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The Journal of Chemical Physics

Zeeman spectroscopy of CaH molecules in a magnetic trap

Břetislav Friedrich, Jonathan D. Weinstein, Robert deCarvalho, John M. Doyle

Published Feb 1, 1999• 43 citations

Abstract

In a recent experiment [Weinstein et al., Nature 395, 148 (1998)] we magnetically trapped 108 ground-state calcium monohydride molecules, CaH(X 2Σ,v″=0, J″=0). The molecules were prepared by laser ablation of a solid sample of CaH2 and loaded via thermalization with a cold (<1 K) He3 buffer gas. The magnetic trap was formed by superconducting coils arranged in the anti-Helmholtz configuration. The detection was done by laser fluorescence spectroscopy excited at 635 nm (in the B 2Σ,v′=0−X 2Σ,v″=0 band) and detected at 692 nm (within the B,v′=0−X,v″=1 band). Both a photomultiplier tube and a CCD camera were used. Due to the thermalization of molecular rotation, only a transition from the lowest rotational state could be detected at zero field, N′=1, J′=3/2←N″=0, J″=1/2. In the magnetic field this rotational transition splits into two features, one shifted towards lower and one towards higher frequencies. The measured shifts are linear in field strength and indicate a small difference (0.02 μB) in the magnetic moments between the ground and excited states. Here we present a theoretical analysis of the observed magnetic shifts. These are identified as arising from a rotational perturbation of the B 2Σ,v′=0 state by a close-lying A 2Π,v′=1 state that lends the B state some of its A character. We find that the Hamiltonian can be well approximated by a 3×3 matrix built out of elements that connect states from within the Σ-doublet and the Π3/22 manifolds. The interaction parameter describing the Σ−Π coupling in the Zeeman Hamiltonian is determined from the observed shifts and the field-free molecular parameters of CaH given by Berg and Klyning [Phys. Scr. 10, 331 (1974)] and by Martin [J. Mol. Spectrosc 108, 66 (1984)].

DOI: 10.1063/1.477942

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In a recent experiment [Weinstein et al., Nature 395, 148 (1998)] we magnetically trapped 108 ground-state calcium monohydride molecules, CaH(X 2Σ,v″=0, J″=0). The molecules were prepared by laser ablation of a solid sample of CaH2 and loaded via thermalization with a cold (<1 K) He3 buffer gas. The magnetic trap was formed by superconducting coils arranged in the anti-Helmholtz configuration. The detection was done by laser fluorescence spectroscopy excited at 635 nm (in the B 2Σ,v′=0−X 2Σ,v″=0 band) and detected at 692 nm (within the B,v′=0−X,v″=1 band). Both a photomultiplier tube and a CCD camera were used. Due to the thermalization of molecular rotation, only a transition from the lowest rotational state could be detected at zero field, N′=1, J′=3/2←N″=0, J″=1/2. In the magnetic field this rotational transition splits into two features, one shifted towards lower and one towards higher frequencies. The measured shifts are linear in field strength and indicate a small difference (0.02 μB) in the magnetic moments between the ground and excited states. Here we present a theoretical analysis of the observed magnetic shifts. These are identified as arising from a rotational perturbation of the B 2Σ,v′=0 state by a close-lying A 2Π,v′=1 state that lends the B state some of its A character. We find that the Hamiltonian can be well approximated by a 3×3 matrix built out of elements that connect states from within the Σ-doublet and the Π3/22 manifolds. The interaction parameter describing the Σ−Π coupling in the Zeeman Hamiltonian is determined from the observed shifts and the field-free molecular parameters of CaH given by Berg and Klyning [Phys. Scr. 10, 331 (1974)] and by Martin [J. Mol. Spectrosc 108, 66 (1984)].

High Resolution Image Download MS PowerPoint Slide Alkaline-earth-metal monohydrides M H ( M = Be, Mg, Ca, Sr, Ba) have long been regarded as promising candidates toward laser cooling and trapping; however, their rich internal level structures that are amenable to magneto-optical trapping have not been completely explored. Here, we first systematically evaluated Franck–Condon factors of these alkaline-earth-metal monohydrides in the A 2 Π 1/2 ← X 2 Σ + transition, exploiting three respective methods (the Morse potential, the closed-form approximation, and the Rydberg–Klein–Rees method). The effective Hamiltonian matrix was introduced for MgH, CaH, SrH, and BaH individually in order to figure out their molecular hyperfine structures of X 2 Σ +, the transition wavelengths in the vacuum, and hyperfine branching ratios of A 2 Π 1/2 ( J ′ = 1/2,+) ← X 2 Σ + ( N = 1,−), followed by possible sideband modulation proposals to address all hyperfine manifolds. Lastly, the Zeeman energy level structures and associated magnetic g factors of the ground state X 2 Σ + ( N = 1,−) were also presented. Our theoretical results here not only shed more light on the molecular spectroscopy of alkaline-earth-metal monohydrides toward laser cooling and magneto-optical trapping but also can contribute to research in molecular collisions involving few-atom molecular systems, spectral analysis in astrophysics and astrochemistry, and even precision measurement of fundamental constants such as the quest for nonzero detection of electron’s electric dipole moment.

