Abstract
Using the variational method and exact Bethe ansatz (BA) method, we studied the effects of an impurity immersed in a one-dimensional (1D) Fermi sea. With attractive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. For equal masses and heavy polaron systems, we calculated the binding energy, effective mass, momentum distribution and Tan contact. In the strongly attractive limit, the impurity forms a dimer with inner fermion in Fermi sea which just accords with the highly imbalanced 1D Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in experiment. We find that the heavy impurity is dressed more deeply with Fermi sea in whole interaction regime. Furthermore, we explore the complete influence of particle-hole excitation in Fermi polaron system in 1D. We find a shocking phenomenon that the hole term in Fermi sea has a great influence on the Tan relation even in the attractive interaction regime.
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