Time-resolved spectroscopy is commonly used to study diverse phenomena in chemistry, biology, and physics. Pump–probe experiments and coherent two-dimensional (2D) spectroscopy have resolved site-to-site energy transfer, visualized electronic couplings, and much more. In both techniques, the lowest-order signal, in a perturbative expansion of the polarization, is of third order in the electric field, which we call a one-quantum (1Q) signal because in 2D spectroscopy it oscillates in the coherence time with the excitation frequency. There is also a two-quantum (2Q) signal that oscillates in the coherence time at twice the fundamental frequency and is fifth order in the electric field. We demonstrate that the appearance of the 2Q signal guarantees that the 1Q signal is contaminated by non-negligible fifth-order interactions. We derive an analytical connection between an nQ signal and (2n + 1)th-order contaminations of an rQ (with r < n) signal by studying Feynman diagrams of all contributions. We demonstrate that by performing partial integrations along the excitation axis in 2D spectra, we can obtain clean rQ signals free of higher-order artifacts. We exemplify the technique using optical 2D spectroscopy on squaraine oligomers, showing clean extraction of the third-order signal. We further demonstrate the analytical connection with higher-order pump–probe spectroscopy and compare both techniques experimentally. Our approach demonstrates the full power of higher-order pump–probe and 2D spectroscopy to investigate multi-particle interactions in coupled systems.
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High-order pump–probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers
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21 June 2023
Research Article|
June 16 2023
High-order pump–probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers
Special Collection:
Celebrating 25 Years of Two-dimensional Infrared (2D IR) Spectroscopy
Julian Lüttig
;
Julian Lüttig
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft)
1
Institut für Physikalische und Theoretische Chemie, Universität Würzburg
, Am Hubland, 97074 Würzburg, Germany
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Peter A. Rose
;
Peter A. Rose
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft)
2
Department of Physics, University of Ottawa
, Ottawa, Ontario K1N 6N5, Canada
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Pavel Malý
;
Pavel Malý
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft)
1
Institut für Physikalische und Theoretische Chemie, Universität Würzburg
, Am Hubland, 97074 Würzburg, Germany
3
Faculty of Mathematics and Physics, Charles University
, Prague, Czech Republic
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Arthur Turkin;
Arthur Turkin
(Resources)
4
Institut für Organische Chemie, Universität Würzburg
, Am Hubland, 97074 Würzburg, Germany
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Michael Bühler
;
Michael Bühler
(Formal analysis, Investigation)
1
Institut für Physikalische und Theoretische Chemie, Universität Würzburg
, Am Hubland, 97074 Würzburg, Germany
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Christoph Lambert
;
Christoph Lambert
(Funding acquisition, Supervision)
4
Institut für Organische Chemie, Universität Würzburg
, Am Hubland, 97074 Würzburg, Germany
5
Center for Nanosystems Chemistry (CNC), Universität Würzburg
, Theodor-Boveri-Weg, 97074 Würzburg, Germany
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Jacob J. Krich
;
Jacob J. Krich
a)
(Conceptualization, Funding acquisition, Project administration, Supervision, Writing – review & editing)
2
Department of Physics, University of Ottawa
, Ottawa, Ontario K1N 6N5, Canada
6
School of Electrical Engineering and Computer Science, University of Ottawa
, Ottawa, Ontario K1N 6N5, Canada
a)Authors to whom correspondence should be addressed: jkrich@uottawa.ca and brixner@uni-wuerzburg.de
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Tobias Brixner
Tobias Brixner
a)
(Conceptualization, Funding acquisition, Project administration, Supervision, Writing – review & editing)
1
Institut für Physikalische und Theoretische Chemie, Universität Würzburg
, Am Hubland, 97074 Würzburg, Germany
5
Center for Nanosystems Chemistry (CNC), Universität Würzburg
, Theodor-Boveri-Weg, 97074 Würzburg, Germany
a)Authors to whom correspondence should be addressed: jkrich@uottawa.ca and brixner@uni-wuerzburg.de
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a)Authors to whom correspondence should be addressed: jkrich@uottawa.ca and brixner@uni-wuerzburg.de
Note: This paper is part of the JCP Special Topic on Celebrating 25 Years of Two-dimensional Infrared (2D IR) Spectroscopy.
J. Chem. Phys. 158, 234201 (2023)
Article history
Received:
December 17 2022
Accepted:
March 06 2023
Citation
Julian Lüttig, Peter A. Rose, Pavel Malý, Arthur Turkin, Michael Bühler, Christoph Lambert, Jacob J. Krich, Tobias Brixner; High-order pump–probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers. J. Chem. Phys. 21 June 2023; 158 (23): 234201. https://doi.org/10.1063/5.0139090
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