Propagation and interation properties of vortex solitons in annular Gaussian potential

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.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.

arXiv:1606.02494Journal of Physics Condensed MatterSep 8, 201616 citations

Dipolar bright solitons and solitary vortices in a radial lattice

Chunqing Huang, Lin Lyu, Hao Huang +5 more

Stabilizing vortex solitons with high values of the topological charge $S$ is a challenging issue in optics, studies of Bose-Einstein condensates (BECs), and other fields. To develop an approach to the solution of this problem, we consider a two-dimensional dipolar BEC under the action of an axisymmetric radially periodic lattice potential, $V(r)\ensuremath{\sim}cos(2r+\ensuremath{\delta})$, with dipole moments polarized perpendicular to the system's plane, which gives rise to isotropic repulsive dipole-dipole interactions. Two radial lattices are considered, with $\ensuremath{\delta}=0$ and $\ensuremath{\pi}$, i.e., a potential maximum or minimum at $r=0$ , respectively. Families of vortex gap soliton (GSs) with $S=1$ and $S\ensuremath{\ge}2$, the latter ones often being unstable in other settings, are completely stable in the present system (at least up to $S=11$ ), being trapped in different annular troughs of the radial potential. The vortex solitons with different $S$ may stably coexist in sufficiently far separated troughs. Fundamental GSs, with $S=0$ , are found too. In the case of $\ensuremath{\delta}=0$, the fundamental solitons are ring-shaped modes, with a local minimum at $r=0.$ At $\ensuremath{\delta}=\ensuremath{\pi}$, they place a density peak at the center.Stabilizing vortex solitons with high values of the topological charge $S$ is a challenging issue in optics, studies of Bose-Einstein condensates (BECs), and other fields. To develop an approach to the solution of this problem, we consider a two-dimensional dipolar BEC under the action of an axisymmetric radially periodic lattice potential, $V(r)\ensuremath{\sim}cos(2r+\ensuremath{\delta})$, with dipole moments polarized perpendicular to the system's plane, which gives rise to isotropic repulsive dipole-dipole interactions. Two radial lattices are considered, with $\ensuremath{\delta}=0$ and $\ensuremath{\pi}$, i.e., a potential maximum or minimum at $r=0$, respectively. Families of vortex gap soliton (GSs) with $S=1$ and $S\ensuremath{\ge}2$, the latter ones often being unstable in other settings, are completely stable in the present system (at least up to $S=11$), being trapped in different annular troughs of the radial potential. The vortex solitons with different $S$ may stably coexist in sufficiently far separated troughs. Fundamental GSs, with $S=0$, are found too. In the case of $\ensuremath{\delta}=0$, the fundamental solitons are ring-shaped modes, with a local minimum at $r=0.$ At $\ensuremath{\delta}=\ensuremath{\pi}$, they place a density peak at the center.

arXiv:1708.02011Physical Review ANov 13, 201719 citations

Stabilizing vortex solitons with high values of the topological charge

S

is a challenging issue in optics, studies of Bose-Einstein condensates (BECs), and other fields. To develop an approach to the solution of this problem, we consider a two-dimensional dipolar BEC under the action of an axisymmetric radially periodic lattice potential, $V(r)\ensuremath{\sim}cos(2r+\ensuremath{\delta})$, with dipole moments polarized perpendicular to the system's plane, which gives rise to isotropic repulsive dipole-dipole interactions. Two radial lattices are considered, with $\ensuremath{\delta}=0$ and $\ensuremath{\pi}$, i.e., a potential maximum or minimum at

r=0

, respectively. Families of vortex gap soliton (GSs) with

S=1

and $S\ensuremath{\ge}2$, the latter ones often being unstable in other settings, are completely stable in the present system (at least up to

S=11

), being trapped in different annular troughs of the radial potential. The vortex solitons with different

S

may stably coexist in sufficiently far separated troughs. Fundamental GSs, with

S=0

, are found too. In the case of $\ensuremath{\delta}=0$, the fundamental solitons are ring-shaped modes, with a local minimum at

r=0.

At $\ensuremath{\delta}=\ensuremath{\pi}$, they place a density peak at the center.