Theoretical Investigation of Spectroscopic Properties of the Alkaline-Earth-Metal Monohydrides toward Laser Cooling and Magneto-Optical Trapping

Alkaline-earth-metal monohydrides MH (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 A²Π_1/2 ← X²Σ⁺ 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 X²Σ⁺, the transition wavelengths in the vacuum, and hyperfine branching ratios of A²Π_1/2(J' = 1/2,+) ← X²Σ⁺(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 X²Σ⁺(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.

Controlling the Scattering Length of Ultracold Dipolar Molecules

By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac field is increased, the long-range well becomes deeper and can support a certain number of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescaled rotational constant B[over ˜]=B/s_{E_{3}} where s_{E_{3}} is a characteristic dipolar energy. We found that molecules with B[over ˜]>10^{8} are immune to any quenching losses when a sufficient ac field is applied, the ratio elastic to quenching processes can reach values above 10^{3}, and that the value and sign of the scattering length can be tuned. The ability to control the molecular scattering length opens the door for a rich, strongly correlated, many-body physics for ultracold molecules, similar to that for ultracold atoms.

Optical stark spectroscopy of the D1Π-X1Σ+(0,0) band of scandium monohydride

The laser induced fluorescence (LIF) spectra of the D(1)Π-X(1)Σ(+)(0,0) band of a rotationally cold (<20 K) molecular beam sample of scandium monohydride, ScH, and scandium monodeuteride, ScD, were recorded without and in the presence of a static electric field. The fine and magnetic hyperfine parameters for the X(1)Σ(+)(v=0) and D(1)Π(v=0) states of ScH and ScD were determined from the analysis of the field-free spectra. An unexpected isotopic dependence of the (45)Sc(I=7/2) magnetic hyperfine interaction was observed. The lowest J-levels of the D(1)Π( v=0) state of ScH are not perturbed, but the corresponding levels for ScD are strongly perturbed. The observed electric field induced splitting, broadenings, and shifts were analyzed to produce permanent electric dipole moments, μ(e), of 1.74 ± 0.15 and 2.177 ± 0.006 D for the X(1)Σ(+)(v=0) and D(1)Π(v=0) states, respectively. The trend in μ(e) for the 3d-metal monohydrides is discussed.

The Zeeman effect in the (0,0) band of the A 7Pi-X 7Sigma(+) transition of manganese monohydride, MnH

The Zeeman tuning of the P(1)(0) line (nu=17 568.35 cm(-1)) of the A (7)Pi-X (7)Sigma(+) (0,0) band of manganese monohydride, MnH, has been investigated. The laser induced fluorescence spectrum of a supersonic molecular beam sample was recorded at a resolution of approximately 40 MHz and with field strengths of up to 362.0 mT. The observed spectrum was successfully fitted using a traditional effective Zeeman Hamiltonian to determine an effective magnetic g-factor for the J=2 level of the F(1)-spin component of the A (7)Pi(v=0) state. Spectral predictions of the P(1)(0) line at field strengths used in magnetic trapping experiments are presented.

The permanent electric dipole moment of chromium monodeuteride, CrD

A number of low-N lines of the X (6)Sigma(+)<--A (6)Sigma(+)(0,0) band of chromium monodeuteride, CrD, have been recorded at near the natural linewidth limit by high resolution laser excitation spectroscopy of a supersonic molecular beam sample. The shifts and splitting of these lines caused by a static electric field have been analyzed to give the permanent electric dipole moments of the X (6)Sigma(+)(upsilon=0) and A (6)Sigma(+)(upsilon=0) states as 3.510(33) and 1.153(3) D, respectively. The dipole moment of the A (6)Sigma(+)(upsilon=0) state can be measured with higher precision because of some interesting near degeneracies in its level structure. The trends in the observed dipole moments for the first-row transition metal monohydrides are rationalized and compared with theoretical predictions.

