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Perrett S, Chatrchyan V, Buckup T, van Thor JJ. Application of density matrix Wigner transforms for ultrafast macromolecular and chemical x-ray crystallography. J Chem Phys 2024; 160:100901. [PMID: 38456527 DOI: 10.1063/5.0188888] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Accepted: 02/12/2024] [Indexed: 03/09/2024] Open
Abstract
Time-Resolved Serial Femtosecond Crystallography (TR-SFX) conducted at X-ray Free Electron Lasers (XFELs) has become a powerful tool for capturing macromolecular structural movies of light-initiated processes. As the capabilities of XFELs advance, we anticipate that a new range of coherent control and structural Raman measurements will become achievable. Shorter optical and x-ray pulse durations and increasingly more exotic pulse regimes are becoming available at free electron lasers. Moreover, with high repetition enabled by the superconducting technology of European XFEL (EuXFEL) and Linac Coherent Light Source (LCLS-II) , it will be possible to improve the signal-to-noise ratio of the light-induced differences, allowing for the observation of vibronic motion on the sub-Angstrom level. To predict and assign this coherent motion, which is measurable with a structural technique, new theoretical approaches must be developed. In this paper, we present a theoretical density matrix approach to model the various population and coherent dynamics of a system, which considers molecular system parameters and excitation conditions. We emphasize the use of the Wigner transform of the time-dependent density matrix, which provides a phase space representation that can be directly compared to the experimental positional displacements measured in a TR-SFX experiment. Here, we extend the results from simple models to include more realistic schemes that include large relaxation terms. We explore a variety of pulse schemes using multiple model systems using realistic parameters. An open-source software package is provided to perform the density matrix simulation and Wigner transformations. The open-source software allows us to define any arbitrary level schemes as well as any arbitrary electric field in the interaction Hamiltonian.
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Affiliation(s)
- Samuel Perrett
- Department of Life Sciences, Faculty of Natural Sciences, Imperial College London, London, United Kingdom
| | - Viktoria Chatrchyan
- Physikalisch Chemisches Institut, Ruprecht-Karls Universität, D-69120 Heidelberg, Germany
| | - Tiago Buckup
- Physikalisch Chemisches Institut, Ruprecht-Karls Universität, D-69120 Heidelberg, Germany
| | - Jasper J van Thor
- Department of Life Sciences, Faculty of Natural Sciences, Imperial College London, London, United Kingdom
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Mewes L, Ingle RA, Al Haddad A, Chergui M. Broadband visible two-dimensional spectroscopy of molecular dyes. J Chem Phys 2021; 155:034201. [PMID: 34293898 DOI: 10.1063/5.0053554] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Two-dimensional Fourier transform spectroscopy is a promising technique to study ultrafast molecular dynamics. Similar to transient absorption spectroscopy, a more complete picture of the dynamics requires broadband laser pulses to observe transient changes over a large enough bandwidth, exceeding the inhomogeneous width of electronic transitions, as well as the separation between the electronic or vibronic transitions of interest. Here, we present visible broadband 2D spectra of a series of dye molecules and report vibrational coherences with frequencies up to ∼1400 cm-1 that were obtained after improvements to our existing two-dimensional Fourier transform setup [Al Haddad et al., Opt. Lett. 40, 312-315 (2015)]. The experiment uses white light from a hollow core fiber, allowing us to acquire 2D spectra with a bandwidth of 200 nm, in a range between 500 and 800 nm, and with a temporal resolution of 10-15 fs. 2D spectra of nile blue, rhodamine 800, terylene diimide, and pinacyanol iodide show vibronic spectral features with at least one vibrational mode and reveal information about structural motion via coherent oscillations of the 2D signals during the population time. For the case of pinacyanol iodide, these observations are complemented by its Raman spectrum, as well as the calculated Raman activity at the ground- and excited-state geometry.
