Mixed frequency/time domain optical analogues of heteronuclear multidimensional NMR

Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.     

Frequency-domain time-resolved four wave mixing spectroscopy of vibrational coherence transfer with single-color excitation

Triply vibrationally enhanced four-wave mixing spectroscopy is employed to observe vibrational coherence transfer between the asymmetric and symmetric CO-stretching modes of rhodium(I) dicarbonyl acetylacetonate (RDC). Coherence transfer is a nonradiative transition of a coherent superposition of quantum states to a different coherent superposition due to coupling of the vibrational modes through the bath. All three excitation pulses in the experiment are resonant with a single quantum coherence, but coherence transfer results in new coherences with different frequencies. The new output frequency is observed with a monochromator that resolves it from the stronger peak at the original excitation frequency. This technique spectrally resolves pathways that include coherence transfer, discriminates against spectral features created solely by radiative transitions, and temporally resolves modulations created by interference between different coherence transfer pathways. Redfield theory simulates the temporal modulations in the impulsive limit, but it is also clear that coherence transfer violates the secular approximation invoked in most Redfield theories. Instead, it requires non-Markovian and bath memory effects. RDC may provide a simple model for the development of theories that incorporate these effects.     

Spectral quantum beating in mixed frequency/time-domain coherent multidimensional spectroscopy

Coherent multidimensional spectroscopy performed in the mixed frequency/time domain exhibits both temporal and spectral quantum beating when two quantum states are simultaneously excited. The excitation of both quantum states can occur because either the spectral width of the states or the excitation pulse exceeds the frequency separation of the quantum states. The quantum beating appears as a line that broadens and splits into two peaks and then recombines as the time delay between excitation pulses increases. The splitting depends on the spectral width of the excitation pulses. We observe the spectral quantum beating between the two nearly degenerate asymmetric carbonyl stretch modes in a nickel tricarbonyl chelate using the nonrephasing, ground state bleaching coherence pathway in triply vibrationally enhanced four-wave mixing as the time delay between the first two excitation pulses changes.     

Frequency- and time-resolved coherence transfer spectroscopy

Frequency-domain two-color triply vibrational enhanced four-wave mixing using a new phase-matching geometry discriminates against coherent multidimensional spectral features created solely by radiative transitions, spectrally resolves pathways with different numbers of coherence transfer steps, and temporally resolves modulations created by interference between coherence transfer pathways. Coherence transfer is a nonradiative transition where a superposition of quantum states evolves to a different superposition. The asymmetric and symmetric C[triple bond]O stretching modes of rhodium(I) dicarbonyl acetylacetonate are used as a model system for coherence transfer. A simplified theoretical model based on Redfield theory is used to describe the experimental results.     

Coherent spectroscopy in dissipative media: time-domain studies of channel phase and signal interferometry

We extend a recently formulated coherence spectroscopy of dissipative media [J. Chem. Phys. 122, 084502 (2005)] from the stationary excitation limit to the time domain. Our results are based on analytical and numerical solutions of the quantum Liouville equation within the Bloch framework. It is shown that the short pulse introduces a new, controllable time scale that allows better insight into the relation between the coherence signal and the phase properties of the material system. We point to the relation between the time-domain coherence spectroscopy and the method of interferometric two-photon photoemission spectroscopy, and propose a variant of the latter method, where the two time-delayed excitation pathways are distinguishable, rather than identical. In particular, we show that distinguishability of the two excitation pathways introduces the new possibility of disentangling decoherence from population relaxation.     

Electronic coherence effects in photosynthetic light harvesting

Photosynthetic light harvesting is a paradigmatic example for quantum effects in biology. In this work, we review studies on quantum coherence effects in the LH2 antenna complex from purple bacteria to demonstrate how quantum mechanical rules play important roles in the speedup of excitation energy transfer, the stabilization of electronic excitations, and the robustness of light harvesting in photosynthesis. Subsequently, we present our recent theoretical studies on exciton dynamical localization and excitonic coherence generation in photosynthetic systems. We apply a variational-polaron approach to investigate decoherence of exciton states induced by dynamical fluctuations due to system-environment interactions. The results indicate that the dynamical localization of photoexcitations in photosynthetic complexes is significant and imperative for a complete understanding of coherence and excitation dynamics in photosynthesis. Moreover, we use a simple model to investigate quantum coherence effects in intercomplex excitation energy transfer in natural photosynthesis, with a focus on the likelihoods of generating excitonic coherences during the process. Our model simulations reveal that excitonic coherence between acceptor exciton states and transient nonlocal quantum correlation between distant pairs of chromophores can be generated through intercomplex energy transfer. Finally, we discuss the implications of these theoretical works and important open questions that remain to be answered.     

Ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate excited states in molecules: Population and vibrational coherence transfers

Results of a theoretical study of ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate π-electronic excited states of molecules were presented. Analytical expressions for temporal behaviors of population and vibrational coherence were derived using a simplified model to clarify the quantum mechanical interferences between the two coherently excited electronic states, which appeared in the nuclear wavepacket simulations [M. Kanno, H. Kono, Y. Fujimura, S.H. Lin, Phys. Rev. Lett 104 (2010) 108302]. The photon-polarization direction of the linearly polarized laser, which controls the populations of the two quasi-degenerate electronic states, determines constructive or destructive interference. Features of the vibrational coherence transfer between the two coupled quasi-electronic states through nonadiabatic couplings are also presented. Information on both the transition frequency and nonadiabatic coupling matrix element between the two states can be obtained by analyzing signals of two kinds of quantum beats before and after transfer through nonadiabatic coupling.     

Coherent spin control of matrix isolated molecules by IR+UV laser pulses: quantum simulations for ClF in Ar

Two coherent sequential IR+UV laser pulses may be used to generate two time-dependent nuclear wave functions in electronic excited triplet and singlet states via single (UV) and two photon (IR+UV) excitation pathways, exploiting spin-orbit coupling and vibrational pre-excitation, respectively. These wave functions evolve from different Franck-Condon domains until they overlap in a domain of bond stretching with efficient intersystem crossing. Here, the coherence of the laser pulses is turned into optimal interferences of the wave packets, yielding the total wave packet at the target place, time, and with dominant target spin. The time resolution of spin control is few femtoseconds. The mechanism is demonstrated by means of quantum model simulations for ClF in an Ar matrix.     

How Quantum Coherence Assists Photosynthetic Light Harvesting

This perspective examines how hundreds of pigment molecules in purple bacteria cooperate through quantum coherence to achieve remarkable light harvesting efficiency. Quantum coherent sharing of excitation, which modifies excited state energy levels and combines transition dipole moments, enables rapid transfer of excitation over large distances. Purple bacteria exploit the resulting excitation transfer to engage many antenna proteins in light harvesting, thereby increasing the rate of photon absorption and energy conversion. We highlight here how quantum coherence comes about and plays a key role in the photosynthetic apparatus of purple bacteria.     

Recent progress in probing atomic and molecular quantum coherence with scanning tunneling microscopy

Quantum coherent physics and chemistry concern the creation and manipulation of an excited-state manifold that contains the superposition and entanglement of multiple quantum levels. Electromagnetic waves such as light and microwave can be used to generate and probe different quantum coherent phenomena. The recent advances in scanning tunneling microscopy (STM) techniques including ultrafast laser coupled STM and electron spin resonance STM combine electromagnetic excitation with tunneling electron detection, bringing the investigation of quantum coherence down to the atomic and molecular level. Here, we survey the latest STM studies of different quantum coherent phenomena covering molecular vibration, electron transfer, surface plasmon resonance, phonon, spin oscillation, and electronic transition, and discuss the state and promise of characterizing and manipulating quantum coherence at the atomic or molecular scale.     

Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy

The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence of excited-state asymmetric vibrations in those experiments.     

Multiresonant coherent multidimensional vibrational spectroscopy of aromatic systems: pyridine, a model system

Multiresonant four wave mixing has been used to measure the coherent multidimensional spectroscopy (CMDS) of representative aromatic ring modes using pyridine as a model system. This work identifies the cross-peaks that appear between several modes and measures their coherent and incoherent dynamics. The work also explores the consequences of using multiresonant CMDS for molecules with transition moments that are typical of most vibrational modes. Typically, CMDS experiments rely on using transitions with exceptionally large transition moments. To observe cross-peaks, the pyridine concentration was raised until absorption effects became very important. These effects interfere with the parametric CMDS coherence pathways, but they do not make important contributions to the nonparametric pathways.     

Coherence transfer echoes

A novel class of echo phenomena in coherent spectroscopy is described where defocusing and refocusing of coherence takes place at two different transition frequencies. Examples of heteronuclear transfer echoes and of multiple quantum transfer echoes in nuclear magnetic resonance are presented.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

Theoretical investigation of the mechanism and dynamics of intramolecular coherent resonance energy transfer in soft molecules: a case study of dithia-anthracenophane

A computational study is conducted on dithia-anthracenophane (DTA), for which there is experimental evidence for coherent resonance energy transfer dynamics, and on dimethylanthracene (DMA), a molecule representing the energy donor and the acceptor in DTA. Electronic excitation energies are calculated by configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT) methods and are compared to experimental ones. Electronic coupling constants are calculated between two DMAs embedded into the ground-state structure of DTA employing methods based on transition densities. The resulting values of electronic coupling provide a more consistent interpretation of experiments than those based on one-half the level spacing of DTA excitation energies. Solvation effects are studied based on the polarizable continuum model (PCM). Solvent-induced polarization and screening effects are shown to make opposite contributions, and the net electronic coupling is little different from the value in a vacuum. The likelihood of coherent population transfer is assessed on the basis of a recently developed theory of coherent resonance energy transfer. The time scale of bath is shown to have an important role in sustaining the quantum coherence. The combination of quantum chemical and dynamical data suggests that the electronic coupling in DTA is in the range of 50-100 cm(-1). The presence of oscillatory excitation population dynamics can be understood from the picture of polaronic excitation moderately dressed with dispersive vibrational modes. The effect of torsional modulation on the excitation energies of DTA and electronic coupling is examined on the basis of optimized structures with the torsional angle constrained. The result suggests that inelastic effect due to torsional motion cannot be disregarded in DTA.     

