Journal
JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS
Volume 49, Issue 23, Pages 1-8Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0953-4075/49/23/235301
Keywords
Bose-Einstein condensates; dark solitons; saddle-center bifurcation; critical velocity
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Funding
- University of Nottingham
- EPSRC [EP/K023624/1, EP/I017828/1]
- European Comission grant QuILMI-Quantum Integrated Light Matter Interface [295293]
- EU (FET Proactive grant Matter-Wave) [601180]
- BSF [2010239]
- ERC under FP7, Marie Curie Actions, People, International Research Staff Exchange Scheme [IRSES-605096]
- University of Nottingham
- EPSRC [EP/K023624/1, EP/I017828/1]
- European Comission grant QuILMI-Quantum Integrated Light Matter Interface [295293]
- EU (FET Proactive grant Matter-Wave) [601180]
- BSF [2010239]
- ERC under FP7, Marie Curie Actions, People, International Research Staff Exchange Scheme [IRSES-605096]
- [NSF-DMS-1312856]
- [NSF-PHY-1602994]
- EPSRC [EP/E036473/1] Funding Source: UKRI
- EPSRC [EP/K023624/1, EP/I017828/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E036473/1, EP/I017828/1, EP/K023624/1] Funding Source: researchfish
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We investigate the flow of a one-dimensional nonlinear Schrodinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose-Einstein condensates in ring traps. Above certain rotation velocities, localized solutions with a nontrivial phase profile appear. In striking difference from the infinite domain, in this case there are many critical velocities. At each critical velocity, the steady flow solutions disappear in a saddle-center bifurcation. These interconnected branches of the bifurcation diagram lead to additions of circulation quanta to the phase of the associated solution. This, in turn, relates to the manifestation of persistent current in numerous recent experimental and theoretical works, the connections to which we touch upon. The complex dynamics of the identified waveforms and the instability of unstable solution branches are demonstrated.
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