The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysis
| Autor: | L. H. Haddad, Lincoln D. Carr |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Physics
Condensed Matter::Quantum Gases Nonlinear Dirac equation General Physics and Astronomy FOS: Physical sciences law.invention Nonlinear system Spin wave law Quantum Gases (cond-mat.quant-gas) Quantum mechanics Bound state Soliton Condensed Matter - Quantum Gases Nonlinear Sciences::Pattern Formation and Solitons Bose–Einstein condensate Quantum fluctuation Linear stability |
| DOI: | 10.48550/arxiv.1402.3013 |
| Popis: | The nonlinear Dirac equation for Bose-Einstein condensates in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic generalization of the Boguliubov-de Gennes equations, we compute soliton lifetimes against quantum fluctuations and classify the different excitation types. For a Bose-Einstein condensate of $^{87}\mathrm{Rb}$ atoms, we find that our soliton solutions are stable on time scales relevant to experiments. Excitations in the bulk region far from the core of a soliton and bound states in the core are classified as either spin waves or as a Nambu-Goldstone mode. Thus, solitons are topologically distinct pseudospin-$1/2$ domain walls between polarized regions of $S_z = \pm 1/2$. Numerical analysis in the presence of a harmonic trap potential reveals a discrete spectrum reflecting the number of bright soliton peaks or dark soliton notches in the condensate background. For each quantized mode the chemical potential versus nonlinearity exhibits two distinct power law regimes corresponding to the free-particle (weakly nonlinear) and soliton (strongly nonlinear) limits. Comment: 31 pages, 12 figures. arXiv admin note: text overlap with arXiv:1305.6532 |
| Databáze: | OpenAIRE |
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