Nature of polaron-molecule transition in Fermi polarons

In this work, we explore the polaron and molecule physics by utilizing a unified variational ansatz with up to two particle-hole(p-h) excitations(V-2ph). We confirm the existence of a first-order transition in 3D and 2D Fermi polarons, and show that the nature of such transition lies in an energy competition between systems with different momenta ${\mathbf Q}=0$ and $|{\mathbf Q}|=k_F$, here ${\mathbf Q}$ is defined as the momentum of Fermi polaron system with respect to the Fermi sea of majority fermions (with Fermi momentum $k_F$). The literally proposed molecule ansatz is identified as an asymptotic limit of $|{\mathbf Q}|=k_F$ state in strong coupling regime, which implies a huge $SO(3)$(for 3D) or $SO(2)$ (for 2D) ground state degeneracy in this regime. The recognization of such degeneracy is crucially important for evaluating the molecule occupation in realistic systems with finite impurity density and at finite temperature. To compare with recent experiment of 3D Fermi polarons, we have calculated various physical quantities under the V-2ph framework and obtained results that are in good agreements with experimental data in the weak coupling and near resonance regime. Further, to check the validity of our conclusion in 2D, we have adopted a different variational method based on the Gaussian sample of high-order p-h excitations(V-Gph), and found the same conclusion on the nature of polaron-molecule transition therein. For 1D system, the V-2ph method predicts no sharp transition and the ground state is always at ${\mathbf Q}=0$ sector, consistent with exact Bethe ansatz solution. The presence/absence of polaron-molecule transition is analyzed to be closely related to the interplay effect of Pauli-blocking and p-h excitations in different dimensions.