The Quantum Rabi Model: Exceptional Points And Generalization

The quantum Rabi model is a model introduced by I.I.Rabi in 1936 to describe the effect of a rapidly varying weak magnetic field on an oriented atom possessing nuclear spin.In the following 80 years,this model has been extensively investigated,including in different experimental settings.First of all,this thesis presents a review of the background and recent developments on diverse aspects of the quantum Rabi model,including several methods to obtain exact analytic solutions of this model,as well as one possible generalization.Besides,in review part we briefly discuss the regular part and exceptional part of the eigenspectrum of the quantum Rabi model.After that,emphasis is given on the author's work on the exceptional eigenspectrum of a generalization known as the asymmetric quantum Rabi model,which is divided into three sections.In section I,we obtain the exceptional part of the eigenspectrum of the asymmetric Rabi model,also known as the biased or driven Rabi model,in terms of the roots of a set of algebraic equations.This approach provides a product form for the wave function components and allows an explicit connection with recent results obtained for the wavefunction in terms of truncated confluent Heun functions.Other approaches are also compared in this section.For particular parameter values the exceptional part of the eigenspectrum consists of doubly degenerate crossing points.We give a proof for the number of roots of the constraint polynomials and discuss the number of crossing points.In section II,we examine the energy surfaces of the asymmetric Rabi model as a function of the coupling strength and the driving term.The energy surfaces are plotted numerically from the known analytic solution.The resulting energy landscape consists of an infinite stack of sheets connected by conical intersection points located at the degenerate Juddian points in the eigenspectrum.Trajectories encircling these points are expected to exhibit a nonzero geometric phase.In section III,we discuss another subset of exceptional spectrum not mentioned in section I because the approach therein only covered a subset of all exceptional points in the eigenspectrum.In this section,we clarify the distinction between the exceptional parts of the eigenspectrum for the asymmetric Rabi model and discuss the subset of exceptional points not determined in this article.These three subsets make up the full exceptional part of eigenspectrum,and the full eigenspectrum is obtained by including the regular eigenspectrum.In addition,some results regarding experiments on the quantum Rabi model and potential developments are also briefly discussed in this thesis.