Abstract
We consider a quantum system such as a qubit, interacting with a bath of fermions as in the Fröhlich polaron model. The interaction Hamiltonian is thus linear in the system variable and quadratic in the fermions. Using the recently developed extension of Feynman-Vernon theory to nonharmonic baths we evaluate quadratic and the quartic terms in the influence action. We find that for this model the quartic term vanish by symmetry arguments. Although the influence of the bath on the system is of the same form as from bosonic harmonic oscillators up to effects to sixth order in the system-bath interaction, the temperature dependence is nevertheless rather different, unless rather contrived models are considered.
Highlights
The theory of open quantum systems has attracted increased attention in recent years, motivated by advances quantum information theory [1] and emerging quantum technologies [2,3]
In this paper we addressed the model of a quantum variable such as a qubit interacting with a fermionic bath
The coupling between the qubit and the bath is quadratic in fermionic operators, and the bath is initially in a thermal state. To investigate this system we employed the extension of the Feynman-Vernon influence functional technique that allows to systematically study higher-order contributions to the Feynamn-Vernon action that arise from system-bath interaction being nonlinear with respect to bath operators
Summary
The theory of open quantum systems has attracted increased attention in recent years, motivated by advances quantum information theory [1] and emerging quantum technologies [2,3]. We are interested in the opposite case where one bosonic degree of freedom, i.e., the qubit, describes the system of interest, and we want to “integrate out” the fermions One problem with such an approach is that. Fermionic functional integrals (Grassman integrals) are mathematically nontrivial objects Another is that for the Fröhlichlike coupling both the bath Hamiltonian and the interaction are quadratic in the fermionic degrees of freedom; the result is two fermionic functional determinants depending on the forward and backward histories of the system of interest acting as external fields. Appendix C presents the detailed argument that in the considered model is no fourth-order contribution to the generalized FeynmanVernon action
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
