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Broken Patterns – Anomalies in the Spectra of Aluminum Monofluoride

Walter, Nicole

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Aluminum monofluoride (AlF) has favorable properties for laser cooling and trapping experiments. The strong A¹Π ← X¹Σ⁺ band near 227 nm and the narrow a³Π ← X¹Σ⁺ band near 367 nm have rotationally and vibrationally closed transitions, making them well-suited for efficient photon scattering. Among the states relevant to laser cooling, the a³Π state is the least characterized, as its differing spin multiplicity from the ground state makes it difficult to access experimentally. This thesis reports on the spectroscopic characterization of the a³Π state and higher triplet states of AlF. Special emphasis is placed on the interpretation of anomalies in the molecular spectra, which occur due to interactions between different electronic states. The presented experiments are performed on supersonically cooled AlF molecules in a molecular beam. Pulsed and continuous-wave dye lasers (270–570 nm) and an RF transmission line (1–500 MHz) are used for resonant excitation. The rotationally resolved spectra of the spin-forbidden a³Π ← X¹Σ⁺ band reveal that this band is weakly allowed due to the spin–orbit interaction of the a³Π state with distant singlet states. The vibrational, rotational, and spin–orbit coupling parameters of the a³Π, v = 0–7 states are extracted from these spectra. This allows the construction of an accurate electronic potential for the a³Π state and determination of the Franck–Condon matrix of the a³Π – X¹Σ⁺ system. All Λ-doublet transitions within the a³Π₁, v = 5, J = 1 level are recorded, and the hyperfine parameters of this level are determined. The observation of a spectral line with a full width at half maximum of 1.27 kHz, belonging to a hyperfine transition within the a³Π₁, v = 0 state, confirms the absence of lifetime broadening for transitions between two metastable levels. The lowest rotational levels of the A¹Π, v = 6 and b³Σ⁺, v = 5 states are nearly isoenergetic and interact via spin–orbit coupling. These strongly mixed levels provide a doorway between the singlet and triplet manifolds. These perturbed levels are characterized from hyperfine-resolved spectra. The lifetimes of selected hyperfine levels, which range from 2 ns to 200 ns depending on the degree of singlet–triplet mixing, are determined by time-delayed ionization, Lamb-dip spectroscopy, and precise analysis of transition lineshapes. Two theoretically predicted triplet states of AlF, the counterparts of the well-characterized D¹Δ and E¹Π states, had not been experimentally identified prior to this work. This thesis reports on the first characterization of the d³Π (v = 0–6) and e³Δ (v = 0–2) states, confirming the predicted energetic ordering of these states. In addition, the f³Σ⁺ (v = 0–2) states are characterized. Interestingly, the spectra of the d³Π, v = 3 ← a³Π, v = 3 band show an intensity distribution that is clearly different from that of all other diagonal bands. This band gets its weak, unexpected rotational structure due to intensity borrowing from the nearby e³Δ, v = 2 ← a³Π, v = 3 band. Analysis of this effect allows for the detailed characterization of the spin–orbit and spin–rotation interactions between the d³Π and e³Δ states.

DOI
10.17169/refubium-49597

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•Dec 12, 2025•0 citations
Aluminum monofluoride (AlF) has favorable properties for laser cooling and trapping experiments. The strong A¹Π ← X¹Σ⁺ band near 227 nm and the narrow a³Π ← X¹Σ⁺ band near 367 nm have rotationally and vibrationally closed transitions, making them well-suited for efficient photon scattering. Among the states relevant to laser cooling, the a³Π state is the least characterized, as its differing spin multiplicity from the ground state makes it difficult to access experimentally. This thesis reports on the spectroscopic characterization of the a³Π state and higher triplet states of AlF. Special emphasis is placed on the interpretation of anomalies in the molecular spectra, which occur due to interactions between different electronic states. The presented experiments are performed on supersonically cooled AlF molecules in a molecular beam. Pulsed and continuous-wave dye lasers (270–570 nm) and an RF transmission line (1–500 MHz) are used for resonant excitation. The rotationally resolved spectra of the spin-forbidden a³Π ← X¹Σ⁺ band reveal that this band is weakly allowed due to the spin–orbit interaction of the a³Π state with distant singlet states. The vibrational, rotational, and spin–orbit coupling parameters of the a³Π, v = 0–7 states are extracted from these spectra. This allows the construction of an accurate electronic potential for the a³Π state and determination of the Franck–Condon matrix of the a³Π – X¹Σ⁺ system. All Λ-doublet transitions within the a³Π₁, v = 5, J = 1 level are recorded, and the hyperfine parameters of this level are determined. The observation of a spectral line with a full width at half maximum of 1.27 kHz, belonging to a hyperfine transition within the a³Π₁, v = 0 state, confirms the absence of lifetime broadening for transitions between two metastable levels. The lowest rotational levels of the A¹Π, v = 6 and b³Σ⁺, v = 5 states are nearly isoenergetic and interact via spin–orbit coupling. These strongly mixed levels provide a doorway between the singlet and triplet manifolds. These perturbed levels are characterized from hyperfine-resolved spectra. The lifetimes of selected hyperfine levels, which range from 2 ns to 200 ns depending on the degree of singlet–triplet mixing, are determined by time-delayed ionization, Lamb-dip spectroscopy, and precise analysis of transition lineshapes. Two theoretically predicted triplet states of AlF, the counterparts of the well-characterized D¹Δ and E¹Π states, had not been experimentally identified prior to this work. This thesis reports on the first characterization of the d³Π (v = 0–6) and e³Δ (v = 0–2) states, confirming the predicted energetic ordering of these states. In addition, the f³Σ⁺ (v = 0–2) states are characterized. Interestingly, the spectra of the d³Π, v = 3 ← a³Π, v = 3 band show an intensity distribution that is clearly different from that of all other diagonal bands. This band gets its weak, unexpected rotational structure due to intensity borrowing from the nearby e³Δ, v = 2 ← a³Π, v = 3 band. Analysis of this effect allows for the detailed characterization of the spin–orbit and spin–rotation interactions between the d³Π and e³Δ states.