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Affiliation(s)
- Lars Mewes
- Laboratoire de Spectroscopie Ultrarapide and LACUS, Ecole Polytechnique Fédérale de Lausanne, ISIC, FSB-BSP, CH-1015 Lausanne, Switzerland
| | - Rebecca A Ingle
- Laboratoire de Spectroscopie Ultrarapide and LACUS, Ecole Polytechnique Fédérale de Lausanne, ISIC, FSB-BSP, CH-1015 Lausanne, Switzerland
| | - Andre Al Haddad
- Laboratoire de Spectroscopie Ultrarapide and LACUS, Ecole Polytechnique Fédérale de Lausanne, ISIC, FSB-BSP, CH-1015 Lausanne, Switzerland
| | - Majed Chergui
- Laboratoire de Spectroscopie Ultrarapide and LACUS, Ecole Polytechnique Fédérale de Lausanne, ISIC, FSB-BSP, CH-1015 Lausanne, Switzerland
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Brühl E, Buckup T, Motzkus M. Experimental and numerical investigation of a phase-only control mechanism in the linear intensity regime. J Chem Phys 2018; 148:214310. [DOI: 10.1063/1.5029805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Affiliation(s)
- Elisabeth Brühl
- Physikalisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Tiago Buckup
- Physikalisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Marcus Motzkus
- Physikalisch-Chemisches Institut, Ruprecht-Karls-Universität Heidelberg, D-69120 Heidelberg, Germany
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Lavigne C, Brumer P. Interfering resonance as an underlying mechanism in the adaptive feedback control of radiationless transitions: Retinal isomerization. J Chem Phys 2017; 147:114107. [PMID: 28938828 DOI: 10.1063/1.5003389] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Control of molecular processes via adaptive feedback often yields highly structured laser pulses that have eluded physical explanation. By contrast, coherent control approaches propose physically transparent mechanisms but are not readily visible in experimental results. Here, an analysis of a condensed phase adaptive feedback control experiment on retinal isomerization shows that it manifests a quantum interference based coherent control mechanism: control via interfering resonances. The result promises deep insight into the physical basis for the adaptive feedback control of a broad class of bound state processes.
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Affiliation(s)
- Cyrille Lavigne
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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Brühl E, Buckup T, Motzkus M. Minimization of 1/f n phase noise in liquid crystal masks for reliable femtosecond pulse shaping. OPTICS EXPRESS 2017; 25:23376-23386. [PMID: 29041638 DOI: 10.1364/oe.25.023376] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Accepted: 08/15/2017] [Indexed: 06/07/2023]
Abstract
Liquid-crystal spatial light modulators (LCM) are a common tool to tailor femtosecond laser pulses. The phase stability of 1 kHz, sub-20 fs visible shaped and unshaped pulses are investigated. Our results show that the spectral phase after the LCM varies from pulse to pulse leading to strong deviations from the predicted pulse shapes. This phase instability is generated only by LCM and is strongly temperature dependent. Based on the experimental data, a numerical model for the phase was developed that takes the temperature-dependent phase instability as well as pixel coupling across the LCM into account. Phase stability after the LCM can be improved by an order of magnitude by combining the control the temperature of the LCM and by using rapid-scan averaging. Reliable pulse shapes on a pulse-to-pulse basis are crucial, especially in coherent control experiments, where small differences between pulse shape are important.
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An organic jelly made fractal logic gate with an infinite truth table. Sci Rep 2015; 5:11265. [PMID: 26086417 PMCID: PMC4471884 DOI: 10.1038/srep11265] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2015] [Accepted: 04/15/2015] [Indexed: 11/18/2022] Open
Abstract
Widely varying logic gates invented over a century are all finite. As data deluge problem looms large on the information processing and communication industry, the thrust to explore radical concepts is increasing rapidly. Here, we design and synthesis a molecule, wherein, the input energy transmits in a cycle inside the molecular system, just like an oscillator, then, we use the molecule to make a jelly that acts as chain of oscillators with a fractal like resonance band. Hence, with the increasing detection resolution, in the vacant space between two energy levels of a given resonance band, a new band appears, due to fractal nature, generation of newer energy levels never stops. This is natural property of a linear chain oscillator. As we correlate each energy level of the resonance band of organic jelly, as a function of pH and density of the jelly, we realize a logic gate, whose truth table is finite, but if we zoom any small part, a new truth table appears. In principle, zooming of truth table would continue forever. Thus, we invent a new class of infinite logic gate for the first time.
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7
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Buckup T, Motzkus M. Multidimensional Time-Resolved Spectroscopy of Vibrational Coherence in Biopolyenes. Annu Rev Phys Chem 2014; 65:39-57. [DOI: 10.1146/annurev-physchem-040513-103619] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Tiago Buckup
- Physikalisch Chemisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany; ,
| | - Marcus Motzkus
- Physikalisch Chemisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany; ,
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Conyard J, Addison K, Heisler IA, Cnossen A, Browne WR, Feringa BL, Meech SR. Ultrafast dynamics in the power stroke of a molecular rotary motor. Nat Chem 2012; 4:547-51. [PMID: 22717439 DOI: 10.1038/nchem.1343] [Citation(s) in RCA: 141] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2012] [Accepted: 03/26/2012] [Indexed: 11/09/2022]
Abstract
Light-driven molecular motors convert light into mechanical energy through excited-state reactions. Unidirectional rotary molecular motors based on chiral overcrowded alkenes operate through consecutive photochemical and thermal steps. The thermal (helix inverting) step has been optimized successfully through variations in molecular structure, but much less is known about the photochemical step, which provides power to the motor. Ultimately, controlling the efficiency of molecular motors requires a detailed picture of the molecular dynamics on the excited-state potential energy surface. Here, we characterize the primary events that follow photon absorption by a unidirectional molecular motor using ultrafast fluorescence up-conversion measurements with sub 50 fs time resolution. We observe an extraordinarily fast initial relaxation out of the Franck-Condon region that suggests a barrierless reaction coordinate. This fast molecular motion is shown to be accompanied by the excitation of coherent excited-state structural motion. The implications of these observations for manipulating motor efficiency are discussed.
