Response of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:mn>60</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>to ultrashort laser pulses

Torralva, Ben; Niehaus, Thomas A.; Elstner, Marcus; Suhai, Sándor; Frauenheim, Thomas; Allen, Roland E.

doi:10.1103/physrevb.64.153105

Cited by 79 publications

(76 citation statements)

References 17 publications

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“…[5][6][7][8][9][10] SAE is assumed to be predominant for very short pulses as it reflects the simple fact that the fundamental interaction of photons with a many-electron system is given by an independent sum of one-electron dipole interactions, while NMED is mediated by electron correlations which require, in addition to a sufficient number of electrons, also an electron-photon interaction time at least comparable to the electron-electron interaction time which is considered to be approximately 50-100 fs. Of similar interest is the role of intermediate electronically excited states in the absorption process [11][12][13] and efficient coupling of electronic to nuclear motion.…”

Section: Introductionmentioning

confidence: 99%

Ultrafast energy redistribution in C60 fullerenes: A real time study by two-color femtosecond spectroscopy

Shchatsinin

Laarmann

Zhavoronkov

et al. 2008

The Journal of Chemical Physics

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Strong-field excitation and energy redistribution dynamics of C 60 fullerenes are studied by means of time-resolved mass spectrometry in a two-color femtosecond pump-probe setup. Resonant pre-excitation of the electronic system via the first dipole-allowed HOMO→ LUMO+ 1͑t 1g ͒ ͑HOMO denotes highest occupied molecular orbital and LUMO denotes lowest unoccupied molecular orbital͒ transition with ultrashort 25 fs pulses at 399 nm of some 10 12 W cm −2 results in a highly nonequilibrium distribution of excited electrons and vibrational modes in the neutral species. The subsequent coupling among the electronic and nuclear degrees of freedom is monitored by probing the system with time-delayed 27 fs pulses at 797 nm of some 10 13 W cm −2 . Direct information on the characteristic relaxation time is derived from the analysis of transient singly and multiply charged parent and fragment ion signals as a function of pump-probe delay and laser pulse intensity. The observed relaxation times el Ӎ 60-400 fs are attributed to different microcanonical ensembles prepared in the pre-excitation process and correspond to different total energy contents and energy sharing between electronic and vibrational degrees. The characteristic differences and trends allow one to extract a consistent picture for the formation dynamics of ions in different charge states and their fullerenelike fragments and give evidence to collective effects in multiple ionization such as plasmon-enhanced energy deposition.

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Section: Introductionmentioning

confidence: 99%

Ultrafast energy redistribution in C60 fullerenes: A real time study by two-color femtosecond spectroscopy

Shchatsinin

Laarmann

Zhavoronkov

et al. 2008

The Journal of Chemical Physics

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“…In this case other effects will ordinarily be of dominant importance. 4,11 As mentioned above, the electronic response in the DFTbased simulations can be characterized by an effective polarizability parameter ␣ k Ј if one fits Eq. ͑7͒ to the results of the simulations.…”

Section: Fig 2 ͑Color Online͒ Maximum Kinetic Energy Ofmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] This problem is directly relevant to the broader issue of coherent control in physical, chemical, [16][17][18][19] and biological [20][21][22][23] systems.…”

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confidence: 99%

Maximum relative excitation of a specific vibrational mode via optimum laser-pulse duration

et al. 2010

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For molecules and materials responding to femtosecond-scale optical laser pulses, we predict maximum relative excitation of a Raman-active vibrational mode with period T when the pulse has a full-width-at-halfmaximum duration Ϸ 0.42T. This result follows from a general analytical model, and is precisely confirmed by detailed density-functional-based dynamical simulations for C 60 and a carbon nanotube, which include anharmonicity, nonlinearity, no assumptions about the polarizability tensor, and no averaging over rapid oscillations within the pulse. The mode specificity is, of course, best at low temperature and for pulses that are electronically off-resonance, and the energy deposited in any mode is proportional to the fourth power of the electric field. For a quarter century there has been considerable interest in optimizing the vibrational response of molecules and materials to ultrafast laser pulses. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] This problem is directly relevant to the broader issue of coherent control in physical, chemical, [16][17][18][19] and biological 20-23 systems.Here we consider excitation via impulsive stimulated Raman scattering and related techniques using femtosecondscale optical pulses. We find that the optimum full-width-athalf-maximum ͑FWHM͒ pulse duration for exciting a specific vibrational mode with angular frequency 2 / T is given by Ϸ 0.42T. Our prediction results from a general analytical model, and is precisely confirmed by completely independent density-functional-based simulations for C 60 24-28 and a small carbon nanotube. [29][30][31] Unlike the model, these simulations include anharmonic effects in the vibrations, nonlinear effects in the response to the applied field and no simplifying assumptions about the electronic polarizability tensor.Our general model consists of the following: ͑1͒ the electric field has the formwith ӷ / and ប off resonance. Since the oscillations of sin 2 ͑ t + ␦͒ will average out to 1/2 over a period that is short compared to the response time of the vibrating nuclei, we will actually replace the square of Eq. ͑1͒ by the envelope functionwith Ē 0 2 = E 0 2 / 2. This form has the following nice features: 32 ͑i͒ the duration is finite and need not be truncated. ͑ii͒ The FWHM duration is exactly half the full duration 2 . ͑iii͒ A plot reveals that it closely resembles a Gaussian. ͑iv͒ The slope is zero at beginning and end. ͑2͒ The initial conditions Q k ͑0͒ = Q k ͑0͒ = 0 are imposed on the normal-mode coordinates Q k ͑t͒. This approximation is valid for the expectation value below Eq. ͑4͒ at low temperature, or an ensemble average at higher temperature, in the linearized Eq. ͑3͒. ͑3͒ The equation of motion is given by the standard ͑Placzek͒ model for Raman-active modes 8,21,33where the anharmonic and damping terms ͑in the normalmode coordinates Q k ͒, nonlinear terms ͓in the electric field E͑t͔͒, and off-diagonal terms ͑in the polarizability tensor ␣͒ have been neglected, with the electric dipole moment given by tot = + ind , ind = ␣ · ...

