Recoil Effects in the Polaron Problem

M. Porsch, J. Röseler

Abstract A general formalism for diagonalizing quadratic forms of boson operators [7], is used to obtain a translationally invariant variational ansatz which is suitable for calculating the polaron self‐energy, effective mass, and energy momentum relation in both coupling limits. The self‐energy and effective mass are calculated in the weak‐coupling limit. The strong coupling limit shows the wellknown α2‐dependence of the self‐energy. Diagonalizing the quadratic part of the recoil term gives rise to an additional self‐energy contribution to the cutoff.

Eduardo C. Marino

A. V. Tulub

A calculation method convenient for the treatment of the system of a quantized field and a non relativistically moving particle interacting with each other strongly enough is developed. With the help of the two canonical transformation used in the paper of Lee, Low, and Pines the effective hamiltonian with the interaction terms included is constructed. The hamiltonian can be diagonalized by the Wentzel method known in the meson pair field theory. A polaron problem is given as an example. (auth)

Janusz Adamowski, B. Gerlach, Hajo Leschke

Baihua Gong

Recently, a mass-gap description of mobile impurities in a Fermi gas was introduced, which connects Anderson's orthogonality catastrophe for static impurities to the quasiparticle picture of Fermi polarons through a recoil-induced energy gap in the fermionic dispersion. That description, however, was restricted to zero temperature and did not address dynamics. Here we generalize the mass-gap model to finite temperature by combining the Lee--Low--Pines transformation with a self-consistent Hartree--Fock decoupling of the recoil-induced interaction, and we study the quench dynamics within this framework using the functional-determinant approach. At finite temperature the effective mass gap obeys the self-consistency equation $Δ(T)=2U_F\tanh[Δ(T)/4k_B T]$, with $U_F=k_F^2/2M$ and $M$ the impurity mass. This equation admits a nonzero solution below the characteristic temperature $T^*=U_F/(2k_B)$ and closes as $(T^*-T)^{1/2}$. We identify this closing as the mean-field signature of the thermal melting of the polaron and molecule quasiparticles. Computing the Ramsey response $S(t)$ after a sudden quench of the impurity--fermion interaction, we find that its long-time oscillations---quantum beats between the bound and in-gap states---disappear precisely above $T^*$. Our work ties the thermodynamic and dynamical fingerprints of polaron formation to a single temperature-dependent mean-field parameter.