Fermionic Excitations in a Nonideal One-Dimensional Bose Gas
It is widely believed that a weakly repulsive one-dimensional Bose gas supports two distinct branches of elementary excitations, the Bogoliubov quasiparticles and dark solitons. Both excitations are bosonic in nature and their spectra follow from the Gross-Pitaevskii equation. In this talk, I will demonstrate that the Gross-Pitaevskii regime does not extend to the low energy limit. Instead, the true low-energy excitations are best described in terms of particles and holes in a Fermi gas with quadratic dispersion relation. I will present phenomenological arguments and exact results supporting this assertion, and discuss possible implications for the experiments on ultracold atomic gases.