Post-Born-Oppenheimer Dynamics Using Isolated Attosecond Pulses

MURI #1: Research Highlights

  1. PASSAGE Method for Isolated Attosecond Pulses
  2. Attosecond Charge Migration
  3. Vibrational wave package probed by attosecond transient absorption
  4. Hybrid Attosecond Pulse Generation
  5. Attosecond Transient Absorption
  6. Attosecond transient absorption of Xe in the presence of strong driving fields
  7. Ab initio calculation of coherence created by attosecond ionization of polyatomic molecules
1. PASSAGE Method for Isolated Attosecond Pulses
Spectra of attosecond pulses Fig. 1. Spectra of attosecond pulses with and without a partial polarization gate for neon (a) and argon (b) as the high harmonic driving gases, with corresponding streak traces for PASSAGE-produced pulses.

Leone and Neumark at Berkeley have a multipronged program using attosecond transient absorption spectroscopy (ATAS) to probe valence reaction dynamics in atoms, molecules, and solids on timescales approaching the electronic domain. Recently, Neumark and Leone took the lead in developing a technique called Polarization ASSisted Amplitude GatE (PASSAGE), which was introduced to achieve single attosecond pulses in the range of 50-70 eV. PASSAGE uses a partial polarization gate in the amplitude gating regime to produce robust, isolated attosecond pulses. They demonstrated that PASSAGE can be used to isolate single attosecond pulses tunably across the broad range of 40-120 eV with pulse energies attainable between 0.1 – 1 nJ.

These high-flux, tunable single attosecond pulses will enable the study of systems ranging from halogenated hydrocarbons and organometallic compounds to semiconductor nanostructures. In addition to the energy range offered by PASSAGE, it was also demonstrated that a soft x-ray single attosecond pulse at 160 eV could be produced using a conventional, few-cycle Ti:Sapphire laser system.

The soft x-ray pulse was isolated by driving high harmonic generation in He with a 4 fs pulse and isolating the highest energy, half-cycle cut-off with a Sn metallic filter. These soft x-ray pulses can be used to probe electron dynamics at the sulfur L-edge, enabling the study of attosecond dynamics in biologically relevant compounds. The PASSAGE work involved a MURI funded co-worker and a NSF funded co-worker and the findings are published in Optica 3, 707 (2016).

2. Attosecond Charge Migration

After ionization of a valence electron, the created hole can migrate throughout the system on an ultrashort time scale, driven solely by the electron correlation. This phenomenon is known as charge migration and its measurement and understanding has become a central topic in attosecond science and naturally in the present MURI program.

Kuleff and Cederbaum recently posed the hitherto unconsidered question whether ionizing a core electron will also lead to charge migration. To explore this regime we developed a new methodology allowing to trace in time and space the electron dynamics triggered by core ionization of molecules. With the help of this technique we found that the created core hole stays put, but in response to it an interesting electron dynamics takes place, which can lead to an intense charge migration in the valence shell. This migration, mainly driven by the electron relaxation effects, is typically faster than that after ionization of a valence electron and transpires on a shorter time scale than the natural decay of the core hole by the Auger process. An example of this process is shown in the figure, where snapshots along the first half period of the charge oscillations triggered by the N1s ionization of the molecule nitrozobenzene are shown. For details, see A. I. Kuleff, N. V. Kryzhevoi, M. Pernpointner, and L. S. Cederbaum, Phys. Rev. Lett. 117, 093002 (2016).

The combination of extremely short duration and wavelength of the laser pulses needed to trace the evolution of this process makes the subject very challenging to attosecond science. The present MURI, however, offers the unique opportunity to combine efforts and achieve an experimental verification of this fascinating phenomenon.

