Population Transfer Dynamics Research Articles

Quantum tomography of molecules using ultrafast electron diffraction.

We propose a quantum tomography (QT) approach to retrieve the temporally evolving reduced density matrix in electronic state basis, where the populations and coherence between the ground state and excited state are reconstructed from the ultrafast electron diffraction signal. In order to showcase the capability of the proposed QT approach, we simulate the nuclear wavepacket dynamics and ultrafast electron diffraction of photoexcited pyrrole molecules using the abinitio quantum chemical CASSCF method. From the simulated time-resolved diffraction data, we retrieve the evolving density matrix in a crude diabatic representation basis and reveal the symmetry of the excited pyrrole wavepacket. Our QT approach opens the route to make a quantum version of "molecular movie" that covers the electronic degree of freedom and equips ultrafast electron diffraction with the power to reveal the coherence between electronic states, relaxation, and dynamics of population transfer.

Redfield Propagation of Photoinduced Electron Transfer Reactions in Vacuum and Solution.

Dynamical simulations of ultrafast electron transfer reactions are of utmost interest. To allow for energy dissipation directly into an external surrounding environment, a solvent coupling model has been deduced, implemented, and utilized to describe the photoinduced electron transfer dynamics within a model triad system herein. The model is based on Redfield theory, and the environment is represented by harmonic oscillators filled with bosonic quanta. To imitate real solvents, the oscillators have been equipped with frequencies and polarization lifetimes characteristic of the corresponding solvent. The population was found to transfer through the energetically lowest electron transfer route regardless of the medium. The condensed population transfer dynamics were observed to be highly dependent on the solvent parameters. In particular, an increase in the solvent coupling entailed a detainment in the population transfer from the initially prepared diabatic state and a promotion in the population transfer through the other electron transfer route. Two explanations based on the diagonal and off-diagonal matrix elements of the Kohn-Sham Fock matrix, respectively, have been provided. The lifetime of the populated partially charge-separated state was prolonged with increasing solvent polarity, and it was explained in terms of attractive interactions between the solvent's dipole moments and the fragments' charges. The high-frequency vibrational fine-structure in the correlation function was demonstrated to be important for the transfer dynamics, and the importance of dephasing effects in polar solvents was verified and precised to concern the optical polarization of the solvents.

Electronic structure, optical properties, and electron dynamics in organic dye-sensitized TiO2 interfaces by local hybrid density functionals

In this work, we present theoretical investigations of dye-sensitized solar cells (DSSCs) using linear response time-dependent density functional theory (LR-TDDFT) and electron dynamics within the hybrid TDDFT/configuration interaction methodology. To evaluate the potential of local hybrid density functionals for such hybrid systems, we study the electronic properties of two organic dyes, both isolated and anchored on a typical semiconductor substrate (TiO 2 ). The implemented strategies can accurately predict electronic structures, optical properties, and energetic alignments of the investigated dye@TiO 2 systems. The accuracy of charge transfer excited states and the hybridization between the interfacial states depend appreciably on the used exchange correlation functional. This work emphasizes the performance of local hybrid functionals in comparison to the most commonly used global hybrid and range-separated hybrid functionals. Investigation of laser-induced charge migration dynamics sheds light on the effect of hybridization between the dye and the substrate at the interface on both the population transfer dynamics and the charge injection rate.

Multi-path effect in population transfer dynamics of the photoassociation of hot Mg atoms by a femtosecond laser pulse

We investigate the thermal photoassociation dynamics of the Mg atoms, from the X1Σg+ state to the (1)1Πg state, or to the other three higher excited states |i〉=(1)1Πu,(2)1Πu,(2)1Σu+. The weak two-photon coupling between X1Σg+ and (1)1Πg, the strong three-photon couplings between X1Σg+ and |i〉, and the one-photon couplings between (1)1Πg and |i〉 can form several different transition paths. We find that X1Σg+⟶+3ℏω|i〉⟶-ℏω(1)1Πg is the major path and the “V”-type Raman transition path from |i〉 to (1)1Πg takes the second place.

