Exploiting transport properties for the detection of optical pumping in heavy ions

We present a kinetic model for optical pumping in ${\mathrm{Lu}}^{+}$ and ${\mathrm{Lr}}^{+}$ ions as well as a theoretical approach to calculate the transport properties of ${\mathrm{Lu}}^{+}$ in its ground ${}^{1}S_0$ and metastable ${}^{3}D_1$ states in helium background gas. Calculations of the initial ion state populations, the field and temperature dependence of the mobilities and diffusion coefficients, and the ion arrival time distributions demonstrate that the ground- and metastable-state ions can be collected and discriminated efficiently under realistic macroscopic conditions.

Figure 1

Laser-induced population transfer from ground- to metastable states in ${\mathrm{Lu}}^{+}$ at $5\times {10}^{-2}\mathrm{mbar}$ He. Level occupation is indicated for each of the modeled states $|i\rangle$ in the course of 10 laser beam exposures. Inset: corresponding five-level system used in the rate-equation model with arrows in blue, yellow, and brown indicating $E1, E2$, and $M1$ transitions, respectively. Laser probing ($h\nu$) of the intermediate ${}^{3}P_1$ state induces optical pumping in the system. Collision-induced relaxation is marked by dashed arrows.

Figure 2

${\mathrm{Lu}}^{+}$–He SO-coupled interaction potentials corresponding to the ${}^{1}S_0$ and ${}^{3}D_1$ states of the ion. Dotted line represents isotropic interaction potential for the ${}^{3}D_1$ state. For the sake of comparison, all potentials are referred to the same dissociation limit.

Figure 3

Reduced zero-field mobilities of the ${\mathrm{Lu}}^{+}$ ions in the ground $X{0}^{+}$ state (solid line) and metastable ${}^{3}D_1$ state (dashed line) as functions of temperature. The dot indicates the experimental result for the ground state [19]. The inset provides an enlarged view of the $100–500\mathrm{K}$ region.

Figure 4

Reduced mobilities of the ${\mathrm{Lu}}^{+}$ ions in the ground $X{0}^{+}$ state (solid lines) and metastable ${}^{3}D_1$ state (dashed lines) as functions of $E/n_0$ at selected temperatures.

Figure 5

Zero-field diffusion coefficients $n_{0}D$ of the ${\mathrm{Lu}}^{+}$ ions in the ground $X{0}^{+}$ state (solid line) and metastable ${}^{3}D_1$ state (dashed line) as functions of temperature. Inset provides an enlarged view of the $100–500\mathrm{K}$ region.

Figure 6

Longitudinal diffusion coefficients $n_0{D}_L$ of the ${\mathrm{Lu}}^{+}$ ions in the ground $X{0}^{+}$ state (solid lines) and metastable ${}^{3}D_1$ state (dashed lines) as functions of $E/n_0$ at selected temperatures. Crosses exemplify the dependence of the transverse coefficient $n_0{D}_T$ of the ground-state ion at $T=300\mathrm{K}$.

Figure 7

Effective kinetic temperatures $T_{\mathrm{eff}}$ of the ${\mathrm{Lu}}^{+}({}^{3}D_1$) ions along the drift field at selected buffer gas temperatures as functions of $E/n_0$ (dashed lines). Solid line exemplifies the same quantity for the ground-state ${\mathrm{Lu}}^{+}$ ion at $300\mathrm{K}$, while crosses show the dependence of $T_{\mathrm{eff}}$ in the direction perpendicular to the field axis at $100\mathrm{K}$.

Figure 8

Relative difference of the drift times for ${\mathrm{Lu}}^{+}$ ions in the ground and metastable states.

Figure 9

(a) Relative drift time distribution (color coded) as function of $t/t_d$ and $E/n_0$ for equal initial ensembles of ${\mathrm{Lu}}^{+}$ in ground and metastable states. Ion losses are neglected. Horizontal lines mark $E/n_0$ sections depicted in panel (b). Drift length is $6\mathrm{cm}$, temperature is $300\mathrm{K}$, and pressure is $1\mathrm{mbar}$. (b) The relative ion fluxes at selected $E/n_0$ values of 10 (black), 20 (blue), and $70\mathrm{Td}$ (red). Legend specifies the corresponding $t_d$ values for the ground-state ions.

Figure 10

Transmission efficiency of the ${\mathrm{Lu}}^{+}({}^{3}D_1$) ions (color coded) as function of $L$ and $p_0$ at selected temperatures. $E/n_0=20\mathrm{Td}$.

Figure 11

Collection efficiency of the ${\mathrm{Lu}}^{+}({}^{3}D_1$) ions (color coded) as function of $L$ and $p_0$ at selected temperatures. $E/n_0=20\mathrm{Td}$.

Figure 12

(a) Ion signal at resonant pumping $I_p\left(t\right)$ (color coded, arbitrary scale) as function of $t/t_d$ and $E/n_0$. (b) The fractions of collected ions, all and metastable. For both panels, $T=100\mathrm{K}$ and $p_0=2\mathrm{mbar}$.

Figure 13

Fraction of the metastable ions collected after the drift as function of $p_0$ and $E/n_0$ at $T=100\mathrm{K}$. Horizontal lines indicate $E/n_0$ values, which correspond to effective temperatures of the metastable ions of 300 and $880\mathrm{K}$.

Figure 14

Off resonance and resonant pumping signals $I_g$ and $I_p$, respectively, at optimum drift conditions and effective temperatures of metastable ions of $880\mathrm{K}$ (red, $p_0=3.5\mathrm{mbar}, E/n_0=38\mathrm{Td}$) and $300\mathrm{K}$ (black, $p_0=2\mathrm{mbar}, E/n_0=15\mathrm{Td}$). $L=4\mathrm{cm}$ and the He temperature is $T=100\mathrm{K}$. Indicated numbers are the respective fractions of ions collected after the drift (areas of the peaks multiplied by $t_d$).