Destruction of p-wave weakly bound molecules in a gas of spin-polarized fermions

José Paulo D'Incao, Chris H. Greene

Yuta Sekino, Yusuke Nishida

Xi‐Wen Guan

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.

Runxin Mao, Xin Guan, Biao Wu

Using exact Bethe ansatz solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated through exact results of the excitation spectrum, the effective mass, binding energy and kinetic energy. Furthermore, a clear distinction between the polaron and molecule is conceived by the probability distribution, single-particle reduced density matrix, and density-density correlations, which are calculated directly from the Bethe ansatz wave function. Such a polaron-molecule crossover presents a universal nature of an impurity immersed into a fermionic medium with an attraction in one dimension.

Shao-Jian Jiang, Fei Zhou

Yinfeng Ma, Xiaoling Cui