Photon Echo Spectra Research Articles

A partially linearized spin-mapping approach for simulating nonlinear optical spectra.

We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.

Probing excited-state dynamics with quantum entangled photons: Correspondence to coherent multidimensional spectroscopy.

Quantum light is a key resource for promoting quantum technology. One such class of technology aims to improve the precision of optical measurements using engineered quantum states of light. In this study, we investigate transmission measurement of frequency-entangled broadband photon pairs generated via parametric down-conversion with a monochromatic laser. It is observed that state-to-state dynamics in the system under study are temporally resolved by adjusting the path difference between the entangled twin beams when the entanglement time is sufficiently short. The non-classical photon correlation enables time-resolved spectroscopy with monochromatic pumping. It is further demonstrated that the signal corresponds to the spectral information along anti-diagonal lines of, for example, two-dimensional Fourier-transformed photon-echo spectra. This correspondence inspires us to anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

Coherent and dissipative quantum process tensor reconstructions in two-dimensional electronic spectroscopy.

A major goal of time-resolved spectroscopy is to resolve the dynamical processes that follow photoexcitation. This amounts to identifying all the quantum states involved and the rates of population transfer between them. Unfortunately, such quantum state and kinetic reconstructions are ambiguous using one-dimensional methods such as transient absorption even when all the states of the system are fully resolved. Higher-dimensionality methods like two-dimensional spectroscopy lift some of the ambiguity, but unless the spectral features are well-separated, current inversion methods generally fail. Here, we show that, using both coherence and population signals of the nonlinear response, it is indeed possible to accurately extract both static and dynamic information from the 2D spectrum even when features are highly congested. Coherences report on the positions of the vibronic states of the system, providing a useful constraint for extracting the full kinetic scheme. We model time-resolved 2D photon echo spectra using a sum-over-states approach and show in which regimes the Hamiltonian and kinetic schemes may be recovered. Furthermore, we discuss how such algorithms may be applied to experimental data and where some of the underlying assumptions may fail. The ability to systematically extract the maximal information content of multidimensional spectroscopic data is an important step toward utilizing the full power of these techniques and elucidating the structure and dynamics of increasingly complex molecular systems.

Effect of the depolarization field on coherent optical properties in semiconductor quantum dots

We study the photon echo spectrum of self-assembled semiconductor quantum dots using femtosecond light pulses. The spectrum shape changes from a single-peaked to a double-peaked structure as the time delay between the two excitation pulses is increased. The spectrum change is reproduced by numerical calculations, which include the depolarization field induced by the biexciton-exciton transition as well as the conventional local-field effect for the exciton--ground-state transition in a quantum dot. Our findings suggest that various optical transitions in tightly localized systems generate a depolarization field, which renormalizes the resonant frequency with a change in the polarization itself, leading to unique optical properties.

A "Universal" Spectroscopic Map for the OH Stretching Mode in Alcohols.

Empirical maps are presented for the OH stretching vibrations in neat alcohols in which the relevant spectroscopic quantities are expressed in terms of the electric field exerted on the hydrogen atom by the surrounding liquid. It is found, by examination of the four lowest linear alcohols, methanol, ethanol, n-propanol, and n-butanol, that a single map can be used for alcohols with different alkyl groups. This "universal" map is in very good agreement with maps optimized for the individual alcohols but differs from those previously developed for water. This suggests that one map can be used for all alcohols, perhaps even those not examined in the present study. The universal map gives IR lineshapes in good agreement with measured spectra for isotopically dilute methanol and ethanol, while the two-dimensional IR photon echo spectra give results that differ from experiments. The role of non-Condon effects, reorientation dynamics, hydrogen bonding, and spectral diffusion is discussed.

Nature does not rely on long-lived electronic quantum coherence for photosynthetic energy transfer

