费米气体中移动杂质的有限温度质量隙与淬火动力学

中文摘要 AI 辅助

近期，针对费米气体中移动杂质的质量隙描述被提出，该描述通过费米子色散中反冲诱导的能隙，将静态杂质的安德森正交灾难与费米极化子的准粒子图像关联起来。然而，该描述仅适用于零温度，未涉及动力学问题。本文中，我们结合Lee-Low-Pines变换与反冲相互作用的自洽Hartree-Fock退耦，将质量隙模型推广至有限温度，并在该框架内采用泛函行列式方法研究淬火动力学。有限温度下，有效质量隙满足自洽方程Δ(T)=2U_F tanh[Δ(T)/(4k_B T)]，其中U_F=k_F²/(2M)，M为杂质质量。该方程在特征温度T*=U_F/(2k_B)以下存在非零解，且随(T*-T)^(1/2)趋近于零。我们将这种闭合现象识别为极化子与分子准粒子热熔化的平均场特征。在杂质-费米相互作用突然淬火后计算拉姆齐响应S(t)，发现其长时间振荡（束缚态与隙间态之间的量子拍频）恰好于T*以上消失。本工作将极化子形成的热力学与动力学特征关联至单一温度依赖的平均场参数。

英文摘要

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.

发表机构

• MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi’an Jiaotong University（西安交通大学物理学院凝聚态物质非平衡合成与调制教育部重点实验室）

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