High-Precision Metrology of Highly Charged Ions via Relativistic Resonance Fluorescence

Resonance fluorescence of laser-driven highly charged ions is investigated with regard to precisely measuring atomic properties. For this purpose an ab initio approach based on the Dirac equation is employed that allows for studying relativistic ions. These systems provide a sensitive means to test correlated relativistic dynamics, quantum electrodynamic phenomena and nuclear effects by applying x-ray lasers. We show how the narrowing of sidebands in the x-ray fluorescence spectrum by interference due to an additional optical driving can be exploited to determine atomic dipole or multipole moments to unprecedented accuracy.

Figure 1

Fluorescence photon spectrum for the $2s\leftrightarrow 2p_{3/2}$ transition in Li-like ${}^{209}\mathrm{Bi}$ as a function of the fluorescence photon frequency ${\omega }_f$. (a) Dashed (red) curve: An x-ray laser ($I_x=5\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$) is in resonance with the ionic electric dipole ($E1$) transition at ${\omega }_{31}=2788.1\mathrm{eV}$ between the hyperfine-split ground state 1 ($2s$ with $F=4$, $M_F=4$) and the uppermost state 3 ($2p_{3/2}$ with $F=5$, $M_F=5$). This curve is multiplied by a factor of $5\times {10}^{11}$. Thick (thin) dashed arrows represent fast $E1$ x-ray (slow $M1$ optical) decays. (b) Continuous (blue) curve: an additional optical driving ($I_o={10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) is applied on the ${\omega }_{21}=0.797\mathrm{eV}$ [27] $M1$ transition between the hyperfine-split magnetic sublevels 1 ($F=4$, $M_F=4$) and 2 ($F=5$, $M_F=5$). The inner sidebands are suppressed. See text for further details.

Figure 2

(a) Density plot of the fluorescence spectrum (logarithmic scale, arb. units) as a function of the fluorescence photon frequency ${\omega }_f$ with respect to the x-ray transition frequency ${\omega }_{31}$ (abscissa) and the laser detuning $\Delta ={\omega }_x-{\omega }_{31}$ (ordinate), with the frequencies normalized by the ${\Gamma }_{31}$ rate. The parameters are for Bi as in Fig. 1. (b) Continuous (blue) curve: ratio of the interference-narrowed width ${\Gamma }_{\mathrm{SB}}$ of the outer sideband peaks to their distance $D_s(0)=4G=4\sqrt{g_{31}^2+g_{21}^2}$ as a function of the optical Rabi frequency $g_{21}$, with further parameters for the Bi three-level system as given in the third line of Table . Dashed (red) curve: deviation of the sideband distance $D_s(\Delta ={\Gamma }_{31})$ from $D_s(0)$. Dotted (green) curve: deviation of the exact sideband distance $D(0)$ from its value in the secular limit $D_s(0)$.