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Directional states of symmetric-top molecules produced by combined static and radiative electric fields
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Figures

Image of FIG. 1.

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FIG. 1.

Illustration of the angles used in Eq. (12) for arbitrary field directions.

Image of FIG. 2.

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FIG. 2.

Schematic of the configurations of the fields and dipoles. An electrostatic, , and a linearly polarized radiative, , field are considered to be either collinear or perpendicular to one another. While the permanent dipole of a symmetric-top molecule is always along the figure axis ( or for a prolate or oblate tensor of inertia), the induced-dipole moment is directed predominantly along the figure axis for an oblate anisotropy of the polarizability tensor, , and perpendicular to it for a prolate polarizability, . See Table I and text.

Image of FIG. 3.

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FIG. 3.

Correlation diagram, for the permanent dipole interaction, between the field-free symmetric-top states and the harmonic librator states obtained in the high-field limit , see also (Ref. 40). At intermediate fields, the states are labeled by .

Image of FIG. 4.

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FIG. 4.

Correlation diagram, for the induced-dipole interaction, between the field-free symmetric-top states (center) and the harmonic librator states obtained in the high-field limit for the prolate, (on the left), and oblate, (on the right) cases. The harmonic librator states are labeled by the librator quantum number and the projection quantum numbers and . At intermediate fields, the states are labeled by . States that form tunneling doublets (only for ) have and are shown in color: red (double-thick grey lines) for doublets with and green (thick grey lines) for doublets with . Members of the degenerate doublets have and are shown in black (thick full lines). See text.

Image of FIG. 5.

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FIG. 5.

Dependence, in collinear fields, of the eigenenergies, panels (a)–(c), orientation cosines, panels (d)–(f), and alignment cosines, panels (g)–(i), of the states with , , and on the dimensionless parameter (which characterizes the permanent dipole interaction with the electrostatic field) for fixed values of the parameter (which characterizes the induced-dipole interaction with the radiative field; for prolate polarizability anisotropy and for oblate polarizability anisotropy). The states are labeled by . Note that panels (a), (d), and (g) pertain to the permanent dipole interaction alone. See text.

Image of FIG. 6.

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FIG. 6.

Dependence, in collinear fields, of the eigenenergies, panels (a)–(c), orientation cosines, panels (d)–(f), and alignment cosines, panels (g)-(i), of the states with , , and on the dimensionless parameter (which characterizes the induced-dipole interaction with the radiative field; for prolate polarizability anisotropy and for oblate polarizability anisotropy) for fixed values of the parameter (which characterizes the permanent dipole interaction with the radiative field). The states are labeled by . Note that panels (a), (d), and (g) pertain to the induced-dipole interaction alone. See text.

Image of FIG. 7.

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FIG. 7.

Effective potential for and along with the eigenenergies of states with (horizontal lines) and their alignment (diamonds) and orientation (circles) amplitudes and . The gray line shows the induced-dipole potential . See Eqs. (28), (23), and (24) and text.

Image of FIG. 8.

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FIG. 8.

Dependence of the -parity mixing parameter on the parameter at [panel (a)] and [panel (b)]. Note that the better the -parity mixing, the closer is the parameter to . See text.

Image of FIG. 9.

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FIG. 9.

Effective potential for and (left panels), (center panels), and (right panels) along with the eigenenergies and orientation amplitudes (shown by dots) and squares of the wavefunctions for states with . The columns are comprised of panels pertaining to increasing values of . Red (grey) curves correspond to , green (light grey) curves to , and blue (full) curves to . See text.

Image of FIG. 10.

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FIG. 10.

Effective potential for and (left panels), (center panels), and (right panels) along with the eigenenergies and orientation amplitudes (shown by dots) and squares of the wavefunctions for states with . The columns are comprised of panels pertaining to increasing values of . Red (grey) curves correspond to , green (light grey) curves to , and blue (full) curves to . See text.

Image of FIG. 11.

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FIG. 11.

Dependence, on perpendicular fields, of the eigenenergies, panels (a) and (b), orientation cosines, panels (c) and (d), and alignment cosines, panels (e) and (f), of the states with , , and on the dimensionless parameter (that characterizes the permanent dipole interaction with the electrostatic field) for fixed values of the parameter (that characterizes the induced-dipole interaction with the radiative field; for prolate polarizability anisotropy and for oblate polarizability anisotropy). The states are labeled by . The orientation cosines are calculated with respect to the electrostatic field and the alignment cosines with respect to the laser field. See text.

Image of FIG. 12.

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FIG. 12.

Dependence, on perpendicular fields, of the eigenenergies, panels (a) and (b), orientation cosines, panels (c) and (d), and alignment cosines, panels (e) and (f), of the states with , , and on the dimensionless parameter (that characterizes the induced-dipole interaction with the radiative field; for prolate polarizability anisotropy and for oblate polarizability anisotropy) for fixed values of the parameter (that characterizes the permanent dipole interaction with the electrostatic field). The states are labeled by . The orientation cosines are calculated with respect to the electrostatic field and the alignment cosines with respect to the laser field. See text.

Image of FIG. 13.

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FIG. 13.

Comparison of the evolution of states for different paths through the parameter space. From top to bottom, these are , and . In the middle panel, the label is interchanged with the label in the other two panels. We dub this effect “label switching.”

Tables

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Table I.

Symmetry combinations of the inertia and polarizability tensors for a polarizable symmetric top molecule. See text.

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Table II.

Eigenenergies for the permanent dipole interaction in the harmonic librator limit. See Refs. 35 and 37.

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Table III.

Eigenenergies for the induced dipole interaction in the harmonic librator limit. See also Ref. 22.

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Table IV.

Values of parameters and for choice symmetric top molecules whose properties were taken from Refs. 38 and 39. The conversion factors are [MHz] and [MHz]. Numbers in parentheses are order-of-magnitude estimates.

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/content/aip/journal/jcp/128/22/10.1063/1.2929850
2008-06-12
2014-04-24

Abstract

We show that combined electrostatic and radiative fields can greatly amplify the directional properties, such as axis orientation and alignment, of symmetric top molecules. In our computational study, we consider all four symmetry combinations of the prolate and oblate inertia and polarizabilitytensors, as well as the collinear and perpendicular (or tilted) geometries of the two fields. In, respectively, the collinear or perpendicular fields, the oblate or prolate polarizability interaction due to the radiative field forces the permanent dipole into alignment with the static field. Two mechanisms are found to be responsible for the amplification of the molecules’ orientation, which ensues once the static field is turned on: (a) permanent-dipole coupling of the opposite-parity tunneling doublets created by the oblate polarizability interaction in collinear static and radiative fields and (b) hybridization of the opposite parity states via the polarizability interaction and their coupling by the permanent dipole interaction to the collinear or perpendicular static field. In perpendicular fields, the oblate polarizability interaction, along with the loss of cylindrical symmetry, is found to preclude the wrong-way orientation, causing all states to become high-field seeking with respect to the static field. The adiabatic labels of the states in the tilted fields depend on the adiabatic path taken through the parameter space comprised of the permanent and induced-dipole interaction parameters and the tilt angle between the two field vectors.

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Scitation: Directional states of symmetric-top molecules produced by combined static and radiative electric fields
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/22/10.1063/1.2929850
10.1063/1.2929850
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