Simulation of femtosecond “double-slit” experiments for a chromophore in a dissipative environment

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

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)

An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

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

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.

Theoretical aspects of femtosecond double-pump single-molecule spectroscopy. II. Strong-field regime

We investigate femtosecond double-pump single-molecule signals in the strong-field regime, which is characterized by nonlinear scaling of the signal with the intensity of the pump pulses.

Theoretical aspects of femtosecond double-pump single-molecule spectroscopy. I. Weak-field regime

We present a theoretical description of double-pump femtosecond single-molecule signals with fluorescence detection.

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S₂(ππ*)–S₁(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system–bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system–bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system–bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S₂) is very efficiently quenched by the system–bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode–mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system–bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system–bath coupling as well as the field-matter coupling.

Simulation of femtosecond two-dimensional electronic spectra of conical intersections

We have simulated femtosecond two-dimensional (2D) electronic spectra for an excited-state conical intersection using the wave-function version of the equation-of-motion phase-matching approach. We show that 2D spectra at fixed values of the waiting time provide information on the structure of the vibronic eigenstates of the conical intersection, while the evolution of the spectra with the waiting time reveals predominantly ground-state wave-packet dynamics. The results show that 2D spectra of conical intersection systems differ significantly from those obtained for chromophores with well separated excited-state potential-energy surfaces. The spectral signatures which can be attributed to conical intersections are discussed.