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Affiliation(s)
- Jamie Conyard
- School of Chemistry, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, UK
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Prokhorenko VI, Halpin A, Johnson PJM, Miller RJD, Brown LS. Coherent control of the isomerization of retinal in bacteriorhodopsin in the high intensity regime. J Chem Phys 2011; 134:085105. [DOI: 10.1063/1.3554743] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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10
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Buckup T, Hauer J, Voll J, Vivie-Riedle R, Motzkus M. A General control mechanism of energy flow in the excited state of polyenic biochromophores. Faraday Discuss 2011; 153:213-25; discussion 293-319. [DOI: 10.1039/c1fd00037c] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Ibrahim H, Héjjas M, Fushitani M, Schwentner N. Phase Sensitive Control of Vibronic Guest−Host Interaction: Br2 in Ar Matrix. J Phys Chem A 2009; 113:7439-50. [DOI: 10.1021/jp900287m] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Heide Ibrahim
- Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany, and Institute for Molecular Science, Myodaiji, Okazaki, 444-8585, Japan
| | - Mónika Héjjas
- Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany, and Institute for Molecular Science, Myodaiji, Okazaki, 444-8585, Japan
| | - Mizuho Fushitani
- Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany, and Institute for Molecular Science, Myodaiji, Okazaki, 444-8585, Japan
| | - Nikolaus Schwentner
- Institut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany, and Institute for Molecular Science, Myodaiji, Okazaki, 444-8585, Japan
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Seidl M, Etinski M, Uiberacker C, Jakubetz W. Pulse-train control of branching processes: elimination of background and intruder state population. J Chem Phys 2008; 129:234305. [PMID: 19102530 DOI: 10.1063/1.3041380] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
The authors introduce and describe pulse train control (PTC) of population branching in strongly coupled processes as a novel control tool for the separation of competing multiphoton processes. Control strategies are presented based on the different responses of processes with different photonicities and/or different frequency detunings to the pulse-to-pulse time delay and the pulse-to-pulse phase shift in pulse trains. The control efficiency is further enhanced by the property of pulse trains that complete population transfer can be obtained over an extended frequency range that replaces the resonance frequency of simple pulses. The possibility to freely tune the frequency assists the separation of the competing processes and reduces the number of subpulses required for full control. As a sample application, PTC of leaking multiphoton resonances is demonstrated by numerical simulations. In model systems exhibiting sizable background (intruder) state population if excited with single pulses, PTC leading to complete accumulation of population in the target state and elimination of background population is readily achieved. The analysis of the results reveals different mechanisms of control and provides clues on the mechanisms of the leaking process itself. In an alternative setup, pulse trains can be used as a phase-sensitive tool for level switching. By changing only the pulse-to-pulse phase shift of a train with otherwise unchanged parameters, population can be transferred to any of two different target states in a near-quantitative manner.
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Affiliation(s)
- Markus Seidl
- Department of Theoretical Chemistry, University of Vienna, 1090 Wien, Austria
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Serrat C, Biegert J. Energy efficient method for two-photon population transfer with near-resonant chirped pulses. OPTICS EXPRESS 2008; 16:19667-19673. [PMID: 19030052 DOI: 10.1364/oe.16.019667] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We investigate a method for complete population inversion in three level systems through pi-pulse bichromatic two-photon coherent excitation and study the dependence on the chirp of the laser pulses. We observe that the population inversion does not monotonously decrease with increasing the time-bandwidth product, and that the excitation depends on the sign of the chirp of the individual pulses. Our results evidence a strategy for coherent population transfer which is energetically superior to adiabatic methods and opens the door for real-world applications, since it alleviates the need for challenging generation of transform-limited pulses at arbitrary wavelengths.
