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Physical Review A

Nonadiabatic laser-induced alignment dynamics of alkali-metal dimers on the surface of a helium droplet

Henrik H. Kristensen, Lorenz Kranabetter, Areg Ghazaryan, Constant A. Schouder, Emil Hansen, Frank Jensen, Robert E. Zillich, Mikhail Lemeshko, Henrik Stapelfeldt

Published Mar 21, 2025• 2 citations
Publisher

Abstract

Alkali-metal dimers, ${\mathrm{Ak}}_{2}$, located on the surface of a helium nanodroplet, are set into rotation through the polarizability interaction with a nonresonant 1-ps-long laser pulse. The time-dependent degree of alignment is recorded using femtosecond-probe-pulse-induced Coulomb explosion into a pair of ${\mathrm{Ak}}^{+}$ fragment ions. The results, obtained for ${\mathrm{Na}}_{2}$, ${\mathrm{K}}_{2}$, and ${\mathrm{Rb}}_{2}$ in both the ground state $1{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ and the lowest-lying triplet state $1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$, exhibit distinct, periodic revivals with a gradually decreasing amplitude. The dynamics differ from that expected for dimers had they behaved as free rotors. Numerically, we solve the time-dependent rotational Schr\"odinger equation, including an effective mean-field potential to describe the interaction between the dimer and the droplet. The experimental and simulated alignment dynamics agree well and their comparison enables us to determine the effective rotational constants of the alkali dimers with the exception of ${\mathrm{Rb}}_{2}$($1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$) that only exhibits a prompt alignment peak but no subsequent revivals. For ${\mathrm{Na}}_{2}$($1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$), ${\mathrm{K}}_{2}$($1{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$), ${\mathrm{K}}_{2}$($1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$), and ${\mathrm{Rb}}_{2}$($1{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$), the alignment dynamics are well described by a two-dimensional rotor model. We ascribe this to a significant confinement of the internuclear axis of these dimers, induced by the orientation-dependent droplet--dimer interaction, to the tangential plane of their residence point on the droplet.

DOI
10.1103/physreva.111.033114

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Nonadiabatic laser-induced alignment dynamics of alkali dimers on the surface of a helium droplet

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Alkali dimers, $\mathrm{Ak}_2$, located on the surface of a helium nanodroplet, are set into rotation through the polarizability interaction with a nonresonant 1-ps-long laser pulse. The time-dependent degree of alignment is recorded using femtosecond-probe-pulse-induced Coulomb explosion into a pair of $\mathrm{Ak}^+$ fragment ions. The results, obtained for $\mathrm{Na}_2$, $\mathrm{K}_2$, and $\mathrm{Rb}_2$ in both the ground state $1 ^1Σ_g^+$ and the lowest-lying triplet state $1 ^3Σ_u^+$, exhibit distinct, periodic revivals with a gradually decreasing amplitude. The dynamics differ from that expected for dimers had they behaved as free rotors. Numerically, we solve the time-dependent rotational Schrödinger equation, including an effective mean-field potential to describe the interaction between the dimer and the droplet. The experimental and simulated alignment dynamics agree well and their comparison enables us to determine the effective rotational constants of the alkali dimers with the exception of $\mathrm{Rb}_2$($1 ^3Σ_u^+$) that only exhibits a prompt alignment peak but no subsequent revivals. For $\mathrm{Na}_2$($1 ^3Σ_u^+$), $\mathrm{K}_2$($1 ^1Σ_g^+$), $\mathrm{K}_2$($1 ^3Σ_u^+$) and $\mathrm{Rb}_2$($1 ^1Σ_g^+$), the alignment dynamics are well-described by a 2D rotor model. We ascribe this to a significant confinement of the internuclear axis of these dimers, induced by the orientation-dependent droplet-dimer interaction, to the tangential plane of their residence point on the droplet.

