Nuclear forward scattering of Bessel beams in $^{229}$Th:CaF$_2$

TL;DR

This paper theoretically investigates how Bessel beams interact with $^{229}$Th-doped crystals at the nuclear level, revealing potential for enhanced control of nuclear transitions and internal structure mapping.

Contribution

It extends nuclear forward scattering formalism to Bessel beams, analyzing their unique effects on nuclear excitation and internal axis distribution in crystals.

Findings

Bessel beams can reveal the distribution of quantization axes inside the crystal.

Propagation of Bessel beams affects the excitation channels due to their orbital angular momentum.

The formalism accounts for nuclear quadrupole splitting and multiple transitions.

Abstract

The coherent pulse propagation of a Bessel beam resonant to the 8.4 eV nuclear clock transition in $^{229}$Th-doped crystals is investigated theoretically. Due to the magnetic dipole character of the clock transition, Bessel beams which present non-uniform transverse profiles and carry orbital angular momentum might enhance excitation channels or offer new control degrees of freedom compared to standard plane waves. We model the nuclear forward scattering of a resonant Bessel beam pulse propagating through the crystal, extending an formalism based on the iterative wave equation for plane waves. Thereby we take into account the nuclear quadrupole splitting in the crystal, considering the possibility of multiple quantization axes and present results for scenarios involving a single nuclear transition and multiple simultaneously driven transitions, analyzing temporal and spatial intensity patterns. Our findings show that the propagation of Bessel beams can be used to determine the relative distribution of different directions of quantization axes inside the crystal.