Franck-Condon Effect in Central Spin System

TL;DR

This paper explores how environmental collective spins influence the absorption spectrum of a central spin, revealing an analog of the Franck-Condon effect where environmental spins act like vibrational modes, leading to vertical transition phenomena.

Contribution

It introduces a novel analogy between the Franck-Condon effect and central spin systems with collective-spin environments, explaining spectral features through environmental spin dynamics.

Findings

Environmental spins cause Franck-Condon-like effects in the central spin spectrum.

Vertical transitions correspond to minimal change in total spin angular momentum.

Environmental collective spins behave as vibrational modes in the analogy.

Abstract

We study the quantum transitions of a central spin surrounded by a collective-spin environment. It is found that the influence of the environmental spins on the absorption spectrum of the central spin can be explained with the analog of the Franck-Condon (FC) effect in conventional electron-phonon interaction system. Here, the collective spins of the environment behave as the vibrational mode, which makes the electron to be transitioned mainly with the so-called "vertical transitions" in the conventional FC effect. The "vertical transition" for the central spin in the spin environment manifests as, the certain collective spin states of the environment is favored, which corresponds to the minimal change in the average of the total spin angular momentum.