Molecular beam optical Stark study of the [18.1] (2)Pi(12)-X (4)Sigma(12) (-) band system of rhodium monosulfide

The optical Stark effect in the (R)R(13)(0.5) branch feature of the [18.1] (2)Pi(12)-X (4)Sigma(12) (-) (v('),v(")=0) band of rhodium monosulfide (RhS) has been recorded and analyzed to determine the permanent electric dipole moment mu(e) of 3.40(2) D for the ground X (4)Sigma(12) (-) (v=0) state and an upper limit of 1.5 D for the [18.1] (2)Pi(12) state. Molecular orbital correlation diagrams are used to interpret the relative values of mu(e) for RhN, RhO, and RhS. The (103)Rh(I=12) magnetic hyperfine interaction in the X (4)Sigma(12) (-) and [18.1] (2)Pi(12) states is analyzed.

Molecular beam optical Stark study of rhodium mononitride

The optical Stark effect in the Q(1) and R(0) lines of the [15.1]1-X (1)Sigma+ (1,0) band of rhodium mononitride (RhN) were recorded and analyzed to determine the permanent electric dipole moments mu for the X (1)Sigma+(upsilon=0) and [15.1]1(upsilon=1) states to be 2.43(5) and 1.75(1) D, respectively. The determined dipole moments are compared to predicted values obtained from density functional theory [Stevens et al., Chem. Phys. Lett. 421, 281 (2006)] and an all-electron ab initio calculation [Shim et al., J. Mol. Struct. THEOCHEM 393, 127 (1997)]. A simple single configuration molecular orbital correlation diagram is used to rationalize the relative values of mu for the 4d mononitrides and RhO. An electronic configuration for the [15.1]1 state is proposed based on the interpretation of the (103)Rh and (14)N magnetic hyperfine interactions.

A molecular beam optical Stark study of the [15.8] and [16.0] Π1∕22-XΣ−4 (0,0) band systems of rhodium monoxide, RhO

The SR11(0) and SR11(1) branch features of the [15.8] and [16.0]2Pi1/2-X 4Sigma- (0,0) subband systems of rhodium monoxide, RhO, have been studied at near the natural linewidth limit of resolution by optical Stark spectroscopy using laser induced fluorescence detection. The Stark shifts and splittings were analyzed to produce the magnitude of the permanent electric dipole moment, |mu|, of 3.81(2) D for the X 4Sigma3/2- (v=0) state. The results are compared to density functional theory calculations. Trends in observed values of |mu| across the 4d series of transition metal monoxides are interpreted in terms of simple single configuration molecular orbital correlation diagrams.

A theoretical study of calcium monohydride, CaH: low-lying states and their permanent electric dipole moments

Potential energy curves, energy parameters, and spectroscopic values for the X (2)Sigma(+), A (2)Pi, B (2)Sigma(+), a (4)Pi, and b (4)Sigma(+), states of CaH have been calculated using the multireference configuration interaction and coupled cluster levels of theory, while employing quantitative basis sets (of augmented quintuple-zeta quality) and taking also into account core/valence correlation and one-electron relativistic effects. For the ground (X (2)Sigma(+)) and the first two following excited states (A (2)Pi, B (2)Sigma(+)) of CaH, the permanent electric dipole moments have been calculated. Our best finite field dipole moment of the A (2)Pi state of 2.425 D (upsilon = 0) is in very good agreement with the experimental literature value of 2.372(12) D. However, a discrepancy is observed in the dipole moment of the X (2)Sigma(+) state. Our most extensive calculation gives mu = 2.623 D (upsilon = 0), which is considerably smaller than the experimental value of mu = 2.94(16) D (upsilon = 0). Small van der Waals minima were found for both "repulsive" quartet states. Spectroscopic constants and energy parameters for all states are in remarkable agreement with available experimental values.

