Driven electronic bridge processes via defect states in $^{229}$Th-doped crystals

TL;DR

This paper explores how defect states in Th-doped crystals can facilitate electronic bridge processes to excite the $^{229m}$Th nuclear isomer, with implications for developing a solid-state nuclear clock.

Contribution

It provides a theoretical analysis of electronic bridge mechanisms involving defect states in Th-doped crystals, highlighting the dominant multipole contributions and potential clock applications.

Findings

Electric dipole dominates the bridge photon emission.

Electric quadrupole is key for the nuclear transition.

Inverse electronic bridge can enhance nuclear clock performance.

Abstract

The electronic defect states resulting from doping $^{229}$Th in CaF$_2$ offer a unique opportunity to excite the nuclear isomeric state $^{229m}$Th at approximately 8 eV via electronic bridge mechanisms. We consider bridge schemes involving stimulated emission and absorption using an optical laser. The role of different multipole contributions, both for the emitted or absorbed photon and nuclear transition, to the total bridge rates are investigated theoretically. We show that the electric dipole component is dominant for the electronic bridge photon. In contradistinction, the electric quadrupole channel of the $^{229}$Th isomeric transition plays the dominant role for the bridge processes presented. The driven bridge rates are discussed in the context of background signals in the crystal environment and of implementation methods. We show that inverse electronic bridge processes quenching the isomeric state population can improve the performance of a solid-state nuclear clock based on $^{229m}$Th.