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Alkali-metal dimers, Ak2{\mathrm{Ak}}_{2}Ak2​, located on the surface of a helium nanodroplet, are set into rotation through the polarizability interaction with a nonresonant 1-ps-long laser pulse. The time-dependent degree of alignment is recorded using femtosecond-probe-pulse-induced Coulomb explosion into a pair of Ak+{\mathrm{Ak}}^{+}Ak+ fragment ions. The results, obtained for Na2{\mathrm{Na}}_{2}Na2​, K2{\mathrm{K}}_{2}K2​, and Rb2{\mathrm{Rb}}_{2}Rb2​ in both the ground state 11\ensuremathΣg+1{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}11\ensuremathΣg+​ and the lowest-lying triplet state 13\ensuremathΣu+1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}13\ensuremathΣu+​, exhibit distinct, periodic revivals with a gradually decreasing amplitude. The dynamics differ from that expected for dimers had they behaved as free rotors. Numerically, we solve the time-dependent rotational Schr"odinger equation, including an effective mean-field potential to describe the interaction between the dimer and the droplet. The experimental and simulated alignment dynamics agree well and their comparison enables us to determine the effective rotational constants of the alkali dimers with the exception of Rb2{\mathrm{Rb}}_{2}Rb2​(13\ensuremathΣu+1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}13\ensuremathΣu+​) that only exhibits a prompt alignment peak but no subsequent revivals. For Na2{\mathrm{Na}}_{2}Na2​(13\ensuremathΣu+1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}13\ensuremathΣu+​), K2{\mathrm{K}}_{2}K2​(11\ensuremathΣg+1{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}11\ensuremathΣg+​), K2{\mathrm{K}}_{2}K2​(13\ensuremathΣu+1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}13\ensuremathΣu+​), and Rb2{\mathrm{Rb}}_{2}Rb2​(11\ensuremathΣg+1{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}11\ensuremathΣg+​), the alignment dynamics are well described by a two-dimensional rotor model. We ascribe this to a significant confinement of the internuclear axis of these dimers, induced by the orientation-dependent droplet--dimer interaction, to the tangential plane of their residence point on the droplet.
Alkali dimers, Ak2\mathrm{Ak}_2Ak2​, located on the surface of a helium nanodroplet, are set into rotation through the polarizability interaction with a nonresonant 1-ps-long laser pulse. The time-dependent degree of alignment is recorded using femtosecond-probe-pulse-induced Coulomb explosion into a pair of Ak+\mathrm{Ak}^+Ak+ fragment ions. The results, obtained for Na2\mathrm{Na}_2Na2​, K2\mathrm{K}_2K2​, and Rb2\mathrm{Rb}_2Rb2​ in both the ground state 11Σg+1 ^1Σ_g^+11Σg+​ and the lowest-lying triplet state 13Σu+1 ^3Σ_u^+13Σu+​, exhibit distinct, periodic revivals with a gradually decreasing amplitude. The dynamics differ from that expected for dimers had they behaved as free rotors. Numerically, we solve the time-dependent rotational Schrödinger equation, including an effective mean-field potential to describe the interaction between the dimer and the droplet. The experimental and simulated alignment dynamics agree well and their comparison enables us to determine the effective rotational constants of the alkali dimers with the exception of Rb2\mathrm{Rb}_2Rb2​(13Σu+1 ^3Σ_u^+13Σu+​) that only exhibits a prompt alignment peak but no subsequent revivals. For Na2\mathrm{Na}_2Na2​(13Σu+1 ^3Σ_u^+13Σu+​), K2\mathrm{K}_2K2​(11Σg+1 ^1Σ_g^+11Σg+​), K2\mathrm{K}_2K2​(13Σu+1 ^3Σ_u^+13Σu+​) and Rb2\mathrm{Rb}_2Rb2​(11Σg+1 ^1Σ_g^+11Σg+​), the alignment dynamics are well-described by a 2D rotor model. We ascribe this to a significant confinement of the internuclear axis of these dimers, induced by the orientation-dependent droplet-dimer interaction, to the tangential plane of their residence point on the droplet.
Rubidium dimers residing on the surface of He nanodroplets are doubly ionized by an intense femtosecond laser pulse leading to fragmentation into a pair of Rb+{\mathrm{Rb}}^{+}Rb+ ions. We show that the kinetic energy of the Rb+{\mathrm{Rb}}^{+}Rb+ fragment ions can be used to identify dimers formed in either the XXX $^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ ground state or in the lowest-lying triplet state, $a\text{ }^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$. From the experiment, we estimate the abundance ratio of dimers in the aaa and XXX states as a function of the mean droplet size and find values between $4\ensuremath{\mathbin:}1$ and $5\ensuremath{\mathbin:}1$. Our technique applies generally to dimers and trimers of alkali atoms, here also demonstrated for Li2{\mathrm{Li}}_{2}Li2​, Na2{\mathrm{Na}}_{2}Na2​, and K2{\mathrm{K}}_{2}K2​, and will enable femtosecond time-resolved measurements of their rotational and vibrational dynamics, possibly with atomic structural resolution.
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 rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.
Spectroscopy of doped helium nanodroplets has become, in recent years, a popular tool for the study of bothfinite size samples of the helium quantum fluid and molecules isolated in this sub Kelvin environment. Whilemany dopants migrate to the center of the droplet, alkali (Ak) atoms in their ground electronic state, becauseof their so weak interaction with He, remain at the surface, the latter being in this way slightly distortedexhibiting a dimple. However, when in their first excited states, Ak atoms are forming exciplexes. These areanisotropic with the central atom surrounded by a ring of He atoms located in the nodal plane of the valenceelectron pz orbital. Structural properties, obtained by DMC and PIMC, are presented here for some Ak -Hen exciplexes.Ak2 dimers in helium environment have also gained interest in this last decade, in connexion with the generationof ultracold molecules. When attached to helium droplets, Ak atoms can float on the surface andform molecules in cold collisions. DMC and PIMC methods are used to compute energetics and structuralinformations for Rb2 in helium. In particular, the orientation of the dimer relative to the droplet surface isexamined.