During the first steps of photosynthesis, the energy of impinging solar photons is transformed into electronic excitation energy of the light-harvesting biomolecular complexes. The subsequent energy transfer to the reaction center is commonly rationalized in terms of excitons moving on a grid of biomolecular chromophores on typical timescales [Formula: see text]100 fs. Today's understanding of the energy transfer includes the fact that the excitons are delocalized over a few neighboring sites, but the role of quantum coherence is considered as irrelevant for the transfer dynamics because it typically decays within a few tens of femtoseconds. This orthodox picture of incoherent energy transfer between clusters of a few pigments sharing delocalized excitons has been challenged by ultrafast optical spectroscopy experiments with the Fenna-Matthews-Olson protein, in which interference oscillatory signals up to 1.5 ps were reported and interpreted as direct evidence of exceptionally long-lived electronic quantum coherence. Here, we show that the optical 2D photon echo spectra of this complex at ambient temperature in aqueous solution do not provide evidence of any long-lived electronic quantum coherence, but confirm the orthodox view of rapidly decaying electronic quantum coherence on a timescale of 60 fs. Our results can be considered as generic and give no hint that electronic quantum coherence plays any biofunctional role in real photoactive biomolecular complexes. Because in this structurally well-defined protein the distances between bacteriochlorophylls are comparable to those of other light-harvesting complexes, we anticipate that this finding is general and directly applies to even larger photoactive biomolecular complexes.

Two-dimensional photon echoes reveal non-Markovian energy transfer in an excitonic dimer.

We show that strong non-Markovian effects can be revealed by the steady-state two-dimensional (2D) photon echo spectra at asymptotic waiting times. For this, we use a simple dimer toy model that is strongly coupled to a harmonic bath with parameters typical for photoactive biomolecules. We calculate the 2D photon echo spectra employing both the numerically exact hierarchy equation of motion and the quasiadiabatic path integral approach and compare these results with approximate results from a time-nonlocal quantum master equation approach. While the latter correctly reproduces the exact population dynamics at long times, it fails at the same time to correctly describe the 2D photon echo spectra at long waiting times. The differences show that non-Markovian effects are much more important for the steady-state 2D photon echoes than for the equilibrium populations. Thus, accurate theoretical descriptions of the energy transfer dynamics in biomolecular complexes have to be based on numerically exact simulations of the environmental fluctuations when nonlinear response functions are analyzed.

Simulations of the infrared, Raman, and 2D-IR photon echo spectra of water in nanoscale silica pores

Vibrational spectroscopy is frequently used to characterize nanoconfined liquids and probe the effect of the confining framework on the liquid structure and dynamics relative to the corresponding bulk fluid. However, it is still unclear what molecular-level information can be obtained from such measurements. In this paper, we address this question by using molecular dynamics (MD) simulations to reproduce the linear infrared (IR), Raman, and two-dimensional IR (2D-IR) photon echo spectra for water confined within hydrophilic (hydroxyl-terminated) silica mesopores. To simplify the spectra the OH stretching region of isotopically dilute HOD in D2O is considered. An empirical mapping approach is used to obtain the OH vibrational frequencies, transition dipoles, and transition polarizabilities from the MD simulations. The simulated linear IR and Raman spectra are in good general agreement with measured spectra of water in mesoporous silica reported in the literature. The key effect of confinement on the water spectrum is a vibrational blueshift for OH groups that are closest to the pore interface. The blueshift can be attributed to the weaker hydrogen bonds (H-bonds) formed between the OH groups and silica oxygen acceptors. Non-Condon effects greatly diminish the contribution of these OH moieties to the linear IR spectrum, but these weaker H-bonds are readily apparent in the Raman spectrum. The 2D-IR spectra have not yet been measured and thus the present results represent a prediction. The simulated spectra indicates that it should be possible to probe the slower spectral diffusion of confined water compared to the bulk liquid by analysis of the 2D-IR spectra.

Efficient tool to calculate two-dimensional optical spectra for photoactive molecular complexes.

We combine the coherent modified Redfield theory (CMRT) with the equation of motion-phase matching approach (PMA) to calculate two-dimensional photon-echo spectra for photoactive molecular complexes with an intermediate strength of the coupling to their environment. Both techniques are highly efficient, yet they involve approximations at different levels. By explicitly comparing with the numerically exact quasiadiabatic path integral approach, we show for the Fenna-Matthews-Olson complex that the CMRT describes the decay rates in the population dynamics well, but final stationary populations and the oscillation frequencies differ slightly. In addition, we use the combined CMRT+PMA to calculate two-dimensional photon-echo spectra for a simple dimer model. We find excellent agreement with the exact path integral calculations at short waiting times where the dynamics is still coherent. For long waiting times, differences occur due to different final stationary states, specifically for strong system-bath coupling. For weak to intermediate system-bath couplings, which is most important for natural photosynthetic complexes, the combined CMRT+PMA gives reasonable results with acceptable computational efforts.

