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. 2018 Sep 25;115(39):E9058-E9066.
doi: 10.1073/pnas.1810102115. Epub 2018 Sep 7.

Pendular Alignment and Strong Chemical Binding Are Induced in Helium Dimer Molecules by Intense Laser Fields

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Free PMC article

Pendular Alignment and Strong Chemical Binding Are Induced in Helium Dimer Molecules by Intense Laser Fields

Qi Wei et al. Proc Natl Acad Sci U S A. .
Free PMC article

Abstract

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.

Keywords: Kramers–Henneberger approximation; chemical bonding; laser-induced properties; pendular alignment; quiver oscillations.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Ground electronic state X1Σg+ of 4He2 dimer. (A) Field-free dimer potential energy curve (1–3). Well depth V(Rm)=3.5×105 a.u. (11 K) at Rm=5.61 a.u. Sole vibrational energy level (dashed blue) E0=4.1×109 a.u. (−1.3 mK) is only slightly below asymptote for separated atoms. Probability distribution of internuclear distance (black, arbitrary units), R2|Ψvib(R)|2, extends beyond 100 a.u. Expectation value for internuclear distance R = 104 a.u. (B) Laser field (I = 0.005 a.u.)-induced alteration of potential energy curve (compared with free-field, dashed red), with downward shift of sole pendular–vibrational level (|000, dashed blue). (C) For stronger laser field (I = 0.01 a.u.). In B and C, the radial curves shown pertain to θ = 0°, whereas the penvib levels incorporate ranges of both R and θ; see Fig. 3 and Table 2.
Fig. 2.
Fig. 2.
Quantities involved in interaction potential, Eq. 1, for ground-state helium dimer. (A) Dependence of polarizability components on internuclear distance. (Inset) Anisotropy is shown. (B) Laser-induced angular alignment of the dimer axis (schematic sketch). Potential minima in the polar regions, near θ = 0° and 180°, are separated by an equatorial barrier that quenches end-for-end rotation. Location of lowest penvib level is indicated by |000 (dashed blue).
Fig. 3.
Fig. 3.
Two-dimensional plots exhibiting radial and angular dependence, corresponding to Fig. 1. (AC) Potential energy surfaces with transparent planes (green) that depict location of the lowest penvib quantum level. (A′–C′) Probability distributions, R2|Ψ(R, θ)|2, square of wavefunctions weighed by the radial Jacobian factor.
Fig. 4.
Fig. 4.
Variation with laser intensity of properties of ground-state helium dimer. (A) The laser-induced bound penvib levels EvJM = |000 and |021 (blue) include the contribution from the centrifugal term, BJ2, in Eq. 2. The dotted curve shows where the |000 level would be if the centrifugal term were omitted. Also shown is the potential depth V(Rm). Numbers close to points indicate the averaged internuclear distance R; compare Fig. 1 B and C and Table 2. (B) Expectation values cos2θ for the penvib levels (blue). Also indicated (±Δθ, black points) are angular amplitudes of the pendular librations, Δθ=arccoscos2θ1/2.
Fig. 5.
Fig. 5.
Variation with laser intensity of pulse options. (A) Helium dimer rotational period, π/B (blue curve), along with dashed curves that indicate shorter and longer pulse durations: Tpd=π/5B and 5π/B, respectively for nonadiabatic and adiabatic options. Also shown is the ionization half-life (red curve) of atomic helium, T1/2=ln2/Γ, derived from single-electron ionization rates, for laser fields of wavelength 780 nm, obtained from accurate theoretical data of ref. . (B) Estimated fraction (%) of dimer molecules surviving ionization after undergoing laser pulses: exp(0.6931Tpd/T1/2).
Fig. 6.
Fig. 6.
(A) “Lines of charge” generating the effective potential acting on each electron in the VKH terms in Eq. 6. These line segments of length 2α0 are parallel to the laser polarization along the z axis (toward unit vector e of Eq. 4) and centered on the nuclei at ±R/2. The internuclear vector R is directed at angle θ from the z axis, here drawn with the azimuth ϕ = 0 about the z axis (eigenproperties do not depend on that uniform angle). (B) Variation with θ of potential well depth: V(α0,Rm,θ)=ϵ(4)(α0,Rm,θ)ϵ(4)(α0,,θ), from eigenvalues of Eq. 6, for X (red) and A (blue) states and for different quiver amplitudes α0=0.2,0.5,1.0,1.5 and 2.0 a.u., respectively. Dots indicate, for the lowest penvib levels, the pendular range of the dimer axis at the radial minimum, Rm.
Fig. 7.
Fig. 7.
KH 4He2 dimer potential energy surfaces for both electronic ground-state X1Σg+ and excited-state A1Σu+, for quiver amplitudes α0= 0, 0.5, 1, 2. (AD, Upper) shows radial R dependence with optimal alignment (θ = 0) compared with field-free (dashed red); note that the zero for the ordinate energy scale is the asymptote for the ground-state separated atoms. (A′–D′, Lower) shows 2D plots of R, θ dependence (Table 1).
Fig. 8.
Fig. 8.
Criteria of Eq. 8 governing quiver amplitude and specifying lower and upper bounds (black curves) for laser frequency, with trial values ω = 10 and 5 (red dashed lines) and corresponding laser intensity (blue curves).
Fig. 9.
Fig. 9.
Franck–Condon transitions between KH potential curves of ground-state X1Σg+ and excited-state A1Σu+. (A and A′) For α0=0.5. From lowest vibrational level of the A state, vA = 0, transition reflects from the steep repulsive region of the X state, dissociates the dimer, and becomes a continuous traveling wave carrying off kinetic energy. Sample transition from higher level, vA = 17, connects turning point to the lowest vibrational level of the X state. Transition energies (units 103 cm−1): continuum peaks at 70, reflecting shape of vA=0, while discrete lines between 116 and 132 reflect higher vA levels with turning points that align with vX=0 (B and B′). For α0=1.0, both X and A potential curves acquire much deeper wells with similar Rm, show only 0 0 transition, shortest but most intense.
Fig. 10.
Fig. 10.
Internal photodissociation of He2 dimer. (A) Franck–Condon (FC) continuum transitions from KH potentials for α0=0,0.2,0.5 (blue, green, red; Fig. 9A) compared with field-free spectrum (black profile). Notation FC2 designates sum of squares of vA|vX. (B) Corresponding kinetic energy carried off as the pair of helium atoms fly apart. The predicted exit velocity of each He atom at the peak distribution for α0=0,0.2,0.5 are similar: 12.5, 13.6, 11.9 km/s, respectively.

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