Geometric representation of adiabatic distributed-Bragg-reflectors and broadening the photonic bandgap

Adiabatic following has been an widely-employed technique for achieving near-complete population transfer in a ‘two-level’ quantum mechanical system. The theoretical basis, however, could be generalized to a broad class of systems exhibiting SU(2) symmetry. In the present work, we present an analogy of population transfer dynamics of a two-level atomic system with that of light propagation in a classical ‘one-dimensional’ photonic crystal, commonly known as distributed-Bragg-reflector (DBR). This formalism facilitates in adapting the idea of adiabatic following, more precisely the rapid adiabatic passage (RAP) which is usually encountered in a broad class of quantum-mechanical systems. We present a chirped DBR configuration in which the adiabatic constraints are satisfied by virtue of optimally chirping the DBR. The reflection spectrum of the configuration exhibit broadening of photonic bandgap (PBG) in addition to a varying degree of suppression of sharp reflection peaks in the transmission band. The intermodal coupling between counter-propagating modes as well as their phase-mismatch, for the DBR configuration, exhibits a longitudinal variation which is usually observed in ‘Allen-Eberly’ scheme of adiabatic population transfer in two-level atomic systems.

Site-specific generation of excited state wavepackets with high-intensity attosecond x rays.

High-intensity attosecond x rays can produce coherent superpositions of valence-excited states through two-photon Raman transitions. The broad-bandwidth, high-field nature of the pulses results in a multitude of accessible excited states. Multiconfigurational quantum chemistry with the time-dependent Schrödinger equation is used to examine population transfer dynamics in stimulated x-ray Raman scattering of the nitric oxide oxygen and nitrogen K-edges. Two pulse schemes initiate wavepackets of different characters and demonstrate how chemical differences between core-excitation pathways affect the dynamics. The population transfer to valence-excited states is found to be sensitive to the electronic structure and pulse conditions, highlighting complexities attributed to the Rabi frequency. The orthogonally polarized two-color-pulse setup has increased selectivity while facilitating longer, less intense pulses than the one-pulse setup. Population transfer in the 1s → Rydberg region is more effective but less selective at the nitrogen K-edge; the selectivity is reduced by double core-excited states. Result interpretation is aided by resonant inelastic x-ray scattering maps.

Population inversion in a strongly driven two-level system at far-off resonance

The population transfer dynamics in a strongly driven two-level system is studied. It is shown that population inversion can be efficiently achieved when a laser pulse whose photon energy is about half of the energy separation of the two levels is turned on suddenly. This situation is realized when a neutral atom or molecule is ionized at the peak of the laser field, followed by the laser-driven population transfer among two states of an atomic or molecular ion. The mechanism of the efficient population transfer for an ion effectively exposed to a laser field with a sudden turn-on is examined by numerical calculations based on the quasi-stationary Floquet theory.

Role of quantum coherence in shaping the line shape of an exciton interacting with a spatially and temporally correlated bath.

Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vibrational line shapes, through such concepts as static heterogeneity and motional narrowing. However, the theory does not properly address the effects of quantum coherences on optical line shape, especially in extended systems where a large number of eigenstates are present. In this work, we study the line shape of an exciton in a one-dimensional lattice consisting of regularly placed and equally separated optical two level systems. We consider both linear array and cyclic ring systems of different sizes. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (SLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigenfunctions are known analytically. This identification is particularly useful for long chains where the eigenvalues of TDTM help understanding crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peaks increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important. In this limit, the line shape shows motional narrowing with peaks at the values predicted by TDTM (constant J and no fluctuation). (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently. (iv) In addition to linear chains of two level systems, we also consider a cyclic tetramer. The cyclic polymers can be designed for experimental verification. (v) We also build a connection between line shape and population transfer dynamics. In the fast modulation limit, both the line shape and the population relaxation, for both correlated and uncorrelated bath, show similar behavior. However, in slow modulation limit, they show profoundly different behavior. (vi) This study explains the unique role of the rate of fluctuation (inverse of the bath correlation time) in the sustenance and propagation of coherence. We also examine the effects of off-diagonal fluctuation in spectral line shape. Finally, we use Tanimura-Kubo formalism to derive a set of coupled equations to include temperature effects (partly neglected in the SLE employed here) and effects of vibrational mode in energy transfer dynamics.

Steering Vibrational Population Transfer via Double-∑-Type Laser Scheme

The vibrational state-selected population transfer from a highly vibrationally excited level to the ground level is of great importance in the preparation of ultra-cold molecules. By using the time-dependent quantum-wave-packet method, the population transfer dynamics is investigated theoretically for the HF molecule. A double-∑-type laser scheme is proposed to transfer the population from the ∣v=16〉 level to the ground vibrational level ∣v=0〉 on the ground electronic state. The scheme consists of two steps: The first step is to transfer the population from ∣v=16〉 to ∣v=7〉 via an intermediate level ∣v=11〉, and the second one is to transfer the population from ∣v=7〉 to ∣v=0〉 via ∣v=3〉. In each step, three vibrational levels form a ∑-type population transfer path under the action of two temporally overlapped laser pulses. The maximal population-transfer efficiency is obtained by optimizing the laser intensities, frequencies, and relative delays. Cases for the pulses in intuitive and counterintuitive sequences are both calculated and compared. It is found that for both cases the population can be efficiently (over 90%) transferred from the ∣v=16〉 level to the ∣v=0〉 level.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.

