Semiclassical theory of the photon echo: Application to polar fluids

Abstract

The photon echo experiment probes the dynamical processes that cause the decay of a coherent macroscopic electric polarization. Application of the technique to liquid solutions permits the study of the molecular motions that are strongly coupled to an electronic transition. We develop a semiclassical approximation to the photon echo observable, based on the use of Wigner equivalents of quantum operators, that we demonstrate to be accurate for all values of the delay time between the two pulses of the photon echo. In this approximation, the echo arises from fluctuations in the spectroscopic transition frequency, as the fluid evolves on a potential surface that is the arithmetic mean of the ground and excited state surfaces. The echo may then be calculated from nonequilibrium molecular dynamics simulations. We use this method to calculate the photon echo for a fluid of dipolar soft spheres. The results are compared to calculations of the absorption spectrum for this model, and to previous calculations of the effects of solvent dynamics on optical spectroscopic observables.

Quasi-classical approaches to vibronic spectra revisited

“…It is worth mentioning that analogous to ACL, one can obtain SACL by starting from the Schofield TCF and following the semiclassical route described in Ref. 45.…”

“…Following Ref. 45, one can derive a semiclassical approximation to the absorption cross section that leads to the dynamics that is performed on the arithmetic mean of the ground and excited state PESs, hence referred to as the averaged classical limit (ACL) method. Note that such a derivation for resonant Raman spectra leads to the known expression derived by Shi and Geva.…”

Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

“…Besides applications in electronic spectroscopy, 14,15,18,19 correlation function (7) proved useful, e.g., in nuclear magnetic resonance spin echo experiments 39 and theories of quantum computation, 37 decoherence, 37,38,40 and inelastic neutron scattering. 22 The fidelity amplitude was also used as a measure of the dynamical importance of diabatic, 23 nonadiabatic, 20 or spin-orbit couplings, 21 and of the accuracy of quantum molecular dynamics on an approximate potential energy surface.…”

“…11,12 In electronic spectroscopy, the DR and closely related approximations are known as phase averaging, 13 Wigner-averaged classical limit, or linearized semiclassical initial value representation 14,15 a) Electronic mail: jiri.vanicek@epfl.ch (LSC-IVR, 16 in the generalized sense 17 ), and have been used by several authors. 14,15,18,19 Although the original formulation of the DR pertains to a single electronic potential energy surface, a generalization to multiple surfaces exists. 20,21 The DR has many other applications: e.g., in inelastic neutron scattering, 22 as a measure of the dynamical importance of diabatic, 23 nonadiabatic, 20 or spin-orbit couplings, 21 and as a measure of the accuracy of quantum molecular dynamics on an approximate potential energy surface.…”

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

“…10 In the context of spectroscopy, the DR has been known as phase-averaging 11 and used to compute electronic spectra within the Born-Oppenheimer approximation. [11][12][13][14][15][16][17][18][19] The DR, which can be directly obtained by the linearization of the path integral, 20 is also closely related to the semiclassical perturbation approximation of Smith, Hubbard, and Miller 21,22 and to the linearized semiclassical initial value representation. 23 Recently, the application of the DR to BornOppenheimer spectra was developed further by improving the accuracy and efficiency using a semiclassical prefactor, 24,25 cellularization, 19,25 and Gaussian basis expansion.…”