Snapshots of the evolution of the charge density
Fig. 2. Snapshots of the evolution of the charge density following nitrogen K-shell ionization of the molecule nitrozobenzene. The positive hole density (electron deficiency) is shown in green and the negative electron density (electron surplus) is depicted in orange. In only about 700 asec the electron density migrates from the benzene ring to the nitroso group. After that time, the charge migrates back. This pure electron dynamics is oscillatory with a period of about 1.4 fs.
3. Vibrational wave package probed by attosecond transient absorption
Reconstruction of the nuclear wave packet

In collaboration with F. Martín’s group, Chang’s team demonstrated attosecond transient absorption spectroscopy (ATAS) as a viable probe of the electronic and nuclear dynamics initiated in excited states of a neutral molecule by a broadband vacuum ultraviolet pulse. Owing to the high spectral and temporal resolution of ATAS, they were able to reconstruct the time evolution of a vibrational wave packet within the excited B’ 1Σu+ electronic state of H2 via the laser-perturbed transient absorption spectrum.

Fig. 3. Reconstruction of the nuclear wave packet in an excited electronic state. Top: Nuclear wave packet in the B’ state generated by the VUV pulse. Middle: Reconstruction of this nuclear wave packet from the ab initio ATAS using the model described in the text. Bottom: Reconstruction of the same nuclear wave packet from the measured ATAS. Y. Cheng et al., PHYSICAL REVIEW A 94, 023403 (2016).

4. Hybrid Attosecond Pulse Generation

Dielectrics, with their very high bandgap, can withstand intensities (with no-apparent long-term damage) that are on the scale of the intensities responsible for attosecond pulse generation in low ionization potential rare gases. In the case of crystalline quartz, we can use intensities up to ~ 4 x 1014 W/cm2 without multi-shot damage. If the material thickness is small, material dispersion can be minimal and this is especially true in the 1.8 micron spectral region. Low dispersion and high intensity opens the opportunity to exploit the high conventional nonlinearity of dielectrics with no dispersion compensation and therefore, with no intervening dispersive elements required to recompress the nonlinearly modified infrared pulses.

Concentrating on 90-micron thick crystalline quartz (a), we transform a few cycle 1.8 micron pulse (b) into a sub-cycle electric field transient (d, e) in a process that we can control with the carrier-envelop-phase of the incident beam. This control arises from the interplay between the conventional nonlinearities such as self-phase-modulation, self-focussing, and second harmonic generation with the carrier-envelop-phase.

Hybrid Attosecond Pulse Generation Fig 4. When an argon gas jet is placed approximately one confocal parameter away and with no optical elements between, we are able to produce especially clean, isolated attosecond pulses that can be tuned with the carrier envelop phase as seen in the spectrum attached to the figure. Clear in the figure is the modulation of the output for all frequencies above the Cooper minimum up to the cut-off at 120 eV.

Hybrid attosecond pulse generation can be used at all intensities relevant to the rare gases, including helium, to efficiently produce robust attosecond pulses.
5. Attosecond Transient Absorption

Sandhu group at the University of Arizona has made progress in two research directions. First concerns mechanisms of Attosecond Transient Absorption (ATA) in dense atomic gases. We explored the interplay between resonant attosecond pulse propagation and laser induced phase in an optically thick helium sample. The experimental lineshapes were modeled by Mette Gaarde and coworkers. As gas density is increased we observed the appearance of new features in XUV transient absorption spectra. By systematic variation of near-infrared (NIR) laser parameters we were able to quantify the collective interactions and establish the criterion for consideration of such effects. We have published these findings in Phys. Rev. A 93, 033405 (2016).

The second research topic pursued in Sandhu group concerns the study of ATA lineshapes of autoionizing molecular states. We were able to track the evolution of such states in electronically and vibrationally resolved fashion. In the case of superexcited oxygen, we demonstrated that the sign of the transient absorption signal is determined by the Fano parameter of the resonance, or equivalently by the underlying electronic symmetry of the excited state. Full MCTDH calculations by McCurdy group show excellent agreement with our experimental observations, as shown in the figure. Invoking a few-level model for the laser modification of autoionizing states, we found that the laser induced attenuation (LIA) model fails to capture the basic features of transient lineshapes, whereas the laser induced phase (LIP) shift model matches our observations (see figure). A joint experimental-theory paper discussing these findings was submitted for publication.