Spectroscopic studies of aluminum monofluoride (AlF) have revealed its highly favorable properties for direct laser cooling. All Q lines of the strong A1Π ← X1Σ+ transition around 227 nm are rotationally closed and thereby suitable for the main cooling cycle. The same holds for the narrow, spin-forbidden a3Π ← X1Σ+ transition around 367 nm, which has a recoil limit in the µK range. We here report on the spectroscopic characterization of the lowest rotational levels in the a3Π state of AlF for v = 0–8 using a jet-cooled, pulsed molecular beam. An accidental AC Stark shift is observed on the a3Π0, v = 4 ← X1Σ+, v = 4 band. By using time-delayed ionization for state-selective detection of the molecules in the metastable a3Π state at different points along the molecular beam, the radiative lifetime of the a3Π1, v = 0, J = 1 level is experimentally determined as τ = 1.89 ± 0.15 ms. A laser/radio frequency multiple resonance ionization scheme is employed to determine the hyperfine splittings in the a3Π1, v = 5 level. The experimentally derived hyperfine parameters are compared to the outcome of quantum chemistry calculations. A spectral line with a width of 1.27 kHz is recorded between hyperfine levels in the a3Π, v = 0 state. These measurements benchmark the electronic potential of the a3Π state and yield accurate values for the photon scattering rate and for the elements of the Franck–Condon matrix of the a3Π–X1Σ+ system.
Aluminum monofluoride (AlF) is an excellent candidate for laser cooling.\footnote{Truppe et al., Physical Review A 100, 052513 (2019)} All Q-lines of the strong A1Π^1\Pi1Π ←\leftarrow← X1Σ+^1\Sigma^+1Σ+ transition are rotationally closed and thereby suitable for the main cooling cycle, while the spin-forbidden a3Π^3\Pi3Π ←\leftarrow← X1Σ+^1\Sigma^+1Σ+ transition can be used to achieve final temperatures in the μ{\mu}μK range. In view of cooling and trapping experiments, it is essential to have a detailed insight into the energy structure of the directly and indirectly involved states. The A1Π,v=6,J=1^1\Pi, v=6, J=11Π,v=6,J=1 and the b3Σ+,v=5,N=2^3\Sigma^+, v=5, N=23Σ+,v=5,N=2 levels are very nearly iso-energetic and strongly interact.\footnote{Barrow et al., Physica Scripta 10, 86 (1974)} Consequently, these levels have a mixed singlet and triplet character. The triplet character of the A1Π^1\Pi1Π state causes a loss from the main laser cooling cycle that has been studied previously.\footnote{Doppelbauer et al., Molecular Physics 119(1-2), e1810351 (2020)} Furthermore, these states with their mixed character are particularly suited as doorway states between the singlet and the triplet manifold for ultracold experiments on AlF. We completed an extensive rotationally resolved spectroscopic investigation of energy levels in this perturbed range using optical-optical double resonance ionization, followed by mass-selective ion detection. Subsequently, we performed hyperfine resolved excitation with a cw laser, using laser induced fluorescence for detection. Both measurement schemes were employed on a supersonic, pulsed molecular beam. The lifetimes of the perturbed levels cover two orders of magnitudes (about 2−2002 - 2002−200~ns), which requires different experimental techniques to determine their exact values. Lifetimes of selected levels have been measured using e.g. time delayed ionization and Lamb-dip experiments. The fine- and hyperfine structure parameters as well as the spin-orbit interaction parameter are determined from the experimental data.
Recently, we determined the detailed energy level structure of the X1Σ+, A1Π and a3Π states of AlF that are relevant to laser cooling and trapping experiments [Truppe et al., Phys. Rev. A. 100 (5), 052513 (2019)]. Here, we investigate the b3Σ+,v=0 state of the AlF molecule. A rotationally resolved (1 + 2)-REMPI spectrum of the b3Σ+,v′=0 ← a3Π, v′′=0 band is presented and the lifetime of the b3Σ+,v=0 state is measured to be 190(2) ns. Hyperfine-resolved, laser-induced fluorescence spectra of the b3Σ+,v′=0 ← X1Σ+, v′′ = 1 and the b3Σ+,v ′ = 0 ← a3Π, v′′ = 0 bands are recorded to determine fine- and hyperfine structure parameters. The interaction between the b3Σ+,v = 0 and the nearby A1Π state is studied and the magnitude of the spin–orbit coupling between the two electronic states is derived using three independent methods to give a consistent value of 10(1) cm-1. The triplet character of the A state causes an A → a loss from the main A−X laser cooling cycle below the 10-6 level.
