Efficient Calculation of Time- and Frequency-Resolved Four-Wave-Mixing Signals

Abstract

"Four-wave-mixing" is the generic name for a family of nonlinear electronic and vibrational spectroscopies. These techniques are widely used to explore dissipation, dephasing, solvation, and interstate coupling mechanisms in various material systems. Four-wave-mixing spectroscopy needs a firm theoretical support, because it delivers information on material systems indirectly, through certain transients, which are measured as functions of carrier frequencies, durations, and relative time delays of the laser pulses. The observed transients are uniquely determined by the three-pulse-induced third-order polarization. There exist two conceptually different approaches to the calculation of the nonlinear polarization. In the standard perturbative approach to nonlinear spectroscopy, the third-order polarization is expressed in terms of the nonlinear response functions. As the material systems become more complex, the evaluation of the response functions becomes cumbersome and the calculation of the signals necessitates a number of approximations. Herein, we review alternative methods for the calculation of four-wave-mixing signals, in which the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. The emphasis is on the recently developed equation-of-motion phase-matching approach (EOM-PMA), which allows us to calculate the three-pulse-induced third-order polarization in any phase-matching direction by performing three (with the rotating wave approximation) or seven (without the rotating wave approximation) independent propagations of the density matrix. The EOM-PMA is limited to weak laser fields (its domain of validity is equivalent to the approach based on the third-order response functions) but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. As an illustration, we apply the EOM-PMA to the calculation of optical three-pulse photon-echo two-dimensional (2D) signals for a generic model system, which represents a characteristic photophysical dynamics of large molecules or chromophores in condensed phases. The EOM-PMA is easy to implement and can straightforwardly be incorporated into any computational scheme, which provides the time-dependent density matrix or wave function of the material system of interest. In particular, EOM-PMA-based computer codes can efficiently be implemented on parallel computers. The EOM-PMA facilitates considerably the computation of four-wave-mixing signals and 2D spectra, in both vibrational and electronic spectroscopy. The EOM-PMA can be extended to higher order optical responses, e.g., heterodyned 3D IR, transient 2D IR, and other six-wave-mixing techniques.

Exciton–vibrational coupling in the dynamics and spectroscopy of Frenkel excitons in molecular aggregates

“…Decomposition algorithms for extracting 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 various spectroscopic signals from the total polarization have been implemented and tested [108,[293][294][295][296] including applications to 2D spectroscopy [297,298]. The scheme has been streamlined to optimize the calculation speed by using auxiliary density matrices [299,300]. Numerous simulations of 2D spectroscopy using these ideas have been published [301][302][303].…”

Mapping of quantum phases by two-dimensional vibronic spectroscopy of wave-packet revivals

“…The theory of optical 2D spectroscopy has been worked out by Mukamel and others [13][14][15][16][17][18][19] employing the densityoperator formalism [20] which incorporates a correct treatment of system-bath dynamics. Within this approach, various applications have been presented [16,[21][22][23][24][25][26][27].…”

Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments

“…[40], we formulated a general approach for computing any N p -pulse induced signal, which combines the EOM phase-matching approach (EOM-PMA) [57,58] and the PBME/FBTS approach. For the full details of this methodology, we would like to direct the reader to Ref.…”