Wigner spectrogram representations of heterodyne-detected four-wave-mixing and fluorescence up-conversion

Two-dimensional fluorescence excitation spectroscopy: A novel technique for monitoring excited-state photophysics of molecular species with high time and frequency resolution

We propose a novel UV/Vis femtosecond spectroscopic technique, two-dimensional fluorescence-excitation (2D-FLEX) spectroscopy, which combines spectral resolution during the excitation process with exclusive monitoring of the excited-state system dynamics at high time and frequency resolution. We discuss the experimental feasibility and realizability of 2D-FLEX, develop the necessary theoretical framework, and demonstrate the high information content of this technique by simulating the 2D-FLEX spectra of a model four-level system and the Fenna-Matthews-Olson antenna complex. We show that the evolution of 2D-FLEX spectra with population time directly monitors energy transfer dynamics and can thus yield direct qualitative insight into the investigated system. This makes 2D-FLEX a highly efficient instrument for real-time monitoring of photophysical processes in polyatomic molecules and molecular aggregates.

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.

Simulation of Nonlinear Femtosecond Signals at Finite Temperature via a Thermo Field Dynamics-Tensor Train Method: General Theory and Application to Time- and Frequency-Resolved Fluorescence of the Fenna-Matthews-Olson Complex

Addressing needs of contemporary nonlinear femtosecond optical spectroscopy, we have developed a fully quantum, numerically accurate wave function-based approach for the calculation of third-order spectroscopic signals of polyatomic molecules and molecular aggregates at finite temperature. The systems are described by multimode nonadiabatic vibronic-coupling Hamiltonians, in which diagonal terms are treated in harmonic approximation, while off-diagonal interstate couplings are assumed to be coordinate independent. The approach is based on the Thermo Field Dynamics (TFD) representation of quantum mechanics and tensor-train (TT) machinery for efficient numerical simulation of quantum evolution of systems with many degrees of freedom. The developed TFD-TT approach is applied to the calculation of time- and frequency-resolved fluorescence spectra of the Fenna-Matthews-Olson (FMO) antenna complex at room temperature taking into account finite time-frequency resolution in fluorescence detection, orientational averaging, and static disorder.

Mapping of Wave Packet Dynamics at Conical Intersections by Time- and Frequency-Resolved Fluorescence Spectroscopy: A Computational Study

Monitoring of wave packet dynamics at conical intersections by time- and frequency-resolved fluorescence spectroscopy has been investigated theoretically for a three-state two-mode model of a conical intersection coupled to a dissipative environment. The ideal and the actually measurable time- and frequency-gated fluorescence spectra are accurately and efficiently simulated by combining the hierarchy equations-of-motion method for dissipative quantum dynamics with the methodology of the equation-of-motion phase-matching approach for the calculation of spectroscopic signals. It is shown that time- and frequency-resolved fluorescence spectra reveal essential aspects of the wave packet dynamics at conical intersections and the effects of environment-induced dissipation. The results of the present work indicate that fluorescence up-conversion spectroscopy with femtosecond time resolution is an efficient tool for the characterization of ultrafast dynamics at conical intersections.

Alternative view of two-dimensional spectroscopy

Femtosecond two-dimensional (2D) spectroscopy has become a widely employed method for the investigation of the dynamics of complex chemical and biological systems. In 2D spectroscopy, the sample is excited with three phase-locked femtosecond pulses, and the signal is heterodyned with the local oscillator field. The 2D spectrum is obtained by double Fourier transform with respect to the time delay between the first two pulses and the time delay between the third pulse and the local oscillator field. We show that 2D optical signals can alternatively be measured and computationally simulated as four-wave-mixing signals generated by two femtosecond pulses and two one-sided continuous-wave (CW) pulses. The first femtosecond pulse and one-sided CW pulse create the doorway state, while the second femtosecond pulse and one-sided CW pulse create the window state. This picture relates 2D spectroscopy to other mixed time-frequency-domain techniques, which is useful for the interpretation of the corresponding signals. Moreover, it allows a computationally efficient evaluation of 2D spectra.