Multiple time scale population transfer-dynamics in coupled electronic states

We regard the wave-packet dynamics in two electronic states which interact via a constant coupling element. Performing numerical calculations it is found that the time-dependent populations exhibit oscillatory variations with two characteristic periods. Whereas, as expected, one period is determined by the vibrational motion, it is shown that Rabi-type oscillations occur which are influenced by the parameters of the potential energy curves, the coupling and the amplitudes in the two states on one hand, and by the nuclear motion on the other. An analysis of the numerical results is performed within various levels of approximation.

Fourth-Order Perturbative Model for Photoinduced Internal Conversion Processes

Essential to the functionality of numerous biological and synthetic molecular systems is the ability to rapidly convert electronic excitation energy into heat. Such internal conversion (IC) transitions often cannot be described by traditional second-order kinetic theories because of time-coincident electronic and nuclear relaxation processes. Here, we present a perturbative fourth-order phenomenological model for photoinduced IC that incorporates effects associated with finite laser bandwidths and nonequilibrium nuclear motions. Specialized knowledge of first-principles computational methods is not required, and many parameters can be obtained with standard spectroscopic measurements. The model is applied to the IC processes that precede electrocyclic ring-opening in α-terpinene. It is shown that the primary factor governing the shape of the population decay profile (Gaussian versus exponential) is the rate at which the wavepacket approaches the geometry corresponding to degeneracy between the excited states. Other parameters such as the displacement in the promoting mode and the thermal fluctuation amplitudes affect the sensitivity of the IC dynamics to motion of the wavepacket but do not alter the basic physical picture. Finally, we suggest a wavepacket representation of the IC process to visualize correlations between population-transfer dynamics and the amount of energy transferred from the system to the bath.

Coherent quantum dynamics in donor–bridge–acceptor systems: beyond the hopping and super-exchange mechanisms

The population transfer dynamics of model donor–bridge–acceptor systems is studied by comparing a recently developed polaron-transformed quantum master equation (PQME) with the well-known Redfield and Förster theories of quantum transport. We show that the PQME approach reduces to these two theories in their respective limits of validity and naturally interpolates between them as a function of the system–bath coupling strength. By exploring the parameter space of our model problem, we identify novel regimes of transport dynamics in bridged systems like those encountered in biological and organic energy transfer problems. Furthermore, we demonstrate that three-level systems like the ones studied herein represent ideal minimal models for the identification of quantum coherent transport as embodied in super-exchange phenomena that cannot be captured by Förster-like hopping approaches.

Ultrafast Vibrational Population Transfer Dynamics in 2-Acetylcyclopentanone Studied by 2D IR Spectroscopy

2-Acetylcyclopentanone (2-ACP), which is a β-dicarbonyl compound, undergoes keto-enol isomerization, and its enol tautomers are stabilized by a cyclic intramolecular hydrogen bond. 2-ACP (keto form) has symmetric and asymmetric vibrational modes of the two carbonyl groups at 1748 and 1715 cm(-1) , respectively, which are well separated from the carbonyl modes of its enol tautomers in the FTIR spectrum. We have investigated 2-ACP dissolved in carbon tetrachloride by 2D IR spectroscopy and IR pump-probe spectroscopy. Vibrational population transfer dynamics between the two carbonyl modes were observed by 2D IR spectroscopy. To extract the population exchange dynamics (i.e., the down- and uphill population transfer rate constants), we used the normalized volumes of the cross-peaks with respect to the diagonal peaks at the same emission frequency and the survival and conditional probability functions. As expected, the downhill population transfer time constant (3.2 ps) was measured to be smaller than the uphill population transfer time constant (3.8 ps). In addition, the vibrational population relaxation dynamics of the two carbonyl modes were observed to be the same within the experimental error and were found to be much slower than vibrational population transfer between two carbonyl modes.

