Variational Approach for Impurity Dynamics at Finite Temperature

Abstract

We present a general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium. By working within the Heisenberg picture and constructing approximate time-dependent impurity operators, we can take the medium to be in any mixed state, such as a thermal state. Our variational method is consistent with all conservation laws and, in certain cases, it is equivalent to a finite-temperature Green's function approach. As a demonstration of our method, we consider the dynamics of heavy impurities that have suddenly been introduced into a Fermi gas at finite temperature. Using approximate time-dependent impurity operators involving only one particle-hole excitation of the Fermi sea, we find that we can successfully model the results of recent Ramsey interference experiments on 40 K atoms in a 6 Li Fermi gas [M. Cetina et al., Science 354, 96 (2016)]. We also show that our approximation agrees well with the exact solution for the Ramsey response of a fixed impurity at finite temperature. Our approach paves the way for the investigation of impurities with dynamical degrees of freedom in arbitrary quantum-mechanical mediums.arXiv:1805.10013v2 [cond-mat.quant-gas]

Many-body quantum dynamics and induced correlations of Bose polarons

“…A intriguing aspect would be to examine whether thermalization of the impurities dynamics takes place for strong repulsions in the framework of the eigenstate thermalization hypothesis [101]. An imperative prospect is to study the robustness of the emergent quasiparticle picture in the current setting in the presence of temperature effects [102,103]. Moreover, the study of induced interactions of two bosonic impurities immersed in a Fermi sea would be an interesting prospect especially in order to expose their dependence on the different statistics of the medium.…”

Fate of the Bose polaron at finite temperature

“…At finite temperature, we investigate the full spectral function of the Bose polaron within our variational approach [41]. Including all two-body correlations involving the impurity and a bosonic excitation, we recover the results of Ref.…”

“…The framework for our investigation of the Bose polaron at finite temperature is the variational approach for impurity dynamics first developed in Ref. [41] in the context of Fermi polarons. A variational method based on including only one excitation of the medium was first used to obtain the zero-temperature ground-state properties of the Fermi polaron [50] as well as the repulsive branch [51,52], and it has been demonstrated that such an approach is equivalent to a diagrammatic formulation [53].…”

“…For completeness, in the following we outline the variational approach of Ref. [41]. The key idea that distinguishes this method from the zero-temperature variational approach developed in Ref.…”

“…The time evolution governed by this equation conserves probability [41]; that is, ĉ 0 (t)ĉ † 0 (t) is constant. Specializing to the stationary variational impurity operators, these have coefficients of the form η j (t) = η j e −iEt .…”