Precision Spectroscopy in Cold Molecules: The Lowest Rotational Interval of ${{\mathrm{He}}_2}^{+}$ and Metastable ${\mathrm{He}}_2$

Multistage Zeeman deceleration was used to generate a slow, dense beam of translationally cold ${\mathrm{He}}_2$ molecules in the metastable $a\hspace{0.17em}{}^3{\mathrm{\Sigma }}_u^{+}$ state. Precision measurements of the Rydberg spectrum of these molecules at high values of the principal quantum number $n$ have been carried out. The spin-rotational state selectivity of the Zeeman-deceleration process was exploited to reduce the spectral congestion, minimize residual Doppler shifts, resolve the Rydberg series around $n=200$ and assign their fine structure. The ionization energy of metastable ${\mathrm{He}}_2$ and the lowest rotational interval of the $X^{+}\hspace{0.17em}{}^2{\mathrm{\Sigma }}_u^{+}$ (${\nu }^{+}=0$) ground state of ${}^4{{\mathrm{He}}_2}^{+}$ have been determined with unprecedented precision and accuracy by Rydberg-series extrapolation. Comparison with ab initio predictions of the rotational energy level structure of ${}^4{{\mathrm{He}}_2}^{+}$ [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] enabled us to quantify the magnitude of relativistic and quantum-electrodynamics contributions to the fundamental rotational interval of ${{\mathrm{He}}_2}^{+}$.

Figure 1

(a) Energy-level diagram showing the rotational levels of ${\mathrm{He}}_2^{*}$ and the triplet $np$ Rydberg states of ${\mathrm{He}}_2$ that converge to the lowest rotational levels of ${{\mathrm{He}}_2}^{+}$. The positions of pure rotational levels of the metastable state are marked by dashed horizontal lines. The spin-rotation fine structure is exaggerated for clarity. Arrows indicate optically allowed transitions. Rapidly autoionizing levels are drawn in blue. (b) Zeeman effect of the $N^{\prime \prime }=1$ and 3 rotational levels of ${\mathrm{He}}_2^{*}$. The low-field-seeking magnetic sublevels used for Zeeman deceleration are shown in red.

Figure 2

Schematic view of the laser system, the Zeeman decelerator, and the magnetically shielded photoexcitation region. YAG, yttrium aluminium garnet; WM, wave meter; SMF, single mode fiber; BBO, beta barium borate crystal; MCP, microchannel plate.

Figure 3

Upper panel: Rydberg spectrum of the $1\to np{1}_{0–2}$ series of ${\mathrm{He}}_2$ with $n\approx 120–200$. Lower panel: Comparison of the experimental spectrum (dots) with a spectrum reconstructed from the sum (bold line) of the individual contributions associated with the $np{1}_1$ (solid line), $np{1}_2$ (dotted line), and $nf{1}_2$ (dashed line) series.

Figure 4

Comparison between spectra obtained from nondecelerated ($1000\mathrm{m}/\mathrm{s}$) and decelerated ($120\mathrm{m}/\mathrm{s}$) ${\mathrm{He}}_2^{*}$ samples. See text for details.