Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup
arXiv:1901.03922 · doi:10.1103/PhysRevA.99.053619
Abstract
We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped target-like trap similar to the potential used to confine a Bose-Einstein condensate in a recent experiment [Eckel, et al.\ {\em Nature} {\bf 506}, 200 (2014)]. In addition to the ground state configuration, we identify a wide variety of excited states involving phase jumps (and associated dark solitons) inside the ring. These configurations are obtained from a systematic bifurcation analysis starting from the linear, small atom density, limit. We study the stability, and when unstable, the dynamics of the most basic configurations. Often these lead to vortical dynamics inside the ring persisting over long time scales in our numerical experiments. To illustrate the relevance of the identified states, we showcase how such dark-soliton configurations (even the unstable ones) can be created in laboratory condensates by using phase-imprinting techniques.
13 pages, 19 figures
References in corpus (48)
- Theory of Bose-Einstein condensation in trapped gases
- Formation and Propagation of Matter Wave Soliton Trains
- Formation of a Matter-Wave Bright Soliton
- Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
- Dark Solitons in Bose-Einstein Condensates
- Watching dark solitons decay into vortex rings in a Bose-Einstein condensate
- Bright gap solitons of atoms with repulsive interaction
- Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
- Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
- Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link
- Observation of Quantum Shock Waves Created with Ultra Compressed Slow Light Pulses in a Bose-Einstein Condensate
- Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
- Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
- Classical bifurcation at the transition from Rabi to Josephson dynamics
- An Atom Michelson Interferometer on a Chip Using a Bose-Einstein Condensate
- Hysteresis in a quantized, superfluid atomtronic circuit
- Driving phase slips in a superfluid atom circuit with a rotating weak link
- Generation of dark-bright soliton trains in superfluid-superfluid counterflow
- Experimental observation of oscillating and interacting matter wave dark solitons
- Atomtronics: ultracold atom analogs of electronic devices
- Extreme tunability of interactions in a Li Bose-Einstein condensate
- Propagation of Bose-Einstein condensates in a magnetic waveguide
- Ring Dark Solitons and Vortex Necklaces in Bose-Einstein Condensates
- Rapid production of Rb BECs in a combined magnetic and optical potential
- A high-accuracy algorithm for designing arbitrary holographic atom traps
- Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review
- A rapidly expanding Bose-Einstein condensate: an expanding universe in the lab
- Interference of Bose-Einstein Condensates on an Atom Chip
- Svortices and the fundamental modes of the "snake instability": Possibility of observation in the gaseous Bose-Einstein Condensate
- Robust Digital Holography For Ultracold Atom Trapping
- Dynamics of Dark-Bright Solitons in Cigar-Shaped Bose-Einstein Condensates
- Matter-wave solitons in radially periodic potentials
- Probing the circulation of ring-shaped Bose-Einstein condensates
- An Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments
- Generation and interaction of solitons in Bose-Einstein condensates
- Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov Analyses
- Persistent currents with non-quantized angular momentum
- Stability and dynamics of vortex clusters in nonrotated Bose-Einstein condensates
- The dynamics of quantum vortices in a toroidal trap
- A two-dimensional paradigm for symmetry breaking: the nonlinear Schrodinger equation with a four-well potential
- Self-heterodyne detection of the {\it in-situ} phase of an atomic-SQUID
- Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with Deflated continuation
- Emergence and Stability of Vortex Clusters in Bose-Einstein Condensates: a Bifurcation Approach near the Linear Limit
- Mean-field model for the interference of matter waves from a three-dimensional optical trap
- Solitons Riding on Solitons: Hypersolitons and the Quantum Newton's Cradle
- Vortex-vortex interactions in toroidally trapped Bose-Einstein condensates
- Bose-Einstein condensation in harmonic double wells
- Bound solitonic states in trapped multidimensional Bose-Einstein condensates