6 Li atoms following a one-sided phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, and its subsequent snaking and decay into a vortex ring. The latter eventually breaks at the boundary of the superuid, nally leaving behind a single, remnant solitonic vortex. The nodal surface is directly imaged and reveals its decay into a vortex ring via a puncture of the initial soliton plane. At intermediate stages we nd evidence for more exotic structures resembling -solitons. The observed evolution of the nodal surface represents dynamics that occurs at the length scale of the interparticle spacing, thus providing new experimental input for microscopic theories of strongly correlated fermions.
The excitation spectrum of massive fermions with self-interaction moving in one space dimension is calculated, using exact solutions for the spin-1/2 chain problem. This spectrum is shown to be the same as in the massive Thirring model, sine-Gordon equation, and Tomonaga-Luttinger with gap, with suitable relations between coupling constants. Solitons and bound solitons occur, corresponding to magnons and bound magnons in the spin chain. The soliton mass is calculated as a function of lattice spacing, and the ratio of binding energy to soliton mass is shown to be given correctly by the WKB approximation.
We developed a comprehensive semiclassical theory of solitons in one-dimensional systems at the BCS-BEC crossover to provide a semiclassical explanation of their excitation spectra. Our semiclassical results agree well with the exact solutions on both the deep BCS and the deep BEC side and explain qualitatively the smooth crossover between them. Especially, we showed that the minimum energy of the
S=1/2 excitation is achieved exactly at the Fermi momentum ${k}_{F}=\ensuremath{\pi}n/2$, where
nmF (
mF is the mass of the fermionic atom) is the total mass density of the system. This momentum remains unchanged along the whole crossover whether the mass is contained in the bosonic molecules as on the deep BEC side or in the fermionic atoms as on the deep BCS side. This phenomenon comes about as a result of a special feature of one-dimensional systems that the conventional quasiparticle is not stable with respect to soliton formation. It is valid not only in exactly solvable models, but also on the level of semiclassical theory. Besides, we also resolved the inconsistency of existing semiclassical theory with the exact solution of solitonlike
S=0 excitations on the deep BCS side by a different proposal of soliton configuration.