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Affiliation(s)
- Carles Serrat
- DTDI - Universitat de Vic, Carrer de la Laura 13, 08500 Vic, Barcelona, Spain
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14
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Hauer J, Buckup T, Motzkus M. Quantum control spectroscopy of vibrational modes: Comparison of control scenarios for ground and excited states in β-carotene. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.03.021] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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15
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Controlling the efficiency of an artificial light-harvesting complex. Proc Natl Acad Sci U S A 2008; 105:7641-6. [PMID: 18509052 DOI: 10.1073/pnas.0711927105] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Adaptive femtosecond pulse shaping in an evolutionary learning loop is applied to a bioinspired dyad molecule that closely mimics the early-time photophysics of the light-harvesting complex 2 (LH2) photosynthetic antenna complex. Control over the branching ratio between the two competing pathways for energy flow, internal conversion (IC) and energy transfer (ET), is realized. We show that by pulse shaping it is possible to increase independently the relative yield of both channels, ET and IC. The optimization results are analyzed by using Fourier analysis, which gives direct insight to the mechanism featuring quantum interference of a low-frequency mode. The results from the closed-loop experiments are repeatable and robust and demonstrate the power of coherent control experiments as a spectroscopic tool (i.e., quantum-control spectroscopy) capable of revealing functionally relevant molecular properties that are hidden from conventional techniques.
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Konradi J, Gaal A, Scaria A, Namboodiri V, Materny A. Influence of electronic resonances on mode selective excitation with tailored laser pulses. J Phys Chem A 2008; 112:1380-91. [PMID: 18225867 DOI: 10.1021/jp0745079] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) gives access to ultrafast molecular dynamics. However, the gain of the temporal resolution entails a poor spectral resolution due to the inherent spectral width of the femtosecond excitation pulses. Modifications of the phase shape of one of the exciting pulses results in dramatic changes of the mode distribution reflected in coherent anti-Stokes Raman spectra. A feedback-controlled optimization of specific modes making use of phase and/or amplitude modulation of the pump laser pulse is applied to selectively influence the anti-Stokes signal spectrum. The optimization experiments are performed under electronically nonresonant and resonant conditions. The results are compared and the role of electronic resonances is analyzed. It can be clearly demonstrated that these resonances are of importance for a selective excitation by means of phase and amplitude modulation. The mode selective excitation under nonresonant conditions is determined mainly by the variation of the spectral phase of the laser pulse. Here, the modulation of the spectral amplitudes only has little influence on the mode ratios. In contrast to this, the phase as well as amplitude modulation contributes considerably to the control process under resonant conditions. A careful analysis of the experimental results reveals information about the mechanisms of the mode control, which partially involve molecular dynamics in the electronic states.
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Affiliation(s)
- J Konradi
- School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, D-28759 Bremen, Germany
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18
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Analysis of vibrational coherences in homodyne and two-dimensional heterodyne photon-echo spectra of Nile Blue. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2007.07.010] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Prokhorenko VI, Nagy AM, Waschuk SA, Brown LS, Birge RR, Dwayne Miller RJ. Response to Comment on "Coherent Control of Retinal Isomerization in Bacteriorhodopsin". Science 2007. [DOI: 10.1126/science.1137032] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Valentyn I. Prokhorenko
- Institute for Optical Sciences, Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada
- Department of Chemistry, University of Connecticut, Storrs, CT, USA
| | - Andrea M. Nagy
- Institute for Optical Sciences, Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada
- Department of Chemistry, University of Connecticut, Storrs, CT, USA
| | - Stephen A. Waschuk
- Institute for Optical Sciences, Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada
- Department of Chemistry, University of Connecticut, Storrs, CT, USA
| | - Leonid S. Brown
- Institute for Optical Sciences, Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada
- Department of Chemistry, University of Connecticut, Storrs, CT, USA
| | - Robert R. Birge
- Institute for Optical Sciences, Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada
- Department of Chemistry, University of Connecticut, Storrs, CT, USA
| | - R. J. Dwayne Miller
- Institute for Optical Sciences, Departments of Chemistry and Physics, University of Toronto, 80 St. George Street, Toronto, Ontario, M5S 3H6, Canada
- Department of Physics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada
- Department of Chemistry, University of Connecticut, Storrs, CT, USA
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Laarmann T, Shchatsinin I, Stalmashonak A, Boyle M, Zhavoronkov N, Handt J, Schmidt R, Schulz CP, Hertel IV. Control of giant breathing motion in c60 with temporally shaped laser pulses. PHYSICAL REVIEW LETTERS 2007; 98:058302. [PMID: 17358909 DOI: 10.1103/physrevlett.98.058302] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2006] [Indexed: 05/14/2023]
Abstract
Femtosecond laser pulses tailored with closed-loop, optimal control feedback were used to excite oscillations in C60 with large amplitude by coherent heating of nuclear motion. A characteristic pulse sequence results in significant enhancement of C2 evaporation, a typical energy loss channel of vibrationally hot C60. The separation between subsequent pulses in combination with complementary two-color pump-probe data and time-dependent density functional theory calculations give direct information on the multielectron excitation via the t(1g) resonance followed by efficient coupling to the radial symmetric a(g)(1) breathing mode.
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Affiliation(s)
- T Laarmann
- Max Born Institute, Max-Born-Strasse 2a, D-12489 Berlin, Germany.
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