On the origin of oscillations in two-dimensional spectra of excitonically-coupled molecular systems

We investigate an artificial molecular dimer made of two dipole coupled cyanine dye monomers in which a strong coherent coupling between electronic and vibrational degrees of freedom arises. Clear signatures of this coupling are reflected in an oscillatory time evolution of the off-diagonal vibronic cross peaks in the two-dimensional optical photon echo spectrum. We find a strong coherence component damped by fast electronic dephasing ( fs) accompanied by a much weaker component which decays on the longer time scales (ps) associated to vibrational dephasing. We find that vibronic coupling does not cause longer dephasing times of the dominant photo echo component but additional weak but long-lived components emerge.

Effect of zinc substitution on molecular dynamics of protoporphyrin-IX

We report the effects of zinc metal substitution on the molecular dynamics of protoporphyrin-IX in dichloromethane solvent by spectrally resolving the femtosecond photon echo spectrum. We have found that the coherence and population dynamics change due to the presence of Zn metal in the protoporphyrin-IX system. Zinc metal reduces the conformational disorder in the molecular structure of protoporphyrin-IX and in turn increases the planarity of the molecule resulting in better delocalization of π-electrons in the system. This effect decreases the inhomogeneous broadening of the photon echo spectra of Zn-substituted protoporphyrin-IX.

Enhanced-Resolution Single-Shot 2DFT Spectroscopy by Spatial Spectral Interferometry.

We demonstrate use of spatial interference for the complete electric field reconstruction of two-dimensional (2D) coherent spectroscopic signals generated through four-wave mixing (4WM) in a single laser shot. Until now, the amplitude and phase characterization of 4WM signals has relied primarily on Fourier transform spectral interferometry (FTSI), which limits the measurement's sensitivity and resolution. We show that spatial spectral interferometry (SSI) is a generalized approach to 4WM signal detection that eliminates these inherent limitations of FTSI without introducing additional experimental complexity. SSI is used to measure the 2D photon echo spectra of two systems with dramatically different line widths, the coupled D line transitions in rubidium vapor and the energy-transfer dynamics in the light-harvesting protein LH2.

Exchange narrowing and exciton delocalization in disordered J aggregates: Simulated peak shapes in the two dimensional spectra

Delocalized excitons in elementary linear J aggregates of two-level molecules absorb a photon into the low-energy edge of an exciton band. Absorption of a second photon is blue-shifted as the lowest energy state is occupied. This setup of states leads to a double-peak feature in a set of two dimensional photon echo spectra for excitonic bands. The delocalization properties of excitons, thus, strongly affect the peak lineshapes and their relative amplitudes. Simulations of various two dimensional spectra of a linear J aggregate are presented and possible schemes to quantitatively characterize the peak profiles are suggested. This allows to relate observable peak lineshapes to the exciton delocalization.

Nonlinear spectroscopy of photon-dressed Dirac electrons in a quantum dot

We study the localization of dressed Dirac electrons in a cylindrical quantum dot (QD) formed on monolayer and bilayer graphene by spatially different potential profiles. Short-lived excitonic states which are too broad to be resolved in linear spectroscopy are revealed by cross-peaks in the photon-echo nonlinear technique. Signatures of the dynamic gap in the two-dimensional photon-echo spectra are discussed.

2D optical photon echo spectroscopy of a self‐assembled quantum dot

Simulations of two dimensional coherent photon echo (2D‐PE) spectra of self‐assembled InAs/GaAs quantum dots (QD) in different charged states are presented revealing the coupling between the individual mono‐exciton transitions and contributions of bi‐excitons . The information about the states is crucial for various application scenarios of QDs, like e.g. highly efficient solar cells. The simulations rely on a microscopic description of the electronic structure by high‐level atomistic many‐body pseudopotential calculations. It is shown that asymmetric diagonal peak shapes and double cross‐peaks are the result of state contributions to the PE signal by analyzing the contributions of the individual pathways excited state emission, ground state bleach and excited state absorption. The results show that from the detuned and contributions the bi‐exciton binding energies of the manifold are revealed in 2D‐PE signals.

