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Time-dependent alignment of molecules trapped in octahedral crystal fields
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Image of FIG. 1.
FIG. 1.

(Color online) Rotational density of the ground librational state in the octahedral crystal potential at . The lobes of the densities point towards ⟨100⟩ crystallographic directions, i.e., towards the corners of the octahedron drawn around the density plot. The arrows represent the ⟨100⟩ and ⟨110⟩ polarization directions of the external alignment field. This reduces the total symmetry to or , respectively.

Image of FIG. 2.
FIG. 2.

(Color online) Energy level spectra pertaining to crystal-field states and light-induced alignment along a cooperative direction. (a) Correlation of the crystal-field energies between the free rotor and librational limits. Blue and red curves mark the gerade and ungerade states, respectively, and the grouping of states into two librational manifolds is indicated. The contour plot below the panel displays the rotational density of the ground state at , . (b) Dependence of the energy levels of symmetry on the alignment-field strength . The and curves undergoing an avoided crossing are emphasized by circular symbols for the data points. Inserted in the panel, the corresponding densities are connected to the data points by lines: The density is given at , 60, and 65, and the density is displayed for .

Image of FIG. 3.
FIG. 3.

(Color online) Dependence of time-dependent alignment cosine and wave-packet properties on the pulse width (FWHM) at in the gas phase. Left panel: Alignment cosine for (see the lower half of the split color bar). Middle panel: Buildup of the wave packet for in terms of occupation numbers of free-rotor states (see the upper half of the color bar). Right panel: Expectation value of the square of the angular momentum operator representing the degree of rotational excitation at (solid) and (dashed).

Image of FIG. 4.
FIG. 4.

Dependence of the time-dependent alignment cosine on the pulse width (FWHM) at for molecules trapped in octahedral fields. Results are shown for cooperative [(a) and (c)] and competitive [(b) and (d)] polarization directions with and symmetries, respectively. The parameters of the external and internal fields are (100,25) in the left panels [(a) and (b)] and (200,50) in the right panels [(c) and (d)]. The alignment curves attached on top or below of the panels display the result for in each of the cases.

Image of FIG. 5.
FIG. 5.

(Color online) Crystal-field energies and corresponding postpulse wave-packet populations: of the occupied crystal-field states for pulse widths in the range . Labeling [(a)–(d)] as in Fig. 4. For (a)→(b) and (c)→(d), the direction of the alignment-field polarization changes from cooperative to competitive. This leads to different occupations of the same crystal-field states.

Image of FIG. 6.
FIG. 6.

Fourier transform power spectra of the time-dependent alignment signals of Fig. 4 for a short alignment pulse, . Arrangement of panels (a)–(d) is adapted from Fig. 4 with negative sign (dashed lines) for competitive field directions in (b) and (d). The peaks can be assigned to energy differences among the states comprising the rotational wave packets evolving in the two crystal fields: for the upper panel and for the lower. The parity of the pairs of states involved in the transitions are indicated by or labels, respectively.

Image of FIG. 7.
FIG. 7.

Components of the postpulse wave packet excited by an alignment pulse with . Beatings between occupied levels of the same symmetry generate the peaks found in frequency-domain representation of alignment signals. The arrows with symbols indicate some of the assignments made in Fig. 6 with the help of energies given in Table I. Panel labeling [(a)–(d)] as before.

Image of FIG. 8.
FIG. 8.

(Color online) Near-adiabatic alignment with at (a) for gas phase molecule, (b) in the crystal field, and (c) in the crystal field. For solid-state cases (b) and (c), and the pulse widths are (black) (solid), 1 (dashed), and 1.5 (dotted), and (blue) (solid), 3 (dashed), and 4 (dotted). For the gas phase (a), only , 1, and 1.5 are applied.

Image of FIG. 9.
FIG. 9.

(Color online) Left panel: Turn on of the alignment in the crystal (solid curve) and in the gas phase (dotted curve) for pulse duration (dashed). Right panel: Adiabatic energy levels (from Ref. 28, and scaled as in Table I) for (circles), (triangles), (diamonds), and (squares) states in the symmetry. The instantaneous pulse intensity should be read from the right panel’s axis. The enumerated arrows indicate the stepwise enhancement of alignment and its connection to the field-induced avoided crossings.


Generic image for table
Table I.

The crystal-field energies scaled up by the ground-state energies, and . The states are labeled according to their irreducible representations in the three point groups , , and to facilitate with selection rules. Even (gerade) states are emphasized by bold numbers.

Generic image for table
Table II.

Intensity dependence of the peak alignment degree for pulse duration in the competitive ( symmetry) and cooperative cases . Maximum degree of alignment is given in parentheses.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Time-dependent alignment of molecules trapped in octahedral crystal fields