferromagnetic mechanism, depending on the electron filling. The ground state also evolves as the Cooper pairs penetrate from the SC leads. We describe the phase diagram in a wide range of the parameter space, varying the gate voltage, the couplings between the dots and leads, and also the Josephson phase between the SC gaps. The results are obtained in the limit of large SC gap, carrying out exact diagonalization of an effective Hamiltonian. We also discuss in detail a classification of the quantum states according to the fixed point of the Wilson numerical renormalization group (NRG). Furthermore, we show that the Bogoliubov zero-energy excitation determines the ground state of a π Josephson junction at small electron fillings.

Tunable fractional Josephson effect in the topological superconducting junction with embedded quantum dots

We investigate the fractional Josephson effect in the junction of two Majorana zero modes contributed by the topological superconducting wires. It shows that when the Majorana zero modes couple indirectly via one quantum dot, shifting the dot level does not change the phase of the Josephson current. However, if the junction is a double-channel geometry, abundant Josephson phase transitions can be observed. Such a result arises from the fermion parity conservation which is related to the quantum interference. Moreover, in the presence of appropriate structural parameters, destructive interference will occur between the two channels, which induces the appearance of the normal Josephson effect. These results will be helpful for describing the fractional Josephson effect modulated by quantum dots.

Hidden two-qubit dynamics of a four-level Josephson circuit.

Multi-level control of quantum coherence exponentially reduces communication and computation resources required for a variety of applications of quantum information science. However, it also introduces complex dynamics to be understood and controlled. These dynamics can be simplified and made intuitive by employing group theory to visualize certain four-level dynamics in a 'Bell frame' comprising an effective pair of uncoupled two-level qubits. We demonstrate control of a Josephson phase qudit with a single multi-tone excitation, achieving successive population inversions between the first and third levels and highlighting constraints imposed by the two-qubit representation. Furthermore, the finite anharmonicity of our system results in a rich dynamical evolution, where the two Bell-frame qubits undergo entangling-disentangling oscillations in time, explained by a Cartan gate decomposition representation. The Bell frame constitutes a promising tool for control of multi-level quantum systems, providing an intuitive clarity to complex dynamics.

Limiting mechanism for critical current in topologically frustrated Josephson junctions

Eutectic Sr$_2$RuO$_4$-Ru samples with $\mu$m-sized Ru-metal inclusions support inhomogeneous superconductivity above the bulk transition of Sr$_2$RuO$_4$ in the so-called 3-Kelvin phase. In Pb/Ru/Sr$_2$RuO$_4$ Josephson junctions as realized by Maeno et al., a Pb film is indirectly coupled to the superconductor Sr$_2$RuO$_4$ mediated by the proximity-induced superconducting Ru-inclusions, yielding an extended Josephson contact through the interface between Ru and Sr$_2$RuO$_4$. Motivated by this experimental setup, we formulate a sine-Gordon model for the Josephson phase of the interface, assuming a simple cylindrical shape for the Ru-inclusion hosting the proximity-induced $s$-wave superconducting phase. Considering the Sr$_2$RuO$_4$ as a chiral $p$-wave superconductor, we discuss two types of Josephson junctions, a frustrated one due to the nature of the order parameter in Sr$_2$RuO$_4$, and an unfrustrated one for the topologically trivial 3-Kelvin phase. While the latter situation displays standard junction behavior, the former yields an unusual limiting mechanism for the critical current, based on a pinning-depinning transition of a spontaneously induced magnetic flux driven by an externally applied current. We analyze different coupling limits and show that different critical currents can arise for the two topologies. This concept fits well to recent experimental data obtained for the above setup showing an anomalous temperature dependence of the critical current at the transition temperature $T_c $ of bulk Sr$_2$RuO$_4$.

Radiation power and linewidth of a semifluxon-based Josephson oscillator

We demonstrate a high-frequency generator operating at ∼200 GHz based on flipping a semifluxon in a Josephson junction of moderate normalized length. The semifluxon spontaneously appears at the π discontinuity of the Josephson phase artificially created by means of two tiny current injectors. The radiation is detected by an on-chip detector (tunnel junction). The estimated radiation power (at the detector) is ∼8 nW and should be compared with the dc power of ∼100 nW consumed by the generator. The measured radiation linewidth, as low as 1.1 MHz, is typical for geometrical (Fiske) resonances, although we tried to suppress such resonances by placing well-matched microwave transformers at its both ends. Making use of a phase-locking feedback loop, we are able to reduce the radiation linewidth to less than 1 Hz measured relative to the reference oscillator and defined just by the resolution of our measurement setup.

