Monitoring of Nonadiabatic Effects in Individual Chromophores by Femtosecond Double-Pump Single-Molecule Spectroscopy: A Model Study

Abstract

We explore, by theoretical modeling and computer simulations, how nonadiabatic couplings of excited electronic states of a polyatomic chromophore manifest themselves in single-molecule signals on femtosecond timescales. The chromophore is modeled as a system with three electronic states (the ground state and two non-adiabatically coupled excited states) and a Condon-active vibrational mode which, in turn, is coupled to a harmonic oscillator heat bath. For this system, we simulate double-pump single-molecule signals with fluorescence detection for different system-field interaction strengths, from the weak-coupling regime to the strong-coupling regime. While the signals are determined by the coherence of the electronic density matrix in the weak-coupling regime, they are determined by the populations of the electronic density matrix in the strong-coupling regime. As a consequence, the signals in the strong coupling regime allow the monitoring of nonadiabatic electronic population dynamics and are robust with respect to temporal inhomogeneity of the optical gap, while signals in the weak-coupling regime are sensitive to fluctuations of the optical gap and do not contain information on the electronic population dynamics.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

“…For a TDM of 1.0 au (2.54 D), λ = 0.03 eV corresponds to a moderate intensity of ∼4 × 10 10 W/cm 2 . The same critical value of λ ∼ 0.03 eV indicates the turnover from the weak-coupling regime to the strong-coupling regime for population-detected double-pump signals evaluated for a similar model (see refs − and section ).…”

“…It is not necessary to perform a phase decomposition of the double-pump population-detected signal, because it can be conveniently decomposed into population and coherence contributions. 553,554 If, for example, the pump pulses are temporally well separated and contributions from the states of manifold {II} can be neglected, the DW approximation yields the double-pump population-detected signal in the form…”

“…It is worthwhile to consider the two-pulse variant of population-detected spectroscopy, that is phase-locked double-pump population-detected spectroscopy, in some detail. This technique, pioneered in femtosecond ensemble molecular spectroscopy by Scherer and co-workers, was extended to single-molecule spectroscopy by van Hulst and co-workers , and to single-molecule microscopy by Fujiwara and Zhou et al , Double-pump population-detected signals were simulated for a number of systems, from molecules − ,− to antenna complexes. − These signals can be calculated via eq through the numerical solution of driven TDSEs or MEs with a system–field interaction Hamiltonian containing two pump pulses separated by the time delay τ. It is not necessary to perform a phase decomposition of the double-pump population-detected signal, because it can be conveniently decomposed into population and coherence contributions. , If, for example, the pump pulses are temporally well separated and contributions from the states of manifold {II} can be neglected, the DW approximation yields the double-pump population-detected signal in the form S ( τ ) = A ( τ ) + ( B false( τ false) e i φ + B * false( τ false) e − i φ ) e − γ τ Here A (τ) is the contribution which results from the evolution of the chromophore in electronic population, B (τ) is the coherence contribution, φ is the relative phase of the pump pulses, and γ is the electronic dephasing rate.…”

The fate of molecular excited states: modeling donor–acceptor dyes

“…The system-bath total Hamiltonian reads: where H ˆSB describes the system-bath interaction and the last term describes the bath Hamiltonian in terms of the creation and annihilation operators b ˆ † i and b ˆi, respectively, for oscillation quanta with frequency o i . The time evolution of the reduced density matrix ŝ; written on the eigenstates of the molecular Hamiltonian is governed by the equation 11,[18][19][20]50,58…”

“…The HEOM, a computationally demanding technique, has been applied successfully to several model systems, [13][14][15][16][17] where, typically, molecular vibrations are not explicitly included into the system, but are clamped into the bath. On the other hand, the less demanding Redfield model is widely exploited to date, [18][19][20][21][22][23][24] particularly to simulate spectroscopic properties of systems where the vibrational coupling is prominent.…”