Energy, decay rate, and effective masses for a moving polaron in a Fermi sea: Explicit results in the weakly attractive limit

Christian Trefzger (1) , Yvan Castin (1)

1 LKB (Lhomond) - Laboratoire Kastler Brossel

We study the properties of an impurity of mass M moving through a spatially homogeneous three-dimensional Fermi gas of particles of same spin state and mass m. In the weakly attractive limit, where the effective coupling constant g\->0^- and perturbation theory can be used, we analytically calculate the complex energy Delta E(\K) of the moving impurity up to order two included in g. This also gives access to its longitudinal and transverse effective masses m_parallel^*(K), m_perp^*(K), as functions of the impurity wave vector K. Depending on the modulus of K and on the impurity-to-fermion mass ratio M/m we identify four regions separated by singularities in derivatives with respect to K of the second-order term of Delta E(K), and we discuss the physical origin of these regions. Remarkably, the second-order term of m_parallel^*(K) presents non-differentiable points, as well as a logarithmic divergence for M=m, when K is on the Fermi surface of the fermions.

Mots clés: polaron; impurity; decay rate; complex energy; Fermi sea; effective mass

Domaines: Gaz Quantiques [cond-mat.quant-gas]

Christian Trefzger, Yvan Castin. Energy, decay rate, and effective masses for a moving polaron in a Fermi sea: Explicit results in the weakly attractive limit. 2013. ⟨hal-00847562v1⟩