Recently, we determined the detailed energy level structure of the X1Σ+, A1Π and a3Π states of AlF that are relevant to laser cooling and trapping experiments [Truppe et al., Phys. Rev. A. 100 (5), 052513 (2019)]. Here, we investigate the b3Σ+,v=0 state of the AlF molecule. A rotationally resolved (1 + 2)-REMPI spectrum of the b3Σ+,v′=0←a3Π,v″=0 band is presented and the lifetime of the b3Σ+,v=0 state is measured to be 190(2) ns. Hyperfine-resolved, laser-induced fluorescence spectra of the b3Σ+,v′=0←X1Σ+,v″=1 and the b3Σ+,v′=0←a3Π,v″=0 bands are recorded to determine fine- and hyperfine structure parameters. The interaction between the b3Σ+,v=0 and the nearby A1Π state is studied and the magnitude of the spin–orbit coupling between the two electronic states is derived using three independent methods to give a consistent value of 10(1) cm−1. The triplet character of the A state causes an A→a loss from the main A−X laser cooling cycle below the 10−6 level.
Here we report on spectroscopic measurements of the aluminum monofluoride molecule (AlF; boson) that are relevant to laser cooling and trapping experiments. We measure the detailed energy-level structure of AlF in the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic ground state, in the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state, and in the metastable $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ state. We determine the rotational, vibrational, and electronic branching ratios from the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state. We also study how the rotational levels split and shift in external electric and magnetic fields. We find that AlF is an excellent candidate for laser cooling on any QQQ line of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ - $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ transition and for trapping at high densities. The energy levels in the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},v=0$ state and within each $\mathrm{\ensuremath{\Omega}}$ manifold in the $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},v=0$ state are determined with a relative accuracy of a few kHz, using laser-radio-frequency multiple resonance and ionization detection schemes in a jet-cooled, pulsed molecular beam. To determine the hyperfine and $\mathrm{\ensuremath{\Lambda}}$-doubling parameters we measure transitions throughout the 0.1-MHz--66-GHz range, between rotational levels in the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},v=0$ state, and between rotational and $\mathrm{\ensuremath{\Lambda}}$-doublet levels in all three spin-orbit manifolds of the $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},v=0$ state. We measure the hyperfine splitting in the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state using continuous wave (cw) laser-induced fluorescence spectroscopy of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0\ensuremath{\leftarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},{v}^{\ensuremath{''}}=0$ band. The resolution is limited by the short radiative lifetime of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0$ state, which we experimentally determine to be $1.90\ifmmode\pm\else\textpm\fi{}0.03$ ns. The hyperfine mixing of the lowest rotational levels in the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ state causes a small loss from the main laser cooling transition of ${10}^{\ensuremath{-}5}$. The off-diagonal vibrational branching from the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0$ state is measured to be $(5.60\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in good agreement with theoretical predictions. The strength of the spin-forbidden $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0\ensuremath{\rightarrow}a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},{v}^{\ensuremath{'}}=0$ transition is measured to be seven orders of magnitude lower than the strength of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0\ensuremath{\rightarrow}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+},{v}^{\ensuremath{''}}=0$ transition. We determine the electric dipole moments $\ensuremath{\mu}(\mathrm{X})=1.515\ifmmode\pm\else\textpm\fi{}0.004$ Debye, $\ensuremath{\mu}(a)=1.780\ifmmode\pm\else\textpm\fi{}0.003$ Debye and $\ensuremath{\mu}(\mathrm{A})=1.45\ifmmode\pm\else\textpm\fi{}0.02$ Debye in $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$, v=0v=0v=0, $a{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}},v=0$ and $A{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}},v=0$, respectively, by recording cw laser excitation spectra in electric fields up to 150 kV/cm.
Magneto-optical trapping of molecules has thus far been restricted to molecules with 2Σ electronic ground states. These species are chemically reactive and only support a simple laser cooling scheme from their first excited rotational level. Here, we demonstrate a magneto-optical trap (MOT) of aluminum monofluoride (AlF), a deeply bound and intrinsically stable diatomic molecule with a 1Σ+ electronic ground state. The MOT operates on the strong A1ΠX1ΠΣ+ transition near 227.5 nm, whose Q(J) lines are all rotationally closed. We demonstrate a MOT of about 64 molecules for the J = 1 level of AlF, more than 104 molecules for J = 2 and 3, and with no fundamental limit in going to higher rotational levels. Laser cooling and trapping of AlF is conceptually similar to the introduction of alkaline-earth atoms into cold atom physics, and is key to leveraging its spin-forbidden a3ΠX1Σ+ transition for precision spectroscopy and narrow-line cooling.