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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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Stooß V, Cavaletto SM, Donsa S, Blättermann A, Birk P, Keitel CH, Březinová I, Burgdörfer J, Ott C, Pfeifer T. Real-Time Reconstruction of the Strong-Field-Driven Dipole Response. PHYSICAL REVIEW LETTERS 2018; 121:173005. [PMID: 30411962 DOI: 10.1103/physrevlett.121.173005] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Indexed: 06/08/2023]
Abstract
The reconstruction of the full temporal dipole response of a strongly driven time-dependent system from a single absorption spectrum is demonstrated, only requiring that a sufficiently short pulse is employed to initialize the coherent excitation of the system. We apply this finding to the time-domain observation of Rabi cycling between doubly excited atomic states in the few-femtosecond regime. This allows us to pinpoint the breakdown of few-level quantum dynamics at the critical laser intensity near 2 TW/cm^{2} in doubly excited helium. The present approach unlocks single-shot real-time-resolved signal reconstruction across timescales down to attoseconds for nonequilibrium states of matter. In contrast to conventional pump-probe schemes, there is no need for scanning time delays in order to access real-time information. The potential future applications of this technique range from testing fundamental quantum dynamics in strong fields to measuring and controlling ultrafast chemical and biological reaction processes when applied to traditional transient-absorption spectroscopy.
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Affiliation(s)
- V Stooß
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany, EU
| | - S M Cavaletto
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany, EU
| | - S Donsa
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria, EU
| | - A Blättermann
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany, EU
| | - P Birk
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany, EU
| | - C H Keitel
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany, EU
| | - I Březinová
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria, EU
| | - J Burgdörfer
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria, EU
| | - C Ott
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany, EU
| | - T Pfeifer
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany, EU
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Kaldun A, Blättermann A, Stooß V, Donsa S, Wei H, Pazourek R, Nagele S, Ott C, Lin CD, Burgdörfer J, Pfeifer T. Observing the ultrafast buildup of a Fano resonance in the time domain. Science 2017; 354:738-741. [PMID: 27846603 DOI: 10.1126/science.aah6972] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2016] [Accepted: 09/30/2016] [Indexed: 11/02/2022]
Abstract
Although the time-dependent buildup of asymmetric Fano line shapes in absorption spectra has been of great theoretical interest in the past decade, experimental verification of the predictions has been elusive. Here, we report the experimental observation of the emergence of a Fano resonance in the prototype system of helium by interrupting the autoionization process of a correlated two-electron excited state with a strong laser field. The tunable temporal gate between excitation and termination of the resonance allows us to follow the formation of a Fano line shape in time. The agreement with ab initio calculations validates our experimental time-gating technique for addressing an even broader range of topics, such as the emergence of electron correlation, the onset of electron-internuclear coupling, and quasi-particle formation.
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Affiliation(s)
- A Kaldun
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - A Blättermann
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - V Stooß
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - S Donsa
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria
| | - H Wei
- Department of Physics, Kansas State University, 230 Cardwell Hall, Manhattan, KS 66506, USA
| | - R Pazourek
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria
| | - S Nagele
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria
| | - C Ott
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | - C D Lin
- Department of Physics, Kansas State University, 230 Cardwell Hall, Manhattan, KS 66506, USA
| | - J Burgdörfer
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8, 1040 Vienna, Austria
| | - T Pfeifer
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany. .,Center for Quantum Dynamics, Universität Heidelberg, 69120 Heidelberg, Germany, EU
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Rao BJ, Gelin MF, Domcke W. Resonant femtosecond stimulated Raman spectroscopy with an intense actinic
pump pulse: Application to conical intersections. J Chem Phys 2017; 146:084105. [DOI: 10.1063/1.4976317] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- B. Jayachander Rao
- Department of Chemistry, Technische Universität München,
D-85747 Garching, Germany
| | - Maxim F. Gelin
- Department of Chemistry, Technische Universität München,
D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technische Universität München,
D-85747 Garching, Germany
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Shu CC, Yuan KJ, Dong D, Petersen IR, Bandrauk AD. Identifying Strong-Field Effects in Indirect Photofragmentation Reactions. J Phys Chem Lett 2017; 8:1-6. [PMID: 28052679 DOI: 10.1021/acs.jpclett.6b02613] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Exploring molecular breakup processes induced by light-matter interactions has both fundamental and practical implications. However, it remains a challenge to elucidate the underlying reaction mechanism in the strong field regime, where the potentials of the reactant are modified dramatically. Here we perform a theoretical analysis combined with a time-dependent wavepacket calculation to show how a strong ultrafast laser field affects the photofragment products. As an example, we examine the photochemical reaction of breaking up the molecule NaI into the neutral atoms Na and I, which due to inherent nonadiabatic couplings are indirectly formed in a stepwise fashion via the reaction intermediate NaI*. By analyzing the angular dependencies of fragment distributions, we are able to identify the reaction intermediate NaI* from the weak to the strong field-induced nonadiabatic regimes. Furthermore, the energy levels of NaI* can be extracted from the quantum interference patterns of the transient photofragment momentum distribution.
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Affiliation(s)
- Chuan-Cun Shu
- School of Engineering and Information Technology, University of New South Wales , Canberra, Australian Capital Territory 2600, Australia
| | - Kai-Jun Yuan
- School of Engineering and Information Technology, University of New South Wales , Canberra, Australian Capital Territory 2600, Australia
- Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke Sherbrooke, Québec J1K 2R1, Canada
| | - Daoyi Dong
- School of Engineering and Information Technology, University of New South Wales , Canberra, Australian Capital Territory 2600, Australia
- Department of Chemistry, Princeton University , Princeton, New Jersey 08544, United States
| | - Ian R Petersen
- School of Engineering and Information Technology, University of New South Wales , Canberra, Australian Capital Territory 2600, Australia
| | - Andre D Bandrauk
- Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke Sherbrooke, Québec J1K 2R1, Canada
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Liu Z, Wang Q, Ding J, Cavaletto SM, Pfeifer T, Hu B. Observation and quantification of the quantum dynamics of a strong-field excited multi-level system. Sci Rep 2017; 7:39993. [PMID: 28051167 PMCID: PMC5209658 DOI: 10.1038/srep39993] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Accepted: 11/30/2016] [Indexed: 11/29/2022] Open
Abstract
The quantum dynamics of a V-type three-level system, whose two resonances are first excited by a weak probe pulse and subsequently modified by another strong one, is studied. The quantum dynamics of the multi-level system is closely related to the absorption spectrum of the transmitted probe pulse and its modification manifests itself as a modulation of the absorption line shape. Applying the dipole-control model, the modulation induced by the second strong pulse to the system’s dynamics is quantified by eight intensity-dependent parameters, describing the self and inter-state contributions. The present study opens the route to control the quantum dynamics of multi-level systems and to quantify the quantum-control process.
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Affiliation(s)
- Zuoye Liu
- School of Nuclear Science and Technology, Lanzhou University, 730000, China
| | - Quanjun Wang
- School of Nuclear Science and Technology, Lanzhou University, 730000, China
| | - Jingjie Ding
- School of Nuclear Science and Technology, Lanzhou University, 730000, China
| | | | - Thomas Pfeifer
- Max-Planck-Institut für Kernphysik, Heidelberg, 69117, Germany
| | - Bitao Hu
- School of Nuclear Science and Technology, Lanzhou University, 730000, China
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Shen H, Zhang Y, Yan TM, Wang Z, Jiang Y. Moderately strong pump-induced ultrafast dynamics in solution. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.07.013] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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