Hyperfine-resolved laser excitation and detection of nuclear isomer in trapped $^{229}$Th$^{3+}$ ions

TL;DR

This paper theoretically investigates hyperfine-resolved laser excitation of the $^{229}$Th nuclear isomer in trapped ions, proposing detection schemes and analyzing parameters for efficient nuclear state identification.

Contribution

It introduces two detection schemes based on hyperfine-resolved fluorescence and analyzes optimal conditions for locating the nuclear transition.

Findings

Detection schemes yield photon rates of 10^4 to 10^5 s^{-1} per ion.

Nuclear transition can be located within one month with current laser technology.

Proper matching of laser linewidth, detuning, and irradiation time is crucial for efficient excitation.

Abstract

We present a comprehensive theoretical investigation of hyperfine-resolved excitation and detection of the low-energy isomeric state of $^{229}$Th in trapped $^{229}\mathrm{Th}^{3+}$ ions. Using a quantum master equation approach, we analyze the dependence of the isomeric population on laser linewidth, detuning, and irradiation time, showing that their proper matching is essential for efficient excitation. We further propose two nuclear-state detection schemes based on three hyperfine-resolved electronic fluorescence channels at 690, 984, and 1088 nm. Our analysis shows that the 690-nm and 984-nm scheme yields detectable photon rates on the order of $10^4~\mathrm{s}^{-1}$ per ion for each wavelength, whereas the 1088-nm scheme achieves a higher rate on the order of $10^5~\mathrm{s}^{-1}$ per ion. By quantifying the trade-off between irradiation time and scan-step size, we show that the nuclear transition can be located within one month for a 100-MHz uncertainty using currently available vacuum-ultraviolet laser technology. These results provide practical guidance for trapped-ion $^{229}\mathrm{Th}$ spectroscopy and the development of nuclear clocks.