Scaling Relations and Topological Quadruple Points in Light-matter Interactions with Anisotropy and Nonlinear Stark Coupling

TL;DR

This paper explores the complex interplay of scaling relations and topological properties in light-matter interactions within the quantum Rabi model, revealing novel topological quadruple points enabled by nonlinear Stark coupling.

Contribution

It introduces the concept of topological quadruple points in the quantum Rabi model with anisotropy and nonlinear Stark coupling, expanding understanding of universality in quantum phase transitions.

Findings

Scaling relations vary with frequency and anisotropy.

Topological quadruple points emerge due to nonlinear Stark coupling.

Topological transitions can be manipulated via nonlinear Stark coupling.

Abstract

Universality is a common quality in different physical parameters that is rooted in the deep nature of physical systems. Scaling relation is a typical universality for critical phenomena around a quantum phase transition, while topological classification provides another type of universality essentially different from the critical universality. Both classes of universalities can be present in a single-qubit system with light-matter interactions, as exhibiting generally in the fundamental quantum Rabi model with anisotropy not only for linear coupling but also for nonlinear Stark coupling (NSC). In low frequencies different levels of scaling relations are demonstrated, holding for anisotropic or/and NSCs, locally or globally. At finite frequencies such a critical universality breaks down and diversity is dominant. However, common topological feature of the ground state can be extracted from the node number, which yields a topological class of universality amidst the critical diversity. Both conventional and unconventional topological transitions emerge, with their meeting, which never occurs in linear interaction, enabled by the nonlinear coupling to form topological quadruple points which are found to be spin-invariant points. Sensitivity analysis indicates that the NSC can be another approach to manipulate topological transitions in addition to coupling anisotropy.