Lamb Shift of Landau Levels in Two-Dimensional Electron Systems in a Multimode Resonator

TL;DR

This paper investigates how including multiple resonator modes affects the Landau level shifts in 2D electron systems, revealing enhanced softening effects beyond single-mode approximations.

Contribution

It introduces a model incorporating many resonator modes and demonstrates how to compute eigenfrequencies using self-energy and matrix eigenvalue methods.

Findings

Including multiple modes significantly enhances the softening of cyclotron frequencies.

The system can be reduced to coupled harmonic oscillators for analysis.

Eigenfrequencies are obtained via self-energy and matrix eigenvalue methods.

Abstract

The use of resonators to modify the behavior of electromagnetic systems demonstrates its potential for application in a wide range of problems. However, existing theoretical studies often resort to the single-mode approximation, rarely considering a second resonator mode. In this paper, we show that including a large number of resonator modes in the model significantly enhances the softening effect of the cyclotron frequency of a two-dimensional electron system. We address this problem by demonstrating the possibility of reducing the system to a set of coupled harmonic oscillators and finding the eigenfrequencies of the oscillators. This is made possible by applying the self-energy method for modes in one polarization and the method for finding the eigenvalues of matrices that have undergone first-rank updating for modes in the perpendicular polarization.