arXiv:2111.12540 · Physical Review Letters

Quantum-State-Sensitive Detection of Alkali Dimers on Helium Nanodroplets by Laser-Induced Coulomb Explosion

Henrik H. Kristensen, Lorenz Kranabetter, Constant A. Schouder, Christoph Stapper, Jacqueline Arlt, Marcel Carto Constantin Mudrich, Henrik Stapelfeldt

Published Mar 4, 2022• 23 citations

arXiv HTML PDF

Abstract

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 ${\mathrm{Rb}}^{+}$ ions. We show that the kinetic energy of the ${\mathrm{Rb}}^{+}$ fragment ions can be used to identify dimers formed in either the $X$ $^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ 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 $a$ and $X$ 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 ${\mathrm{Li}}_{2}$, ${\mathrm{Na}}_{2}$, and ${\mathrm{K}}_{2}$, and will enable femtosecond time-resolved measurements of their rotational and vibrational dynamics, possibly with atomic structural resolution.

DOI: 10.1103/physrevlett.128.093201

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

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arXiv:2111.12540 · Physical Review Letters

Quantum-State-Sensitive Detection of Alkali Dimers on Helium Nanodroplets by Laser-Induced Coulomb Explosion

Henrik H. Kristensen, Lorenz Kranabetter, Constant A. Schouder, Christoph Stapper, Jacqueline Arlt, Marcel Carto Constantin Mudrich, Henrik Stapelfeldt

Published Mar 4, 2022• 23 citations

arXiv HTML PDF

Abstract

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

{\mathrm{Rb}}^{+}

ions. We show that the kinetic energy of the

{\mathrm{Rb}}^{+}

fragment ions can be used to identify dimers formed in either the

X

^{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

a

and

X

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

{\mathrm{Li}}_{2}

{\mathrm{Na}}_{2}

, and

{\mathrm{K}}_{2}

, and will enable femtosecond time-resolved measurements of their rotational and vibrational dynamics, possibly with atomic structural resolution.

DOI: 10.1103/physrevlett.128.093201

Related papers

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

Henrik H. Kristensen, Lorenz Kranabetter, Areg Ghazaryan +6 more

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.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.

Physical Review AMar 21, 20252 citations

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.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.

arXiv:2502.14521Feb 20, 20251 citation

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Spectroscopy of silver dimers in triplet states

Andreas Przystawik, Paul Radcliffe, Sebastian Göde +2 more

Silver dimers embedded in ultracold helium nanodroplets are ionized by two-photon excitation via a strong resonance which extends from 3.85 eV up to 4.1 eV. The corresponding photoelectron spectra reveal that the ionization threshold is shifted by more than 1.4 eV towards lower values when compared to the gas phase. This gives strong evidence that weakly bound dimers in the lowest lying triplet state are present, thus enabling convenient spectroscopy of the triplet Ag 2 . A comparison with predictions from theory allows an assignment of the structure in the spectra. The successful identification of triplet silver dimers embedded in helium droplets shows exemplarily that the formation of such weakly bound systems is not restricted to surface locations as with the alkalis, but represents a general feature of the ultracold helium droplet environment.Silver dimers embedded in ultracold helium nanodroplets are ionized by two-photon excitation via a strong resonance which extends from 3.85 eV up to 4.1 eV. The corresponding photoelectron spectra reveal that the ionization threshold is shifted by more than 1.4 eV towards lower values when compared to the gas phase. This gives strong evidence that weakly bound dimers in the lowest lying triplet state are present, thus enabling convenient spectroscopy of the triplet Ag 2 . A comparison with predictions from theory allows an assignment of the structure in the spectra. The successful identification of triplet silver dimers embedded in helium droplets shows exemplarily that the formation of such weakly bound systems is not restricted to surface locations as with the alkalis, but represents a general feature of the ultracold helium droplet environment.