Possible Resonance Effect of Axionic Dark Matter in Josephson Junctions

We provide theoretical arguments that dark-matter axions from the galactic halo that pass through Earth may generate a small observable signal in resonant S/N/S Josephson junctions. The corresponding interaction process is based on the uniqueness of the gauge-invariant axion Josephson phase angle modulo 2π and is predicted to produce a small Shapiro steplike feature without externally applied microwave radiation when the Josephson frequency resonates with the axion mass. A resonance signal of so far unknown origin observed by C. Hoffmann et al. [Phys. Rev. B 70, 180503(R) (2004)] is consistent with our theory and can be interpreted in terms of an axion mass m(a)c2=0.11 meV and a local galactic axionic dark-matter density of 0.05 GeV/cm3. We discuss future experimental checks to confirm the dark-matter nature of the observed signal.

Theory of supercurrent transport in SIsFS Josephson junctions

We present the results of theoretical study of Current-Phase Relations (CPR) in Josephson junctions of SIsFS type, where 'S' is a bulk superconductor and 'IsF' is a complex weak link consisting of a superconducting film 's', a metallic ferromagnet 'F' and an insulating barrier 'I'. We calculate the relationship between Josephson current and phase difference. At temperatures close to critical, calculations are performed analytically in the frame of the Ginsburg-Landau equations. At low temperatures numerical method is developed to solve selfconsistently the Usadel equations in the structure. We demonstrate that SIsFS junctions have several distinct regimes of supercurrent transport and we examine spatial distributions of the pair potential across the structure in different regimes. We study the crossover between these regimes which is caused by shifting the location of a weak link from the tunnel barrier 'I' to the F-layer. We show that strong deviations of the CPR from sinusoidal shape occur even in a vicinity of Tc, and these deviations are strongest in the crossover regime. We demonstrate the existence of temperature-induced crossover between 0 and pi states in the contact and show that smoothness of this transition strongly depends on the CPR shape.

Complete gate control of supercurrent in graphene p–n junctions

In a conventional Josephson junction of graphene, the supercurrent is not turned off even at the charge neutrality point, impeding further development of superconducting quantum information devices based on graphene. Here we fabricate bipolar Josephson junctions of graphene, in which a p-n potential barrier is formed in graphene with two closely spaced superconducting contacts, and realize supercurrent ON/OFF states using electrostatic gating only. The bipolar Josephson junctions of graphene also show fully gate-driven macroscopic quantum tunnelling behaviour of Josephson phase particles in a potential well, where the confinement energy is gate tuneable. We suggest that the supercurrent OFF state is mainly caused by a supercurrent dephasing mechanism due to a random pseudomagnetic field generated by ripples in graphene, in sharp contrast to other nanohybrid Josephson junctions. Our study may pave the way for the development of new gate-tuneable superconducting quantum information devices.

Single flux transistor: The controllable interplay of coherent quantum phase slip and flux quantization

The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.

Memory cell based on a φ Josephson junction

The φ Josephson junction has a doubly degenerate ground state with the Josephson phases ±φ. We demonstrate the use of such a φ Josephson junction as a memory cell (classical bit), where writing is done by applying a magnetic field and reading by applying a bias current. In the “store” state, the junction does not require any bias or magnetic field, but just needs to stay cooled for permanent storage of the logical bit. Straightforward integration with rapid single flux quantum logic is possible.

A tunable macroscopic quantum system based on two fractional vortices

We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created κ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the κ discontinuities with injector currents, we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realization of this tunable macroscopic quantum system is possible with today's technology.

Heat transport through a Josephson junction

We discuss heat transport through a Josephson tunnel junction under various bias conditions. We first derive the formula for the cooling power of the junction valid for arbitrary time dependence of the Josephson phase. Combining it with the classical equation of motion for the phase, we find the time averaged cooling power as a function of bias current or bias voltage. We also find the noise of the heat current and, more generally, the full counting statistics of the heat transport through the junction. We separately consider the metastable superconducting branch of the current-voltage characteristics allowing quantum fluctuations of the phase in this case. This regime is experimentally attractive since the junction has low power dissipation, low impedance and therefore may be used as a sensitive detector.