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Physical Review Letters

Alignment and Trapping of Molecules in Intense Laser Fields

Břetislav Friedrich, Dudley R. Herschbach

Published Jun 5, 1995• 818 citations
Publisher

Abstract

The anisotropic interaction of the electric field vector of intense laser radiation with the dipole moment induced in a polarizable molecule by the laser field creates aligned pendular states. These are directional superpositions of field-free states, corresponding to oblate spheroidal wave functions, with eigenenergies that decrease with increasing field strength. We present calculations demonstrating the utility of these states for both laser alignment and spatial trapping of molecules.

DOI
10.1103/physrevlett.74.4623

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The anisotropic interaction of the electric field vector of intense laser radiation with the dipole moment induced in a polarizable molecule by the laser field creates aligned pendular states. These are directional superpositions of field-free states, corresponding to oblate spheroidal wave functions, with eigenenergies that decrease with increasing field strength. We present calculations demonstrating the utility of these states for both laser alignment and spatial trapping of molecules.
Intense pulsed-laser fields have provided means to both induce spatial alignment of molecules and enhance strength of chemical bonds. The duration of the laser field typically ranges from hundreds of picoseconds to a few femtoseconds. Accordingly, the induced "laser-dressed" properties can be adiabatic, existing only during the pulse, or nonadiabatic, persisting into the subsequent field-free domain. We exemplify these aspects by treating the helium dimer, in its ground [Formula: see text] and first excited [Formula: see text] electronic states. The ground-state dimer when field-free is barely bound, so very responsive to electric fields. We examine two laser realms, designated (I) "intrusive" and (II) "impelling." I employs intense nonresonant laser fields, not strong enough to dislodge electrons, yet interact with the dimer polarizability to induce binding and pendular states in which the dimer axis librates about the electric field direction. II employs superintense high-frequency fields that impel the electrons to undergo quiver oscillations, which interact with the intrinsic Coulomb forces to form an effective binding potential. The dimer bond then becomes much stronger. For I, we map laser-induced pendular alignment within the X state, which is absent for the field-free dimer. For II, we evaluate vibronic transitions from the X to A states, governed by the amplitude of the quiver oscillations.
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.
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.
We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar 23Na40K^{23}\mathrm{Na}^{40}\mathrm{K}23Na40K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of 5.26(15)5.26(15)5.26(15) kV/cm and an angle of $54.{7}^{\ensuremath{\circ}}$ between this field and the polarization of the optical laser lead to a trapping design for 23Na40K^{23}\mathrm{Na}^{40}\mathrm{K}23Na40K molecules where decoherence due to electric field strength and laser-intensity fluctuations, as well as fluctuations in the direction of its polarization, are kept to a minimum. One-standard-deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions, pairs of hyperfine-rotational states of v=0v=0v=0 molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.