The permanent electric dipole moments and magnetic g factors of uranium monoxide

Permanent electric dipole moments and magnetic g factors for uranium monoxide (UO) have been determined from analyses of optical Stark and Zeeman spectra recorded at a spectral resolution that approaches the natural linewidth limit. Numerous branch features in the previously characterized [L. A. Kaledin et al., J. Mol. Spectrosc. 164, 27 (1994)] (0,0) [18403]5-X(1)4 and (0,0) [18404]5-X(1)4 electronic transitions were recorded in the presence of tunable static electric (Stark effect) or magnetic (Zeeman effect) fields. The lines exhibited unusually large Zeeman tuning effects. A ligand field model and an ab initio electronic structure calculation [R. Tyagi, Ph.D. thesis, The Ohio State University (2005)] were used to interpret the ground state properties. The results indicate that the low energy electronic states of UO are sufficiently ionic for the meaningful application of ligand field theory models. The dipole moments and g factors were distinctly different for the three electronic states examined, which implies that these properties may be used to deduce the underlying electronic state configurations.

High resolution laser induced fluorescence spectroscopy of the [18.8]Φi3−XΦi3 (0,0) band of cobalt monofluoride

The fine and hyperfine interaction parameters in the [18.8] (3)Phi (upsilon=0) and X (3)Phi (upsilon=0) states of cobalt monofluoride, CoF, have been determined from an analysis of high-resolution laser induced fluorescence spectra of the [18.8] (3)Phi(3)-X (3)Phi(3) and [18.8] (3)Phi(4)-X (3)Phi(4) band systems. The previously reported pure rotational transitions of the X (3)Phi(4)(upsilon=0) state [T. Okabayashi and M. Tanimoto, J. Mol. Spectrosc. 221, 149 (2003)] were included in the data set. The hyperfine parameters for (59)Co (I=72) and (19)F (I=12) have been interpreted using atomic data together with a proposed molecular orbital description for the [18.8](3)Phi(i) and X (3)Phi(i) states. A comparison of the hyperfine parameters in the X (3)Phi state of cobalt monohydride, CoH, with those of the X (3)Phi state of CoF reveals that the bonding in the two molecules is significantly different. It is shown that, in a situation where the Omega substates of a multiplet degenerate electronic state are analyzed separately, the Fermi contact parameter b can be determined with fair accuracy from the apparent centrifugal distortion of the hyperfine structure.

A molecular-beam optical Stark study of lines in the (1,0) band of the FΔ7∕24-XΔ7∕24 transition of iron monohydride, FeH

A supersonic molecular beam of iron monohydride, FeH, has been generated using a laser ablation/chemical reaction scheme and probed at near-natural linewidth resolution by optical Stark spectroscopy utilizing laser-induced fluorescence detection. The observed Stark splitting in Q(3.5) and R(3.5) lines of the F4delta(7/2) <-- X4delta(7/2) (1,0) transition were analyzed to determine values for the magnitudes of the permanent electric dipole moments, absolute value(mu), which were found to be 2.63(3) and 1.29(3) D for the X4delta (v = 0) and F4delta (v = 1) states, respectively. A comparison with ab initio theoretical predictions is made. The lambda doubling in the low-J levels of the F4delta(7/2) (v = 1) state is also modeled.

The permanent electric dipole moment and hyperfine interaction in ruthenium monoflouride (RuF)

Ruthenium monofluoride, RuF, has been detected using low-resolution laser-induced fluorescence (LIF) in the visible and near infrared spectral regions. A visible band, designated as [18.2]5.5-X 4Phi(9/2), has been recorded field-free and in the presence of a static electric field using high-resolution LIF spectroscopy. The r0 internuclear distances for the [18.2]5.5 and X 4Phi(9/2) states were determined to be 1.911 and 1.916 A, respectively. The vibrational interval DeltaG(1/2) of 534(15) cm-1 for the X 4Phi(9/2) state was determined from the analysis of the dispersed LIF. The Stark shifts of the visible band were analyzed to produce permanent electric dipole moments of 1.97(8) and 5.34(7) D for the [18.2]5.5 and X 4Phi(9/2), states, respectively. The fluorine magnetic hyperfine structure associated with spectral features was analyzed. The hyperfine structure and dipole moments are interpreted using a molecular-orbital correlation model and compared with FeF and other ruthenium-containing molecules.