Solitons in One Dimensional Systems at BCS-BEC Crossover

Abstract

We developed a comprehensive semiclassical theory of solitons in one dimensional systems at 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 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 $k_F=\pi n/2$, where $n{m}_F$ ($m_F$ 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 soliton-like $S=0$ excitations on the deep BCS side by a new proposal of soliton configuration.

arXiv comment15 pages, 12 figures

References in corpus (6)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• An exactly solvable model of the BCS-BEC crossover
• Dilute Fermi gas in quasi-one-dimensional traps: From weakly interacting fermions via hard core bosons to weakly interacting Bose gas
• Photo-Solitonic Effect
• Moving solitons in a one-dimensional fermionic superfluid
• Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions

Cited by in corpus (3)

• Ring solitons and soliton sacks in imbalanced fermionic systems
• On Solving Cubic-Quartic Nonlinear Schrödinger Equation in a Cnoidal Trap
• Exact Solutions to Two-Component Many-Body Systems in One Dimension