Journal of Physics B Atomic Molecular and Optical PhysicsSep 25, 200630 citations

Quantum dynamics of Rb atoms desorbing off the surface of He nanodroplets

Nikolay V. Dozmorov, Alexey V. Baklanov, Johannes von Vangerow +3 more

The desorption of excited rubidium atoms off the surface of helium nanodroplets is studied in detail using femtosecond time-resolved photoion and photoelectron imaging spectroscopy in combination with quantum wave-packet simulations. The good agreement of the measured time-dependent velocity distributions with the simulation when exciting the Rb dopant atoms into the $6p$ state supports the pseudodiatomic model for the Rb-He droplet interaction, even on the level of quantum wave-packet dynamics. Time-resolved photoelectron spectra reveal the partitioning of excitation energy into the dopant and the droplet degrees of freedom.The desorption of excited rubidium atoms off the surface of helium nanodroplets is studied in detail using femtosecond time-resolved photoion and photoelectron imaging spectroscopy in combination with quantum wave-packet simulations. The good agreement of the measured time-dependent velocity distributions with the simulation when exciting the Rb dopant atoms into the $6p$ state supports the pseudodiatomic model for the Rb-He droplet interaction, even on the level of quantum wave-packet dynamics. Time-resolved photoelectron spectra reveal the partitioning of excitation energy into the dopant and the droplet degrees of freedom.

arXiv:1809.04846Physical Review AOct 2, 201811 citations

Submersion of rubidium clusters in helium nanodroplets

Arne Schiller, Paul Martini, Elias Jabbour Al Maalouf +1 more

Abstract Alkali atoms and small clusters are known to reside on the surface of a helium droplet rather than its inside as most other dopant species. A theoretical investigation suggested that alkali clusters (Li–Rb) exceeding a certain critical size can become submerged in the droplet, which was experimentally confirmed for sodium and potassium. Here, we report an analogous experimental study of rubidium cluster submersion by means of electron impact mass spectrometry. We recorded size distributions of Rb cluster ions at various electron energies between 8 and 160 eV. Our data suggest that Rb clusters attached to helium droplets undergo a gradual submersion transition similar to potassium, ultimately leading to the full submersion of clusters larger than $\sim 100~\hbox {Rb}$ ∼ 100 Rb atoms. Our findings are consistent with previous theoretical and experimental studies. Graphic abstractAbstract Alkali atoms and small clusters are known to reside on the surface of a helium droplet rather than its inside as most other dopant species. A theoretical investigation suggested that alkali clusters (Li–Rb) exceeding a certain critical size can become submerged in the droplet, which was experimentally confirmed for sodium and potassium. Here, we report an analogous experimental study of rubidium cluster submersion by means of electron impact mass spectrometry. We recorded size distributions of Rb cluster ions at various electron energies between 8 and 160 eV. Our data suggest that Rb clusters attached to helium droplets undergo a gradual submersion transition similar to potassium, ultimately leading to the full submersion of clusters larger than $$\sim 100~\hbox {Rb}$$ ∼ 100 Rb atoms. Our findings are consistent with previous theoretical and experimental studies. Graphic abstract

The European Physical Journal DApr 1, 20217 citations

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

{\mathrm{Rb}}^{+}

ions. We show that the kinetic energy of the

{\mathrm{Rb}}^{+}

fragment ions can be used to identify dimers formed in either the

X

^{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

a

and

X

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

{\mathrm{Li}}_{2}

{\mathrm{Na}}_{2}

, and

{\mathrm{K}}_{2}

, and will enable femtosecond time-resolved measurements of their rotational and vibrational dynamics, possibly with atomic structural resolution.

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.

Alkali dimers,

\mathrm{Ak}_2

\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.

6p

state supports the pseudodiatomic model for the Rb-He droplet interaction, even on the level of quantum wave-packet dynamics. Time-resolved photoelectron spectra reveal the partitioning of excitation energy into the dopant and the droplet degrees of freedom.

\sim 100~\hbox {Rb}

∼ 100 Rb atoms. Our findings are consistent with previous theoretical and experimental studies. Graphic abstract