We show that congruent electric, magnetic and non-resonant optical fields acting concurrently on a polar paramagnetic (and polarizable) molecule offer possibilities to both amplify and control the directionality of the ensuing molecular states that surpass those available in double-field combinations or in single fields alone.At the core of these triple-field effects is the lifting of the degeneracy of the projection quantum number M by the magnetic field superimposed on the optical field and a subsequent coupling of the members of the 'doubled' (for states with ≠ M 0) tunneling doublets due to the optical field by even a weak electrostatic field.
We show that congruent electric, magnetic and non-resonant optical fields acting concurrently on a polar paramagnetic (and polarizable) molecule offer possibilities to both amplify and control the directionality of the ensuing molecular states that surpass those available in double-field combinations or in single fields alone.At the core of these triple-field effects is the lifting of the degeneracy of the projection quantum number M by the magnetic field superimposed on the optical field and a subsequent coupling of the members of the 'doubled' (for states with ≠ M 0) tunneling doublets due to the optical field by even a weak electrostatic field.
This chapter describes a versatile technique to control molecular rotation and translation. The technique is based on the combined effect of external electric fields that act concurrently on the molecular permanent and induced dipole moments. This synergistic effect arises for any polar molecule, as only an anisotropic polarizability, along with a permanent dipole moment, is required. This is always available in polar molecules. The effect of the combined fields can be achieved either by superimposing an electrostatic and a far-off resonant optical field (i.e., one that supplies electric field strength but does not cause transitions) that act, respectively, on the molecule's permanent and induced electric dipole, or by making use of a unipolar electromagnetic pulse that seizes the permanent and induced dipole moments simultaneously. If the combined electric fields are homogeneous, only molecular rotation is affected, whereas inhomogeneous fields affect both molecular rotation and translation. As noted in the chapter, the ability to manipulate molecular rotation and translation has wide-ranging applications – in research areas as diverse as reaction dynamics, spectroscopy, higher harmonic generation and molecular orbital imaging, the focusing and trapping of molecules, as well as quantum simulation and computing.
A detailed treatment of an electro-optical trap for polar molecules, realized by embedding an optical trap within a uniform electrostatic field, is presented and the trap's properties analyzed and discussed. The electro-optical trap offers significant advantages over an optical trap that include an increased trap depth and conversion of alignment of the trapped molecules to marked orientation. Tilting the polarization plane of the optical field with respect to the electrostatic field diminishes both the trap depth and orientation and lifts the degeneracy of the $\ifmmode\pm\else\textpm\fi{}M$ states of the trapped molecules. These and other features of the electro-optical trap are examined in terms of the eigenproperties of the polar and polarizable molecules subject to the combined permanent and induced electric dipole interactions at play.
We study the dynamics of paramagnetic molecular superrotors in an external magnetic field. An optical centrifuge is used to create dense ensembles of oxygen molecules in ultrahigh rotational states. In is shown, for the first time, that the gas of rotating molecules becomes optically birefringent in the presence of a magnetic field. The discovered effect of "magneto-rotational birefringence" indicates the preferential alignment of molecular axes along the field direction. We provide an intuitive qualitative model, in which the influence of the applied magnetic field on the molecular orientation is mediated by the spin-rotation coupling. This model is supported by the direct imaging of the distribution of molecular axes, the demonstration of the magnetic reversal of the rotational Raman signal, and by numerical calculations.
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 properties of molecule-optical elements such as lenses or prisms based on the interaction of molecules with optical fields depend in a crucial way on the molecular quantum state and its alignment created by the optical field. Herein, we consider the effects of state-dependent alignment in estimating the optical dipole force acting on the molecules and, to this end, introduce an effective polarizability which takes proper account of molecular alignment and is directly related to the alignment-dependent optical dipole force. We illustrate the significance of including molecular alignment in the optical dipole force by a trajectory study that compares previously used approximations with the present approach. The trajectory simulations were carried out for an ensemble of linear molecules subject to either propagating or standing-wave optical fields for a range of temperatures and laser intensities. The results demonstrate that the alignment-dependent effective polarizability can serve to provide correct estimates of the optical dipole force, on which a state-selection method applicable to nonpolar molecules could be based. We note that an analogous analysis of the forces acting on polar molecules subject to an inhomogeneous static electric field reveals a similarly strong dependence on molecular orientation.
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.