Imaging the breakdown of molecular-frame dynamics through rotational uncoupling

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Imaging the breakdown of molecular-frame dynamics through rotational uncoupling

Lucas J. Zipp, Adi Natan, and Philip H. Bucksbaum

Phys. Rev. A 95, 061403(R) – Published 22 June 2017

Abstract

We demonstrate the breakdown of molecular-frame dynamics induced by the uncoupling of molecular rotation from electronic motion in molecular Rydberg states. We observe this non-Born-Oppenheimer regime in the time domain through photoelectron imaging of a coherent molecular Rydberg wave packet in $N_{2}$ . The photoelectron angular distribution shows a radically different time evolution than that of a typical molecular-frame-fixed electron orbital, revealing the uncoupled motion of the electron as it precesses around the averaged anisotropic potential of the rotating ion core.

Received 19 July 2016

DOI:https://doi.org/10.1103/PhysRevA.95.061403

Physics Subject Headings (PhySH)

Atomic & molecular processes in external fields Electronic structure of atoms & molecules

Molecules Rydberg atoms & molecules

Atomic, Molecular & Optical

Authors & Affiliations

Lucas J. Zipp^1,2,*, Adi Natan¹, and Philip H. Bucksbaum^1,2,3

¹Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
²Department of Physics, Stanford University, Stanford, California 94305, USA
³Department of Applied Physics, Stanford University, Stanford, California 94305, USA

^*lzipp@stanford.edu

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Issue

Vol. 95, Iss. 6 — June 2017

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Images

Figure 1
Breakdown of molecular-frame dynamics. The outer lobes (blue-yellow color scale) correspond to the Rydberg electron density with a $4 f$ orbital radial distribution, while the inner lobe (white) shows the angular distribution of the nuclei, with an artificially chosen radial distribution for better visualization. The simulated homonuclear diatomic system starts out in a localized rotational wave packet centered at $| J = 30, M = 30 〉$ with an $f$ Rydberg electron aligned along the internuclear axis in a $Λ = 0$ state. The electron and ion-core position densities are plotted at times corresponding to fractions of the classical nuclear rotation period, $T_{c} = π / [B \sqrt{J (J + 1)}]$ . Each row displays the dynamics for a different value of the electronic splitting parameter $a$ , as given in Eq. (2). The top row corresponds to the Born-Oppenheimer regime, while the bottom row shows completely uncoupled nuclear and rotational dynamics (see Supplemental Material for full movies).
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Figure 2
The simulated electron and ion-core angular distribution time evolution of a $n f$ Rydberg electron. A model $N_{2}$ -like diatomic molecule is pumped to an $n f$ Rydberg state with a five-photon excitation and subsequently probed through single-photon ionization (linear polarization of pump and probe along the $x$ axis). The upper row of images show the electron position density of the Rydberg electron (before probing) at times corresponding to peak ion-core alignment and antialignment which occur near $T r e v$ and $T r e v / 2$ . A $4 f$ hydrogenic radial wave function is used for visualization. The molecular alignment direction for each image is depicted by the ball-and-stick graphic. The $β_{2}$ parameter of the photoelectron angular distribution and the $〈{cos}^{2}〉$ alignment value of the ion-core distribution is also shown. (a) Simulation for multiphoton excitation restricted to the $Λ = 0$ eigenstate of the $f$ manifold with $a = 2400 B$ , where $B$ is the rotational constant of the cation core. The PAD displays a typical Born-Oppenheimer molecular alignment signal. (b) and (c) Simulation for multiphoton excitation assuming all levels of the $f$ manifold are accessible, with an electronic splitting of $a = 6 B$ and $a = 0.6 B$ , showing the progressive development of $l$ -uncoupled dynamics.
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Figure 3
Direct observation of $l$ -uncoupling dynamics. (a) Polar plots of the experimentally extracted photoelectron angular distribution from the $4 f$ Rydberg manifold in $N_{2}$ at selected probe times. (b) $β$ values extracted from a least-squares fit of the data to Eq. (3). The error is plotted as a shaded region (where larger than the line thickness) corresponding to the standard error from three separate pump-probe scans. (c) Simulated ion-core alignment after multiphoton excitation in $N_{2}$ . The top plot corresponds to excitation to a single $Σ$ state in the Born-Oppenheimer regime, while the lower plot shows the expected ion-core alignment signal for excitation to the $4 f$ Rydberg manifold.
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Figure 4
Fourier analysis. The amplitude of the discrete Fourier transform of the time-dependent $β_{2}$ value is shown for both experiment and model. The shaded area around the experimental curve corresponds to the standard error from the three separate pump-probe scans. The phases of the three prominent frequency components are also plotted for experiment and model (diamond markers). The standard errors of the extracted phases are smaller than the marker dimensions.
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