Non-Markovian Dynamics of Spectral Narrowing for Excitons in the Layered Semiconductor GaSe Observed Using Optical Four-Wave Mixing Spectroscopy

We have investigated non-markovian dephasing by using time-resolved and spectrally resolved four-wave mixing measurements in a layered semiconductor GaSe. When the time interval between the first and second excitation pulses is increased, photon echo spectra exhibit narrowing only in a regime of a few picoseconds. In the initial dephasing of these signals, fast damping is observed. The narrowing of the spectrally resolved signal is consistent with the Fourier transformation of the time-resolved signals. Spectral narrowing is crucial evidence of the transition from non-markovian to markovian dynamics. By comparing experimental data with calculation results based on the non-markovian theory, we have found that the correlation time of the exciton-phonon interaction is 1.1 ps.

An analytic approach to 2D electronic PE spectra of molecular systems

The three-pulse photon echo (3 P- PE) spectra of finite molecular systems and simplified line broadening models is presented. The Fourier picture of a heterodyne detected three-pulse rephasing PE signal in the δ-pulse limit of the external field is derived in analytic form. The method includes contributions of one and two-excitonic states and allows direct calculation of Fourier PE spectrogram from corresponding Hamiltonian. As an illustration, the proposed treatment is applied to simple systems, e.g. 2-site two-level system (TLS) and n-site TLS model of photosynthetic unit. The importance of relation between Fourier picture of 3 P- PE dynamics (corresponding to nonzero population time, T) and coherent inter-state coupling is emphasized.

Quantum Coherence and Disorder-Specific Effects in Simulations of 2D Optical Spectra of One-Dimensional J-aggregates

Time-resolved two-dimensional photon-echo (2D PE) spectra of linear J-aggregates containing four molecules per unit cell--a model system for a concentrated water solution of the pseudo-isocyanine dye--is theoretically considered. Analysis of a single unit cell and the full-sized aggregate is consistently carried out. Spectral features of a single unit cell are sorted out by assigning them to specific double-sided Feynman diagrams. Two different approaches of disorder are employed, the resulting differences in the spectra are discussed, and the conditions for their utilization are described. Special attention is paid to quantum coherence dynamics of a single unit cell and the full-sized J-aggregate. Possibilities of probing quantum coherences, as well as performing quantum control via two-color 2D PE spectroscopy, are discussed.

Unraveling the Correlated Dynamics of the Double Hydrogen Bonds of Nucleic Acid Base Pairs in Solution

Quantum mechanics/molecular mechanics hybrid simulations (CPMD/GROMOS) of nonlinear infrared spectra are performed for a modified adenine-uracil base pair in CDCl(3) solution. Employing a mapping between hydrogen bond distances and fundamental as well as overtone transition frequencies on the basis of on-the-fly snapshot potential energy curves, energy gap correlation functions are established. These correlation functions are utilized to determine pump-probe and two-dimensional photon echo spectra. Analysis of the latter yields off-diagonal peaks signifying correlated fluctuations of the N-H···N and N-H···O hydrogen bonds.

Water Hydrogen Bond Dynamics in Aqueous Solutions of Amphiphiles

The hydrogen bond dynamics of water in a series of amphiphilic solute solutions are investigated through simulations and analytic modeling with an emphasis on the interpretation of experimentally accessible two-dimensional infrared (2D IR) photon echo spectra. We evidence that for most solutes the major effect in the hydration dynamics comes from the hydrophilic groups. These groups can retard the water dynamics much more significantly than can hydrophobic groups by forming strong hydrogen bonds with water. By contrast, hydrophobic groups are shown to have a very moderate effect on water hydrogen bond breaking kinetics. We also present the first calculation of the 2D IR spectra for these solutions. While 2D IR spectroscopy is a powerful technique to probe water hydrogen bond network fluctuations, interpretations of aqueous solution spectra remain ambiguous. We show that a complementary approach through simulations and calculation of the spectra lifts the ambiguity and provides a clear connection between the simulated molecular picture and the experimental spectroscopy data. For amphiphilic solute solutions, we show that, in contrast with techniques such as NMR or ultrafast anisotropy, 2D IR spectroscopy can discriminate between waters next to the solutes hydrophobic and hydrophilic groups. We also evidence that the water dynamics slowdown due to the hydrophilic groups is dramatically enhanced in the 2D IR spectral relaxation, because these groups can induce a slow chemical exchange with the bulk, even when recognized exchange signatures are absent. Implications for the understanding of water around chemically heterogeneous systems such as protein surfaces and for the interpretation of 2D IR spectra in these cases are discussed.