State-Selective Ionization and Trapping of Single H$_2^+$ Ions with (2+1) Multiphoton Ionization

TL;DR

This work addresses the challenge of preparing a single H2+ ion in a well-defined rovibrational state for high-precision spectroscopy. It introduces a (2+1) REMPI scheme that loads H2+ from residual gas in a cryogenic trap, achieving high rotational selectivity and access to excited rotational states; quantum logic spectroscopy verifies the intended states and reveals long-lived rotational excitations. The results include precise loading into L+ = 1 with high probability, observed L+ = 2 states, and QLS-confirmed spin-rotation transitions, enabling robust single-ion spectroscopy with potential for fundamental-constant tests and isotopologue studies. The approach eliminates the need for molecular beams or buffer-gas quenching, offering a compact, state-selective loading mechanism for hydrogen molecular ions in precision experiments.

Abstract

We report on efficient rovibrational state-selective loading of single H$_2^+$ molecular ions into a cryogenic linear Paul trap using (2+1) resonance-enhanced multi-photon ionization (REMPI). The H$_2^+$ ions are created by resonant two-photon excitation of H$_2$ molecules from the $X\;^1Σ_g^+$ state to the $E,F\;^1Σ_g^+$ state, followed by non-resonant one-photon ionization. The H$_2^+$ ions are produced from residual gas and sympathetically cooled by a co-trapped, laser-cooled $^9$Be$^+$ ion. By tuning the wavelength of the REMPI laser, we observe the loading of single H$_2^+$ ions via the ($ν' = 0$, $L' = 0, 1, 2, 3$) rovibrational levels of the $E,F\;^1Σ_g^+$ intermediate state. We measure the success probability for the production of H$_2^+$ in the ($ν^+ = 0$, $L^+ = 1$) state via the ($ν' = 0$, $L' = 1$) level to be 85(6)% by quantum logic spectroscopy (QLS) of the hyperfine structure of this rovibrational state. Furthermore, we load an H$_2^+$ ion via the ($ν' = 0$, $L' = 2$) level and confirm its rovibrational state to be ($ν^+ = 0$, $L^+ = 2$) by QLS. We perform QLS probes on the ion over 19 h and observe no decay of the rotationally excited state. Our work demonstrates an efficient state-selective loading mechanism for single-ion, high-precision spectroscopy of hydrogen molecular ions.

Figures (7)

• Figure 1: $\mathrm{H}_2\;$ energy level diagram for (2+1) REMPI. The potential energy curves for the ground state $X\;^1\Sigma_g^+$, intermediate state $E,F\;^1\Sigma_g^+$, and ionic ground state $X\;^2\Sigma_g^+$ are shown sharp1970potential. Two-photon absorption brings $\mathrm{H}_2\;$ from the ground state to the inner well of the $E, F$ state resonantly, from which the last photon non-resonantly ionizes the molecule. Energy levels for vibrational states are drawn inside the potential energy curves. On the right, the rotational sublevels of the vibrational ground states are shown, with examples of different two-photon rotational transitions Q(1) and Q(2). The rotational level spacings are exaggerated for visualization. Rovibrational quantum numbers for the ground state, intermediate state, and ionic ground state are given the labels $(v", L")$, $(v', L')$, and $(v^+, L^+)$, respectively.
• Figure 2: Schematic of experimental setup. (a) Oblique view of the RF electrodes and laser beams used in the setup (not to scale). The RF electrodes are 2.5mm long and have an ion-electrode distance of 300µm. The DC endcap electrodes are not show in the figure. For the chosen confinement strength the ions are 8.6µm apart, and the beam waist radii at the trap range from 5µm to 20µm for the different laser beams. All laser beams propagate in the $x$-$z$ plane. The axial offset of the 202nm/235nm beam is estimated to be 40µm from the ions' position, suppressing the dissociation of the loaded $\mathrm{H}_2^+\;$ ion (see main text). The 313nm and 1050nm beams are used to control $^9\mathrm{Be}^+\;$ and $\mathrm{H_2^+}$, respectively. (b) Top view of the REMPI beam delivery optics (not to scale). A three-lens arrangement with two lenses outside and one lens inside the vacuum chamber focus the 202nm beam at approximately the trap center. The layers of the vacuum chamber are V: outer ultra-high vacuum chamber with optical viewports; H: heat shield at $\approx\qty{75}{\kelvin}$ with apertures for optical access; C: cryogenic inner chamber with final focusing lenses. During beryllium ionization at 235nm, the diverging lens is removed which compensates for the chromatic focal distance shift, and a 16dB reflective neutral density filter (ND) is inserted to attenuate the REMPI laser, since the beryllium ionization does not require as much power. A mirror on a kinematic piezoelectric mount (PM) is used to compensate for beam pointing differences between the the 202nm and 235nm beams originating from the REMPI laser.
• Figure 3: H$\mathbf{_2^+}$ loading probability per 50 pulse burst as a function of REMPI wavelength. The wavelength values are given in air. Error bars indicate the 68% confidence interval for the mean number of ions assuming Poissonian statistics. Straight lines are drawn between data points to guide the eye. We can identify the resonances as the Q(0), Q(1), and Q(2) transitions between the ground $X\;^1\Sigma_g^+\;$ state and intermediate $E,F\;^1\Sigma_g^+\;$ state hannemann2006frequency. We also observed two loading events at a wavelength of 202.26nm, corresponding to the Q(3) transition. This single data point was measured separately after the scan and is not included in the plot.
• Figure 4: H$\mathbf{_2^+}$ loading probability per 50 pulse burst as a function of REMPI pulse energy. The vertical error bars indicate 68% confidence intervals for the mean number of ions assuming Poissonian loading statistics. The pulse energy error bars indicating the expected 1$\sigma$ uncertainties in pulse energy are smaller than the markers. We then fit a power-law curve to the data points using maximum likelihood estimation assuming Poissonian statistics, from which we extract an exponent of $1.28 \pm 0.31$.
• Figure 5: QLS signal from the spin-rotation structure of H$\mathbf{_2^+}$ in the ($\mathbf{\nu^+ = 0, L^+ = 2}$) state. After loading a $\mathrm{H}_2^+\;$ molecule using the Q(2) resonance, we confirm the rotational state by probing several transitions in the spin-rotation/Zeeman structure of $\mathrm{H}_2^+\;$ by QLS. The observed transition frequencies are in agreement with theoretical predictions for $L^+ = 2$. The figures show two example scans of the same transitions over time, scanning the frequency of the QLS probe around the expected resonance. The left plot is briefly after $\mathrm{H}_2^+\;$ loading, the right 19 later. The QLS signal appears and disappears randomly due to changes in the spin-rotation/Zeeman state, likely caused by the QLS operations and/or the ac magnetic field of the Paul trap off-resonantly driving magnetic dipole transitions in the spin-rotation structure. The observation of the QLS signal of $L^+ = 2$ over 19 indicates that the rotational state is not decaying due to e.g. collisions with residual gas.