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arXiv:1810.06069 · New Journal of Physics

Transverse Josephson vortices and localized states in stacked Bose–Einstein condensates

J A Gil Granados, A Muñoz Mateo, M Guilleumas, X Viñas

Published Feb 22, 2019• 7 citations
arXivHTMLPDF

Abstract

The stacks of Bose–Einstein condensates coupled by long Josephson junctions present a rich phenomenology feasible to experimental realization and specially suitable for technological applications as the nonlinear-optics and superconducting analogs have already proved. Among this, we show that transverse Bloch waves excited in arrays of one-dimensional coupled condensates can carry tunneling superflows whose dynamical stability depends on the quasimomentum. Across the stacks with periodic boundary conditions, forming closed ring-shaped systems, such Bloch states yield transverse Josephson vortices with a generic non-integer circulation in units of h / m . Additionally, the superpositions of degenerate linear Bloch waves can suppress the supercurrents and give rise to families of nonlinear standing-wave states with strong (transverse) spatial localization. Stable states of this type can also be found in finite size systems.

DOI
10.1088/1367-2630/ab09ad

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The stacks of Bose–Einstein condensates coupled by long Josephson junctions present a rich phenomenology feasible to experimental realization and specially suitable for technological applications as the nonlinear-optics and superconducting analogs have already proved. Among this, we show that transverse Bloch waves excited in arrays of one-dimensional coupled condensates can carry tunneling superflows whose dynamical stability depends on the quasimomentum. Across the stacks with periodic boundary conditions, forming closed ring-shaped systems, such Bloch states yield transverse Josephson vortices with a generic non-integer circulation in units of h / m . Additionally, the superpositions of degenerate linear Bloch waves can suppress the supercurrents and give rise to families of nonlinear standing-wave states with strong (transverse) spatial localization. Stable states of this type can also be found in finite size systems.
The stacks of Bose-Einstein condensates coupled by long Josephson junctions present a richphenomenology feasible to experimental realization and specially suitable for technologicalapplications as the nonlinear-optics and superconducting analogs have already proved. Among this,we show that transverse Bloch waves excited in arrays of one-dimensional coupled condensates cancarry tunneling superflows whose dynamical stability depends on the quasimomentum. Across thestacks with periodic boundary conditions, forming closed ring-shaped systems, such Bloch states yieldtransverse Josephson vortices with a generic non-integer circulation in units ofh/m. Additionally, thesuperpositions of degenerate linear Bloch waves can suppress the supercurrents and give rise tofamilies of nonlinear standing-wave states with strong(transverse)spatial localization. Stable states ofthis type can also be found infinite size systems.
Abstract Considerable progress in experimental studies of atomic gases in a toroidal geometry opens up novel prospects for the investigation of fundamental properties of superfluid states and creation of new configurations for atomtronic circuits. In particular, a setting with Bose–Einstein condensates loaded in a dual-ring trap suggests a possibility to consider the dynamics of tunneling between condensates with different angular momenta. Accordingly, we address the tunneling in a pair of coaxial three-dimensional (3D) ring-shaped condensates separated by a horizontal potential barrier. A truncated (finite-mode) Galerkin model and direct simulations of the underlying 3D Gross–Pitaevskii equation are used for the analysis of tunneling superflows driven by an initial imbalance in atomic populations of the rings. The superflows through the corresponding Bose–Josephson junction are strongly affected by persistent currents in the parallel rings. Josephson oscillations of the population imbalance and angular momenta in the rings are obtained for co-rotating states and non-rotating ones. On the other hand, the azimuthal structure of the tunneling flow demonstrates formation of Josephson vortices (fluxons) with zero net current through the junction for hybrid states , built of counter-rotating persistent currents in the coupled rings.
Coupled coaxially stacked toroidal condensates with persistent currents suggest an appealing physical platform for investigation of various phenomena related to interacting superflows from Josephson effects in the regime of weak interactions to the quantum Kelvin-Helmholtz instability for merging rings. We suggest experimentally accessible methods to prepare states with different topological charges in two coupled coaxial ring-shaped atomic Bose-Einstein condensates. Our results open up the way to direct observation of rotational Josephson vortices in atomic Bose-Einstein condensates.
We investigate matter-wave solitons in a binary Bose-Einstein condensate (BEC) with spin-orbit (SO) coupling, loaded in a one-dimensional (1D) deep optical lattice and a three-dimensional anisotropic magnetic trap, which creates an array of elongated sub-BECs with transverse tunneling. We show that the system supports 1D continuous and discrete solitons localized in the longitudinal (along the array) and the transverse (across the array) directions, respectively. In addition, such solitons are always unpolarized in the zero-momentum state but polarized in finite-momentum states. We also show that the system supports stable two-dimensional semidiscrete solitons, including single- and multiple-peaked ones, localized in both the longitudinal and transverse directions. Stability diagrams for single-peaked semidiscrete solitons in different parameter spaces are identified. The results reported here are beneficial not only for understanding the physical property of SO-coupled BECs but also for generating new types of matter-wave solitons.
Superfluid properties of Bose-Einstein condensates (BEC) in toroidal quasi-one-dimensional traps are investigated in the presence of periodic scattering length modulations along the ring. The existence of several types of stable periodic waves, ranging from almost uniform to very fragmented chains of weakly interacting and equally spaced solitons, is demonstrated. We show that these waves may support persistent atomic currents and sound waves with spectra of Bogoliubov type. Fragmented condensates can be viewed as arrays of Josephson junctions and the current as a BEC manifestation of the dc-Josephson effect. The influence of linear defects on BEC superfluidity has been also investigated. We found that for subcritical velocities, linear defects that are static with respect to the lattice (while the condensate moves in respect to both the optical lattice and the defect) preserve the BEC superfluidity.
The control over the geometry and topology of quantum systems is crucial for advancing novel quantum technologies. This work provides a synthesis of recent insights into the behavior of quantum vortices within atomic Bose–Einstein condensates (BECs) subject to curved geometric constraints. We highlight the significant impact of the curvature on the condensate density and phase distribution, particularly in quasi-one-dimensional waveguides for different angular momentum states. An engineered periodic transport of the quantized vorticity between density-coupled ring-shaped condensates is discussed. The significant role of curved geometry in shaping the dynamics of rotational Josephson vortices in long atomic Josephson junctions is illustrated for the system of vertically stacked toroidal condensates. Different methods for the controlled creation of rotational Josephson vortices in coupled ring systems are described in the context of the formation of long-lived vortex configurations in shell-shaped BECs with cylindrical geometry. Future directions of explorations of vortices in curved geometries with implications for quantum information processing and sensing technologies are discussed.