Multidimensional optical spectroscopy of a single molecule in a current-carrying state

The nonlinear optical signals from an open system consisting of a molecule connected to metallic leads, in response to a sequence of impulsive pulses, are calculated using a superoperator formalism. Two detection schemes are considered: coherent stimulated emission and incoherent fluorescence. The two provide similar but not identical information. The necessary superoperator correlation functions are evaluated either by converting them to ordinary (Hilbert space) operators which are then expanded in many-body states, or by using Wick's theorem for superoperators to factorize them into nonequilibrium two point Green's functions. As an example we discuss a stimulated Raman process that shows resonances involving two different charge states of the molecule in the same signal.

Transient Phenomena in Time- and Frequency-Gated Spontaneous Emission

The effect of overlapping pump and gate pulses on time- and frequency-gated spontaneous emission spectra is explored for a model of material dynamics that accounts for strong nonadiabatic and electron-vibrational coupling effects, vibrational relaxation, and optical dephasing, thus representing characteristic features of photoinduced excited-state dynamics in large molecules in the gas phase or in condensed phases. The behaviors of the sequential, coherent, and doorway-window contributions to the spontaneous emission spectrum are studied separately. The interrelation between the sequential and coherent contributions is demonstrated to be sensitive to the carrier frequencies of the pump and gate pulses and also to the optical dephasing rate, opening the possibility of an experimental determination of the latter. The coherent contribution is shown to dominate the spectrum at specific emission frequencies.

Time- and frequency-resolved fluorescence spectra of nonadiabatic dissipative systems: What photons can tell us

The monitoring of the excited-state dynamics by time- and frequency-resolved spontaneous emission spectroscopy has been studied in detail for a model exhibiting an excited-state curve crossing. The model represents characteristic aspects of the photoinduced ultrafast dynamics in large molecules in the gas or condensed phases and accounts for strong nonadiabatic and electron-vibrational coupling effects, as well as for vibrational relaxation and optical dephasing. A comprehensive overview of the dependence of spontaneous emission spectra on the characteristics of the excitation and detection processes (such as carrier frequencies, pump/gate pulse durations, as well as optical dephasing) is presented. A systematic comparison of ideal spectra, which provide simultaneously perfect time and frequency resolution and thus contain maximal information on the system dynamics, with actually measurable time- and frequency-gated spectra has been carried out. The calculations of real time- and frequency-gated spectra demonstrate that complementary information on the excited-state dynamics can be extracted when the duration of the gate pulse is varied.

Signatures of beta-peptide unfolding in two-dimensional vibrational echo spectroscopy: a simulation study

An ensemble of exciton Hamiltonians for the amide-I band of the folded and unfolded states of a helical beta-heptapeptide is generated using a molecular dynamics (MD) simulation. The correlated fluctuations of its parameters and their signatures in two-dimensional (2D) vibrational echo spectroscopy are computed. This technique uses infrared pulse sequences to provide ultrafast snapshots of molecular structural fluctuations, in analogy with multidimensional NMR. The present study demonstrates that, by combining a method of calculating the vibrational Hamiltonian from MD snapshots and the nonlinear exciton equations (NEE), it may be possible to simulate realistic multidimensional IR spectra of chemically and biologically interesting systems.

Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations

Femtosecond visible and infrared analogues of multiple-pulse nuclear magnetic resonance techniques provide novel snapshot probes into the structure and electronic and vibrational dynamics of complex molecular assemblies such as photosynthetic antennae, proteins, and hydrogen-bonded liquids. A classical-oscillator description of these spectroscopies in terms of interacting quasiparticles (rather than transitions among global eigenstates) is developed and sets the stage for designing new pulse sequences and inverting the multidimensional signals to yield molecular structures. Considerable computational advantages and a clear physical insight into the origin of the response and the relevant coherence sizes are provided by a real-space analysis of the underlying coherence-transfer pathways in Liouville space.