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The Journal of Chemical Physics

Fine structure, alignment, and orientation of 32S16O and 16O18O molecules in congruent electric and magnetic fields

Andreea Boca, Břetislav Friedrich

Published Feb 22, 2000• 23 citations
Publisher

Abstract

We analyze the eigenproperties of the SO and 16O18O ground-state (3Σ) molecules in congruent electric and magnetic fields. The energy levels are found to exhibit avoided crossings for states with the same projection M of the total angular momentum on the common axis of the fields. The avoided crossings are due to a first-order Stark effect which connects intersecting levels of aligned Zeeman states of opposite parity and makes them strongly oriented. We exemplify the enhancement of orientation and other generic features of the combined electric and magnetic dipole interaction in polar 3Σ molecules by evaluating the expectation values of the orientation and alignment cosines as a function of field-strength parameters for a selection of states with |M|⩽5. The molecular states created by the congruent fields can be used to state-select and focus molecules, to orient the molecular axis in studies of collision stereodynamics, to facilitate assignments of spectral transitions, and in molecular trapping. In particular, we found that mixed-isotope O2 and 17O2 are the only chalcogen molecules which are suitable for spatial trapping in a static trap, owing to their rotational ground state which correlates with a low-field seeking Zeeman state.

DOI
10.1063/1.480514

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•Apr 1, 2016•5 citations
We analyze the eigenproperties of the SO and 16O18O ground-state (3Σ) molecules in congruent electric and magnetic fields. The energy levels are found to exhibit avoided crossings for states with the same projection M of the total angular momentum on the common axis of the fields. The avoided crossings are due to a first-order Stark effect which connects intersecting levels of aligned Zeeman states of opposite parity and makes them strongly oriented. We exemplify the enhancement of orientation and other generic features of the combined electric and magnetic dipole interaction in polar 3Σ molecules by evaluating the expectation values of the orientation and alignment cosines as a function of field-strength parameters for a selection of states with |M|⩽5. The molecular states created by the congruent fields can be used to state-select and focus molecules, to orient the molecular axis in studies of collision stereodynamics, to facilitate assignments of spectral transitions, and in molecular trapping. In particular, we found that mixed-isotope O2 and 17O2 are the only chalcogen molecules which are suitable for spatial trapping in a static trap, owing to their rotational ground state which correlates with a low-field seeking Zeeman state.
The authors present a detailed study of low-temperature collisions between CaD molecules and He atoms in superimposed electric and magnetic fields with arbitrary orientations. Electric fields do not interact with the electron spin of the molecules directly but modify their rotational structure and, consequently, the spin-rotation interactions. The authors examine molecular Stark and Zeeman energy levels as functions of the angle between the fields and show that rotating fields may induce and shift avoided crossings between the Zeeman levels of the rotationally ground and rotationally excited states of the molecule. The dynamics of molecular collisions are extremely sensitive to external fields near these avoided crossings and it is shown that molecular collisions may be controlled by varying both the strength and the relative orientation of the fields. The effects observed in this study are due to interactions of the isolated molecules with external fields so the conclusions should be relevant for collisions of molecules with other atoms or collisions of molecules with each other. This study demonstrates that electric fields may be used to enhance or suppress spin-rotation interactions in molecules. The spin-rotation interactions induce nonadiabatic couplings between states of different total spins in systems of two open-shell species and it is suggested that electric fields might be used for controlling nonadiabatic spin transitions and spin-forbidden chemical reactions of cold molecules in a magnetic trap.
We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration, taking into account both the s -wave and p -wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the p -wave interaction on the ultralong-range molecular states for a pure B -field configuration. In the presence of external fields, the angular degrees of freedom acquire vibrational character, and we encounter two- and three-dimensional oscillatory adiabatic potential energy surfaces for the parallel and crossed field configuration, respectively. The equilibrium configurations of local potential wells can be controlled via the external field parameters for both field configurations depending on the specific degree of electronic excitation. This allows us to tune the molecular alignment and orientation. The resulting electric dipole moment is in the order of several kDebye, and the rovibrational level spacings are in the range of 2– . Both properties are analyzed with varying field strengths.
We examine the rotational states of a pair of polar (2)Σ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules ΔJi = 0, ± 1, ΔNi = 2n (n = 0, ±1, ±2,…), and ΔMi = 0, ± 1 imposed by the electric dipole-dipole operator. Here Ji, Ni and Mi are the total, rotational and projection angular momentum quantum numbers of molecules i = 1, 2 in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the pair of coupled rotors.
We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the rovibrational ground state of a ${}^{2}\ensuremath{\Sigma}$ electronic state and the Zeeman state with the electron spin projection MS=12{M}_{S}=\frac{1}{2}MS​=21​ on the magnetic field axis. This is the lowest-energy state of ${}^{2}\ensuremath{\Sigma}$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule-molecule interaction potentials, which yield the expectation intervals for the cross sections and the elastic-to-inelastic cross-section ratios. We find that the elastic-to-inelastic cross-section ratios under conditions corresponding to trapped molecular ensembles at $T\ensuremath{\sim}{10}^{\ensuremath{-}3}$ K exceed 100 for the majority of ${}^{2}\ensuremath{\Sigma}$ molecules. The range of ${}^{2}\ensuremath{\Sigma}$ molecules expected to be collisionally unstable in magnetic traps at $T<{10}^{\ensuremath{-}3}$ K is limited to molecules with the spin-rotation interaction constant ${\ensuremath{\gamma}}_{\mathrm{SR}}>0.5$ cm${}^{\ensuremath{-}1}$ and the rotational constant Be<4{B}_{e}<4Be​<4 cm${}^{\ensuremath{-}1}$.
The effect of external fields on directional states of a linear molecule trapped in a crystal field of octahedral symmetry is studied numerically. Adiabatic field-dressed energy levels are obtained by solving the time-independent Schr\"odinger equation for the rotational degrees of freedom of the confined molecule. In the absence of external fields, the internal octahedral crystal field serves to transform free-rotor states to angularly confined librational states of defined parity which arrange in near-degenerate sets of high multiplicity. Interaction of a linearly polarized, nonresonant laser field with the polarizability or of a static electric field with the dipole moment create alignment or orientation of the molecular axis, respectively. In the latter case, the combined effect of the internal (octahedral) and external static field is instrumental in creating orientation by coupling different tunneling states. Depending on the polarization direction of the external fields with respect to the symmetry axes provided by the crystal field, cooperative and competitive effects are distinguished. If the direction of the external field coincides with the minima of the crystal field, high degrees of alignment or orientation can be achieved for specific states, even for low field strengths. Otherwise, high efficiency of this mechanism is restricted to high fields and low temperatures. Strategies for an experimental realization are outlined.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.