Excited-state vibronic wave-packet dynamics in ${\mathrm{H}}_{2}$ probed by XUV transient four-wave mixing

Excited-state vibronic wave-packet dynamics in $H_{2}$ probed by XUV transient four-wave mixing

Wei Cao, Erika R. Warrick, Ashley Fidler, Stephen R. Leone, and Daniel M. Neumark

Phys. Rev. A 97, 023401 – Published 1 February 2018

Abstract

The complex behavior of a molecular wave packet initiated by an extreme ultraviolet (XUV) pulse is investigated with noncollinear wave mixing spectroscopy. A broadband XUV pulse spanning 12–16 eV launches a wave packet in $H_{2}$ comprising a coherent superposition of multiple electronic and vibrational levels. The molecular wave packet evolves freely until a delayed few-cycle optical laser pulse arrives to induce nonlinear signals in the XUV via four-wave mixing (FWM). The angularly resolved FWM signals encode rich energy exchange processes between the optical laser field and the XUV-excited molecule. The noncollinear geometry enables spatial separation of ladder and V- or Λ-type transitions induced by the optical field. Ladder transitions, in which the energy exchange with the optical field is around 3 eV, appear off axis from the incident XUV beam. Each vibrationally revolved FWM line probes a different part of the wave packet in energy, serving as a promising tool for energetic tomography of molecular wave packets. V- or Λ-type transitions, in which the energy exchange is well under 1 eV, result in on-axis nonlinear signals. The first-order versus third-order interference of the on-axis signal serves as a mapping tool of the energy flow pathways. Intra- and interelectronic potential energy curve transitions are decisively identified. The current study opens possibilities for accessing complete dynamic information in XUV-excited complex systems.

Received 7 December 2017

DOI:https://doi.org/10.1103/PhysRevA.97.023401

Physics Subject Headings (PhySH)

Third order nonlinear optical processes Ultrafast optics Ultrafast phenomena

Atomic, Molecular & OpticalNonlinear Dynamics

Authors & Affiliations

Wei Cao¹, Erika R. Warrick^2,3, Ashley Fidler^2,3, Stephen R. Leone^2,3,4, and Daniel M. Neumark^2,3

¹School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
²Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Department of Chemistry, University of California, Berkeley, California 94720, USA
⁴Department of Physics, University of California, Berkeley, California 94720, USA

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Vol. 97, Iss. 2 — February 2018

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Figure 1
Schematic of noncollinear transient wave mixing spectroscopy in $H_{2}$ . The high-order-harmonics pulse (violet vertical arrow) promotes the molecule into a coherent superposition of multiple vibronic states in the $n p$ manifold. A delayed NIR pulse intersects with the HHG pulse at a crossing angle and drives transitions that are responsible for different energy flow pathways in the excited molecules. The laser-matter interaction induces a polarization dipole (purple arched arrow) that is detectable by a charge-coupled device (CCD) camera (inset).The energy flow pathway between the NIR pulse and molecules determines the direction of the transmitted XUV signal to conserve the momentum.
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Figure 2
A 2D image of the differential XUV spectrum versus angle after the nonlinear wave mixing in $H_{2}$ gas. The NIR pulse and the high-harmonic pulse overlap in time at a noncollinear angle. The differential spectrum is obtained by subtracting the spectrum with the negative time delay spectrum (NIR arrives first). The zero angle indicates the propagation direction of harmonics. The color scale indicates emission or absorption in arbitrary units. Phase-matching diagrams for ladder-type and Λ- or V-type transitions are also shown.
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Figure 3
Angle-resolved and time-resolved off-axis FWM signal for $v = 1$ (a) and $v = 3$ (c) on the $B$ electronic state; the integration window for each vibrationally resolved FWM signal is about 0.05 eV. The delay step size is 1 fs. (b,d) are the Fourier transformations along the delay axis for $v = 1$ and $v = 3$ , respectively.
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Figure 4
Absorption spectrum (optical density) of the on-axis signal as a function of time delay; positive delay means NIR arrives later.
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Figure 5
Fourier analysis along the delay axis in the absorption spectrogram of Fig. 4, separated into low-energy (a) and higher-energy transitions (c,e,f). The coherences in panel (a) are from energy exchange between vibrational transitions of the $B$ state. The energy exchange pathways in panels (c,e,f) involve the higher-lying Rydberg states and are more complex. They can involve only vibrational (c) or electronic transitions (e), or combinations of the two (f). The cyan diamonds (white stars) are the predicted values corresponding to the positive (negative) energy flow from the molecule to the laser field, respectively. The relevant PECs are shown in (b,d). The vibrational energy levels are adopted from Refs. [28, 29, 34].
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Physical Review A

covering atomic, molecular, and optical physics and quantum information

Excited-state vibronic wave-packet dynamics in $H_{2}$ probed by XUV transient four-wave mixing

Wei Cao, Erika R. Warrick, Ashley Fidler, Stephen R. Leone, and Daniel M. Neumark

Phys. Rev. A 97, 023401 – Published 1 February 2018

Abstract

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Physical Review A

covering atomic, molecular, and optical physics and quantum information

Excited-state vibronic wave-packet dynamics in H2 probed by XUV transient four-wave mixing

Wei Cao, Erika R. Warrick, Ashley Fidler, Stephen R. Leone, and Daniel M. Neumark

Phys. Rev. A 97, 023401 – Published 1 February 2018

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Excited-state vibronic wave-packet dynamics in $H_{2}$ probed by XUV transient four-wave mixing