Ground-state

{}^{52}\mathrm{Cr}

atoms have been magnetically trapped using buffer-gas loading. The atoms are produced by laser ablation of solid

{}^{52}\mathrm{Cr},

thermalized by collisions with a cryogenically cooled helium buffer gas, and trapped by an anti-Helmholtz quadrupole magnetic field. The atoms are detected by absorption spectroscopy on the ${a}^{7}{S}_{3}\ensuremath{\leftrightarrow}{z}^{7}{P}_{3}$ transition at 427.6 nm. Using this technique, approximately

{10}^{11}

atoms are loaded into the trap in a single ablation pulse. Loading has been demonstrated at temperatures from 0.3 to 1.4 K.

Abstract We demonstrate optical cycling and laser cooling of a cryogenic buffer-gas beam of calcium monohydride (CaH) molecules. We measure vibrational branching ratios for laser cooling transitions for both excited electronic states A and B. Furthermore, we measure that repeated photon scattering via the A ← X transition is achievable at a rate of ∼ 1.6 × 1 0 6 photons s−1 and demonstrate interaction-time limited scattering of ∼ 200 photons by repumping the largest vibrational decay channel. We also demonstrate a sub-Doppler cooling technique, namely the magnetically assisted Sisyphus effect, and use it to cool the transverse temperature of a molecular beam of CaH. Using a standing wave of light, we lower the transverse temperature from 12.2(1.2) mK to 5.7(1.1) mK. We compare these results to a model that uses optical Bloch equations and Monte Carlo simulations of the molecular beam trajectories. This work establishes a clear pathway for creating a magneto-optical trap (MOT) of CaH molecules. Such a MOT could serve as a starting point for production of ultracold hydrogen gas via dissociation of a trapped CaH cloud.

Using helium buffer gas cooling, we have prepared dense samples of ground-state molecular calcium monohydride (CaH X 2Σ) at cryogenic temperatures. We have used optical pumping to polarise the spin state of the CaH molecules and we have measured the inelastic collisions of molecular CaH with atomic helium at temperatures from 2 to 7 K. The measured CaH electronic spin depolarisation rate coefficient increases rapidly with increasing temperature, increasing from 2 × 10−13 cm3 s−1 to over 10−11 cm3 s−1. The strong dependence of rate coefficient on temperature is attributed to the CaH population in the first excited rotational state.

The Zeeman effect in the excited A 2Pi(3/2) state of CaF is measured and analyzed over a wide range of magnetic fields. It is found that the splitting of the Zeeman levels is largely determined by the coupling between different rotational states and there are no low-field seeking states in the J=3/2 manifold of Zeeman levels at high magnetic fields. A model of the Zeeman spectrum based on the ligand-field theory of CaF is shown to be accurate in the interval of magnetic fields 0-5 Tesla. This demonstrates that the magnetic moment of the CaF(A 2Pi(3/2)) molecule is effectively determined by the spin angular momentum of a single electron and the orbital motion of the valence electron around the Ca2+ core. An analysis of the Zeeman spectrum as a function of the molecular rotational constant indicates that 2Pi(3/2) molecules should have significant rotational constants (at least as large as twice the rotational constant of CaF) to be amenable to magnetic trapping in high fields.

Atomic europium has been magnetically trapped using buffer-gas loading. Laser ablated

\mathrm{Eu}(^{8}S_{7/2})

atoms are thermalized to 800 mK in a

{}^{4}\mathrm{He}

buffer gas (to 250 mK in a

{}^{3}\mathrm{He}

buffer gas). Anti-Helmholtz superconducting coils produce a quadrupole magnetic field to trap the

{M}_{J}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7/2

state of Eu. Detection is via absorption spectroscopy at 462.7 nm. Up to $1\ifmmode\times\else\texttimes\fi{}{10}^{12}\mathrm{Eu}$ atoms are loaded at a central density of $5\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. Atoms can be held for longer than 100 s.