Coherence-Enhanced Optical Determination of the ${}^{229}\mathrm{Th}$ Isomeric Transition

The impact of coherent light propagation on the excitation and fluorescence of thorium nuclei in a crystal lattice environment is investigated theoretically. We find that in the forward direction, the fluorescence signal exhibits characteristic intensity modulations dominated by a sped-up initial decay signal that is orders of magnitude faster. This feature can be exploited for the optical determination of the isomeric transition energy. In order to obtain a unmistakable signature of the isomeric nuclear fluorescence, we put forward a novel scheme for the direct measurement of the transition energy via electromagnetically modified nuclear forward scattering involving two fields that couple to three nuclear states.

Figure 1

(a) Quadrupole level splitting for the ${}^{229}\mathrm{Th}$ ground and isomeric states in the ${}^{229}\mathrm{Th}\mathrm{\text{:}}{\mathrm{CaF}}_2$ crystal lattice environment. (b) A left circularly polarized probe field drives the $|\frac{5}{2},\frac{5}{2}⟩\to |\frac{3}{2},\frac{3}{2}⟩$ transition. (c) The electromagnetically modified forward scattering setup. The red thick arrow denotes the strong coupling field while the blue thin arrow shows the weak probe field. The detunings of the probe and coupling fields to the respective resonance frequencies are denoted by ${\Delta }_p$ and ${\Delta }_c$, respectively.

Figure 2

The time spectra of the forward scattered signal (a) without the coupling field and (b) with the coupling field. For all spectra the detunings ${\Delta }_p={\Delta }_c=\Delta$ take values between $0\le \Delta \le {10}^{10}\Gamma$. The yellow filled area below the gray dashed double-dotted line delimits the region $0\le \Delta \le {10}^5\Gamma$. In (a) the values for $\Delta ={10}^9\Gamma$ and ${10}^{10}\Gamma$ are smaller than the displayed scale.