Abstract
The nonlinear Dirac equation for Bose–Einstein condensates (BECs) 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 BEC of 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- domain walls between polarized regions of . 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.
Highlights
Vacuum states with broken symmetry play an important role in the study of quantum many-body physics, since they provide clues to the principles that govern the full symmetric theory [1, 2, 3]
Topological solitons are defects typically associated with spontaneous symmetry breaking
For the ordinary dark soliton and bright solitons found in Ref. [25], the currents are peaked at the soliton cores with the current jpxspin for solitons associated with the real Dirac operator pointing in the negative x direction and in the positive direction for the complex case
Summary
Vacuum states with broken symmetry play an important role in the study of quantum many-body physics, since they provide clues to the principles that govern the full symmetric theory [1, 2, 3]. We will show that quasi-particle excitations far from the soliton exist as scattering states which respect this asymmetry Because of this feature, it is convenient to think of the switching point from the A to B sublattice as a defect analogous to a domain wall. In magnetic systems domain walls appear as topologically stable solitons separating two distinct regions of different magnetic polarization [47] Another context is the case of two interpenetrating BECs comprised of atoms in different hyperfine states, wherein one finds regions across which the relative phase of the two condensates changes by 2π [48]. A particular example which highlights this fact is the recent simulation of tachyon condensation using two-component BECs [53] In such analogs one finds that spontaneous symmetry breaking occurs in a two-dimensional subspace of the full system, i.e., a domain wall in the larger space.
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