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“…͑4͒, one does not need any new parameters in a calculation that employs either a semiempirical 13,14 or a first-principles-based [15][16][17][18][19] Hamiltonian H 0 whose elements are known as a function of ͑X − XЈ͒. On the other hand, this prescription is in one respect a rather crude approximation: It omits intra-atomic excitations and would therefore give no excitation at all for isolated atoms.…”

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confidence: 99%

“…Here we are mainly concerned with the issue of how one can efficiently and accurately couple electrons to the electromagnetic field in such an approach, where matrix elements of various operators between localized basis functions ͑or "atomic orbitals"͒ can be calculated from first principles, and then used in large-scale calculations for complex systems, such as materials and molecules, responding to applied fields, such as ultrashort laser pulses. [9][10][11][12][13][14][15][16][17][18][19] Our starting point is, of course, the time-dependent Schrödinger equation, iប ‫ץ‬ ‫ץ‬t ͑x,t͒ = Ĥ ͑x,t͒, ͑1͒…”

mentioning

confidence: 99%

Coupling of electrons to the electromagnetic field in a localized basis

Allen

2008

Phys. Rev. B

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A simple formula is obtained for coupling electrons in a complex system to the electromagnetic field. It includes the effect of intra-atomic excitations and nuclear motion, and can be applied in, e.g., first-principlesbased simulations of the coupled dynamics of electrons and nuclei in materials and molecules responding to ultrashort laser pulses. Some additional aspects of nonadiabatic dynamical simulations are also discussed, including the potential of "reduced Ehrenfest" simulations for treating problems where standard Ehrenfest simulations will fail. DOI: 10.1103/PhysRevB.78.064305 PACS number͑s͒: 78.20.Bh, 71.15.Pd It is now possible to perform first-principles simulations of the coupled dynamics of electrons and nuclei with all nuclear coordinates included 1-4 rather than a subset of nominal reaction coordinates. For very large systems or when many trajectories are necessary, it is convenient to use a first-principles-based scheme 5-8 with a valence-electron Hamiltonian and ion-ion repulsive potential derived from calculations using density functional or other first-principles techniques. Here we are mainly concerned with the issue of how one can efficiently and accurately couple electrons to the electromagnetic field in such an approach, where matrix elements of various operators between localized basis functions ͑or "atomic orbitals"͒ can be calculated from first principles, and then used in large-scale calculations for complex systems, such as materials and molecules, responding to applied fields, such as ultrashort laser pulses. [9][10][11][12][13][14][15][16][17][18][19] Our starting point is, of course, the time-dependent Schrödinger equation, iប ‫ץ‬ ‫ץ‬t ͑x,t͒ = Ĥ ͑x,t͒, ͑1͒Some time ago, Graf and Vogl 20 obtained a result, used in Refs. 13-19, which is the time-dependent version of the Peierls substitution: If H 0 is the Hamiltonian matrix in a localized basis with no applied field,and H is the approximate Hamiltonian when there is an applied field with vector potential A͑x , t͒, then they are related bywith A͑t͒ = ͓A͑XЈ,t͒ + A͑X,t͔͒/2. ͑5͒Here ᐉ labels a localized basis function centered on a nucleus whose instantaneous position is X͑ᐉ , t͒, and we adopt the convention of normally suppressing the indices ᐉ and ᐉЈ as well as the time t by just writing X and XЈ. We will ignore any applied scalar potential A 0 , any B · B spin interactions, and the coupling of ion cores or nuclei to the applied fields since these effects can be easily included when necessary.With the prescription of Eq. ͑4͒, one does not need any new parameters in a calculation that employs either a semiempirical 13,14 or a first-principles-based [15][16][17][18][19] Hamiltonian H 0 whose elements are known as a function of ͑X − XЈ͒. On the other hand, this prescription is in one respect a rather crude approximation: It omits intra-atomic excitations and would therefore give no excitation at all for isolated atoms.Here a more general version of the result of Ref. 20 will be obtained in a form that is almost equally convenient for...

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Response ofC60andCnto ultrashort laser pulses

Cited by 79 publications

References 17 publications

Ultrafast energy redistribution in C60 fullerenes: A real time study by two-color femtosecond spectroscopy

Ultrafast energy redistribution in C60 fullerenes: A real time study by two-color femtosecond spectroscopy

Maximum relative excitation of a specific vibrational mode via optimum laser-pulse duration

Coupling of electrons to the electromagnetic field in a localized basis

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