Semiclassical Description of Electronic Excitation Population Transfer in a Model Photosynthetic System

Recently, Fleming’s group observed direct evidence that the electronic excitation energy (and population) transfers coherently rather than through incoherent hopping motions in the Fenna−Mathews−Olson pigment−protein complex. Ishizaki and Fleming further developed a hierarchy equation approach to describe this excitation population transfer dynamics in a model photosynthetic system. Here, we treat this same model system via the linearized approximation to the semiclassical (SC) initial value representation (IVR) for time correlation functions, in combination with the Meyer−Miller−Stock−Thoss model for the electronic degrees of freedom. Our approach is able to describe the long-lived quantum coherent dynamics, in excellent agreement with Ishizaki−Fleming’s results. Moreover, the advantage of the linearlized SC-IVR approach is that it can be applied to any molecular model for which classical MD simulations are feasible, all the way up to a full all-atom MD simulation, while at the same time treating the electronic and nuclear dynamics in a consistent fashion.

Raman fingerprints on a spinor BEC

We present examples of ring structures that arise in a 87Rb spinor condensate through the application of Raman laser pulses that couple the internal spin states of the F = 2 ground state manifold. The appearance of fringes within the context of the population transfer dynamics is discussed, and several pulse protocol options are compared.

Relaxation in the Exciton Fine Structure of Semiconductor Nanocrystals

A spectroscopic study is reported of relaxation in the exciton fine structure of CdSe nanorods measured using ultrafast cross-polarized heterodyned third-order transient grating (CPH-3TG) spectroscopy. The CPH-3TG spectroscopy probes the dynamics of population transfer between states accompanying exciton spin flip (radiationless transitions in the exciton fine structure associated with changes in the sign of the total angular momentum). Analysis of the data enabled elucidation of pathways for exciton fine structure relaxation (EFSR) involving all of the exciton fine structure states. The mechanism and origin of the EFSR dynamics in CdSe nanorods are discussed in the exciton state picture with an analogy to molecular radiationless transition processes such as internal conversion and intersystem crossing. Key conclusions are that the fast transitions are between states with total angular momentum of ±1 and ∓2 and that the rate of this transition follows an inverse diameter to the fourth power size dependence, which originates from the Dresselhaus spin−orbit coupling effect.

Two-dimensional electronic spectroscopy of the B800–B820 light-harvesting complex

Emerging nonlinear optical spectroscopies enable deeper insight into the intricate world of interactions and dynamics of complex molecular systems. 2D electronic spectroscopy appears to be especially well suited for studying multichromophoric complexes such as light-harvesting complexes of photosynthetic organisms as it allows direct observation of couplings between the pigments and charts dynamics of energy flow on a 2D frequency map. Here, we demonstrate that a single 2D experiment combined with self-consistent theoretical modeling can determine spectroscopic parameters dictating excitation energy dynamics in the bacterial B800-B820 light-harvesting complex, which contains 27 bacteriochlorophyll molecules. Ultrafast sub-50-fs dynamics dominated by coherent intraband processes and population transfer dynamics on a picosecond time scale were measured and modeled with one consistent set of parameters. Theoretical 2D spectra were calculated by using a Frenkel exciton model and modified Förster/Redfield theory for the calculation of dynamics. They match the main features of experimental spectra at all population times well, implying that the energy level structure and transition dipole strengths are modeled correctly in addition to the energy transfer dynamics of the system.

Direct Frequency Comb Measurements of Absolute Optical Frequencies and Population Transfer Dynamics

A phase-stabilized femtosecond laser comb is directly used for high-resolution spectroscopy and absolute optical frequency measurements of one- and two-photon transitions in laser-cooled 87Rb atoms. Absolute atomic transition frequencies, such as the 5S1/2 F=2-->7S1/2 F"=2 two-photon resonance measured at 788,794 768,921 (44) kHz, are determined without a priori knowledge about their values. Detailed dynamics of population transfer driven by a sequence of pulses are uncovered and taken into account for the measurement of the 5P states via resonantly enhanced two-photon transitions.

Adiabatic population transfer in a liquid: taking advantage of a decaying target state.

The feasibility of efficient population transfer between an initial state and a decaying target state of the same parity without populating an intermediate state, in the presence of large-amplitude stochastic energy level fluctuations that mimic the dephasing in a solute molecule due to the influence of a solvent, is demonstrated theoretically. In particular, it is shown that a decaying target state, whose decay rate constant is large compared with the band width of picosecond laser pulses but small compared with the associated peak Rabi frequencies, can dramatically suppress the dephasing-induced nonadiabaticity associated with the dynamics of population transfer, resulting in, irrespective of the correlation time of stochastic energy level fluctuations, negligible population in the intermediate state and complete population transfer to the decaying target state. These results should further motivate experimental studies of optical control of molecular dynamics in a liquid. An interesting connection between our results and the quantum Zeno and anti-Zeno effects is also discussed.