Particle number fractionalization of a one-dimensional atomic Fermi gas   with synthetic spin-orbit coupling
  We propose an experimental scheme to simulate the fractionalization of particle number by using a one-dimensional spin-orbit coupled ultracold fermionic gas. The wanted spin-orbit coupling, a kink-like potential, and a conjugation-symmetry-breaking mass term are properly constructed by laser-atom interactions, leading to an effective low-energy relativistic Dirac Hamiltonian with a topologically nontrivial background field. The designed system supports a localized soliton excitation with a fractional particle number that is generally irrational and experimentally tunable, providing a direct realization of the celebrated generalized-Su-Schrieffer-Heeger model. In addition, we elaborate on how to detect the induced soliton mode with the FPN in the system. 
Dan-Wei Zhang, L.-B. Shao, Zheng-Yuan Xue, Hui Yan, Z. D. Wang, and   Shi-Liang Zhu
cond-mat.quant-gas quant-ph