Hybrid Attosecond Pulse Generation Fig 5. Clockwise from the top left: Experimental transient absorption spectrogram for autoionizing oxygen states; MCTDHF calculation of the same; Experiment-theory lineshape comparison for pair of resonances with opposite signs of Fano parameters; Comparison of laser induced attenuation and laser induced phase shift models.
6. Attosecond transient absorption of Xe in the presence of strong driving fields
Transient absorption spectrum

We have performed attosecond transient absorption spectroscopy on xenon 4d−16p states, and experimentally investigate the absorption dynamics in strong driving fields beyond the ionization threshold.i The attosecond temporal resolution and the wide spectral coverage of our apparatus allow characterization of the entire absorption structure and the sub-cycle delay dependence in the strongly-driven system. When driven at a field intensity of 1.6 × 1014 W/cm2, the system shows both the neutral and ionic state features. The neutral absorption peak originally at 65.1 eV is broadened down to 58 eV accompanied by half-cycle delay-dependent oscillations. Three-state model numerical simulations are performed, and the broad feature is identified as originating from the strong driving between 4d−16p and 4d−16s states. The mechanism behind the broad induced absorption and its sub-cycle delay dependence can be intuitively explained within the Floquet formalism. Avoided crossings between Floquet states are found to play a significant role in the absorption dynamics of strongly-driven systems.

i Y. Kobayashi, H. TImmers, M. Sabbar, S. R. Leone, and D. M. Neumark, Phys. Rev. A (submitted)

Fig. 6. (a) Experimental transient absorption spectrum as a function of delay τ. The peak intensity of the NIR pulse is 1.6×1014 W/cm2, and the delay step ∆τ is 200 as. Assignments of the signals are given in the right side of the spectrum. (b) Analysis of the averaged center of the peak in 62 eV to 65 eV overlaid on the absorption spectrum. (c) Transient absorption spectrum simulated within a three-state model.

7. Ab initio calculation of coherence created by attosecond ionization of polyatomic molecules

Using the Complex Kohn Variational approach developed in in the McCurdy group we calculated the degree of coherence left in the glycine molecular ion after attosecond photoionization. A surprisingly strong dependence was found on the direction of polarization in the molecular frame in this and other molecules suggesting a new class of attosecond pump/probe experiments to probe correlated attosecond ionization dynamics. To generate a coherent combination of ion states the pulse must not only eject electrons with the same energy, but in the same direction (same momentum) when producing different ionic states. The broad bandwidth of attosecond pulses can guarantee that the energies of ejected electrons overlap as shown in Fig. 7 (a), but the details of the photoionization amplitudes and electron correlation during the ejection process determine the distribution of final momenta in each ionization channel, and therefore determine the degree of coherence that can be observed in the final ion. Fig 7 (b) shows how the amount of coherence produced in the ion depends on the direction of polarization in the molecular frame, vanishing completely for some orientations and maximizing for other orientations in a measurable way.

Energetics of attosecond photoionization Coherence parameter calculated for the glycine molecular ion
Fig. 7. (a) Energetics of attosecond photoionization to produce a coherent superposition of two states of a molecular ion. (b) The coherence parameter calculated for the glycine molecular ion from the reduced density matrix of the ion plotted as a function of the direction of polarization ε in the body frame for a 500 attosecond pulse centered at 20.4 eV

In glycine the coherence between the two lowest energy states, 12A' and 22A' of the NH2CH2COOH+ ion created by removing electrons from the two highest occupied molecular orbitals of the neutral molecule depends sensitively on the inclusion of electron correlation (channel coupling) in the calculation of photoionization amplitudes and will lead to an observable 3 femtosecond beating in pump/probe experiments.

Contact Webmaster © University of Central Florida