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Semifluxons in superconductivity and cold atomic gases

R. Walser, E. Goldobin, Oliver Crasser, D. Koelle, R. Kleiner, W. P. Schleich

Published Apr 30, 2008• 5 citations
Publisher

Abstract

Josephson junctions (JJs) and junction arrays are well-studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is also possible to devise two different types of junctions: depending on the sign of the critical current density , they are called 0- or π-junctions. In turn, a 0–π junction is formed by joining two of these junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0–π boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0–π JJ is created by the phase of a complex valued Rabi frequency and we derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon.

DOI
10.18725/oparu-42727

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Josephson junctions (JJs) and junction arrays are well-studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is also possible to devise two different types of junctions: depending on the sign of the critical current density , they are called 0- or π-junctions. In turn, a 0–π junction is formed by joining two of these junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0–π boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0–π JJ is created by the phase of a complex valued Rabi frequency and we derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon.
Josephson junctions and junction arrays are well studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is also possible to device two different types of junctions: depending on the sign of the critical current density, they are called 0- or pi-junction. In turn, a 0-pi junction is formed by joining two of such junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0-pi boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0-pi Josephson junction is created by the phase of a complex valued Rabi-frequency and we a derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon.
We propose to create pairs of semifluxons starting from a flat-phase state in long, optical 0-$\ensuremath{\pi}$-0 Josephson junctions formed with internal electronic states of atomic Bose-Einstein condensates. In this optical system, we can dynamically tune the length aaa of the $\ensuremath{\pi}$ junction, the detuning $\ensuremath{\delta}$ of the optical transition, or the strength ${\ensuremath{\Omega}}_{0}$ of the laser coupling to induce transitions from the flat-phase state to such a semifluxon-pair state. Similarly as in superconducting 0-$\ensuremath{\pi}$-0 junctions, there are two, energetically degenerate semifluxon-pair states. A linear mean-field model with two internal electronic states explains this degeneracy and shows the distinct static field configuration in a phase diagram of the junction parameters. This optical system offers the possibility to dynamically create a coherent superposition of the distinct semifluxon-pair states and observe macroscopic quantum oscillation.
Josephson junctions with a phase drop of $\ensuremath{\pi}$ in the ground state allow us to create vortices of supercurrent carrying only half of the magnetic flux quantum ${\ensuremath{\Phi}}_{0}\ensuremath{\approx}2.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }\text{ }\mathrm{Wb}$. Such semifluxons have twofold degenerate ground states denoted $\ensuremath{\uparrow}$ (with flux $+{\ensuremath{\Phi}}_{0}/2$ and supercurrent circulating clockwise) and $\ensuremath{\downarrow}$ (with flux $\ensuremath{-}{\ensuremath{\Phi}}_{0}/2$ and supercurrent circulating counterclockwise). We investigate a molecule consisting of two coupled semifluxons in a 0-$\ensuremath{\pi}$-0 long Josephson junction. The fluxes (polarities) of semifluxons are measured by two on-chip SQUIDs. By varying the dc bias current applied to the 0-$\ensuremath{\pi}$-0 junction, we demonstrate controllable manipulation and switching between two states, $\ensuremath{\uparrow}\ensuremath{\downarrow}$ and $\ensuremath{\downarrow}\ensuremath{\uparrow}$, of a semifluxon molecule. These results provide a major step towards employing semifluxons as bits or qubits for classical and quantum digital electronics.
Atomtronics has the potential for engineering new types of functional devices, such as Josephson junctions (JJs). Previous studies have mainly focused on JJs whose ground states have zero or $\ensuremath{\pi}$ superconducting phase difference across the junctions, while arbitrary phase-tunable JJs may have important applications in superconducting electronics and quantum computation. Here we show that a phase-tunable JJ can be implemented in a spin-orbit-coupled cold atomic gas with the magnetic tunneling barrier generated by a spin-dependent focused laser beam. We consider the JJ confined in either a linear harmonic trap or a circular ring trap. In the ring trap, the magnetic barrier induces a spontaneous mass current for the ground state of the JJ, demonstrating the magnetoelectric effects of cold atoms.
Long Josephson tunnel junctions are non-linear transmission lines that allow propagation of current vortices (fluxons) and electromagnetic waves and are used in various applications within superconductive electronics. Recently, the Josephson vortex has been proposed as a new superconducting qubit. We describe a simple method to create a double-well potential for an individual fluxon trapped in a long elliptic annular Josephson tunnel junction characterized by an intrinsic non-uniform width. The distance between the potential wells and the height of the inter-well potential barrier are controlled by the strength of an in-plane magnetic field. The manipulation of the vortex states can be achieved by applying a proper current ramp across the junction. The read-out of the state is accomplished by measuring the vortex depinning current in a small magnetic field. An accurate one-dimensional sine-Gordon model for this strongly non-linear system is presented, from which we calculate the position-dependent fluxon rest-mass, its Hamiltonian density and the corresponding trajectories in the phase space. We examine the dependence of the potential properties on the annulus eccentricity and its electrical parameters and address the requirements for observing quantum-mechanical effects, as discrete energy levels and tunneling, in this two-state system.
Driven atomic Josephson junctions allow one to monitor phase-coherent dynamics with unprecedented control and flexibility of the system's physical conditions. While cold-atom manifestations of the Josephson effect have been extensively studied in a wide variety of settings, atomic Josephson junctions in synthetic electromagnetic fields remain largely unexplored. Here, we show that synthetic magnetic fields can induce Fraunhofer-like modulations of the critical current in atomic Josephson junctions. Although this effect presents analogies to the Fraunhofer patterns found in superconducting devices, distinctive features emerge due to the neutral nature of the superfluid. We investigate the underlying spatial interference mechanisms and elucidate the role of Josephson vortices in the formation of spatially modulated current distributions based on numerical simulations. Our results open up new avenues for matter-wave circuits to deepen our understanding of spatial coherence in Josephson junctions, which are fundamental to the development of novel quantum technologies.