Vibrational coherence transfer characterized with Fourier-transform 2D IR spectroscopy

Two-dimensional infrared (2D IR) spectroscopy of the symmetric and asymmetric C[Triple Bond]O stretching vibrations of Rh(CO)(2)acac in hexane has been used to investigate vibrational coherence transfer, dephasing, and population relaxation in a multilevel vibrational system. The transfer of coherence between close-lying vibrational frequencies results in extra relaxation-induced peaks in the 2D IR spectrum, whose amplitude depends on the coherence transfer rate. Coherence transfer arises from the mutual interaction of the bright CO stretches with dark states, which in this case reflects the mutual d-pi(*) back bonding of the Rh center to both the terminal carbonyls and the acetylacenonate ligand. For 2D IR relaxation experiments with variable waiting times, coherent dynamics lead to the modulation of peak amplitudes, while incoherent population relaxation and exchange results in the growth of the relaxation-induced peaks. We have modeled the data by propagating the density matrix with the Redfield equation, incorporating all vibrational relaxation processes during all three experimental time periods and including excitation reorientation effects arising from relaxation. Coherence and population transfer time scales from the symmetric to the asymmetric stretch were found to be 350 fs and 3 ps, respectively. We also discuss a diagrammatic approach to incorporating all vibrational relaxation processes into the nonlinear response function, and show how coherence transfer influences the analysis of structural variables from 2D IR spectroscopy.     

Inhomogeneous dephasing masks coherence lifetimes in ensemble measurements

An open question at the forefront of modern physical sciences is what role, if any, quantum effects may play in biological sensing and energy transport mechanisms. One area of such research concerns the possibility of coherent energy transport in photosynthetic systems. Spectroscopic evidence of long-lived quantum coherence in photosynthetic light-harvesting pigment protein complexes (PPCs), along with theoretical modeling of PPCs, has indicated that coherent energy transport might boost efficiency of energy transport in photosynthesis. Accurate assessment of coherence lifetimes is crucial for modeling the extent to which quantum effects participate in this energy transfer, because such quantum effects can only contribute to mechanisms proceeding on timescales over which the coherences persist. While spectroscopy is a useful way to measure coherence lifetimes, inhomogeneity in the transition energies across the measured ensemble may lead to underestimation of coherence lifetimes from spectroscopic experiments. Theoretical models of antenna complexes generally model a single system, and direct comparison of single system models to ensemble averaged experimental data may lead to systematic underestimation of coherence lifetimes, distorting much of the current discussion. In this study, we use simulations of the Fenna-Matthews-Olson complex to model single complexes as well as averaged ensembles to demonstrate and roughly quantify the effect of averaging over an inhomogeneous ensemble on measured coherence lifetimes. We choose to model the Fenna-Matthews-Olson complex because that system has been a focus for much of the recent discussion of quantum effects in biology, and use an early version of the well known environment-assisted quantum transport model to facilitate straightforward comparison between the current model and past work. Although ensemble inhomogeneity is known to lead to shorter lifetimes of observed oscillations (simply inhomogeneous spectral broadening in the time domain), this important fact has been left out of recent discussions of spectroscopic measurements of energy transport in photosynthesis. In general, these discussions have compared single-system theoretical models to whole-ensemble laboratory measurements without addressing the effect of inhomogeneous dephasing. Our work addresses this distinction between single system and ensemble averaged observations, and shows that the ensemble averaging inherent in many experiments leads to an underestimation of coherence lifetimes in individual systems.     

Single-shot gradient-assisted photon echo electronic spectroscopy

Two-dimensional electronic spectroscopy (2D ES) maps the electronic structure of complex systems on a femtosecond time scale. While analogous to multidimensional NMR spectroscopy, 2D optical spectroscopy differs significantly in its implementation. Yet, 2D Fourier spectroscopies still require point-by-point sampling of the time delay between two pulses responsible for creating quantum coherence among states. Unlike NMR, achieving the requisite phase stability at optical frequencies between these pulse pairs remains experimentally challenging. Nonetheless, 2D optical spectroscopy has been successfully demonstrated by combining passive and active phase stabilization along with precise control of optical delays and long-term temperature stability, although the widespread adoption of 2D ES has been significantly hampered by these technical challenges. Here, we exploit an analogy to magnetic resonance imaging (MRI) to demonstrate a single-shot method capable of acquiring the entire 2D spectrum in a single laser shot using only conventional optics. Unlike point-by-point sampling protocols typically used to record 2D spectra, this method, which we call GRadient-Assisted Photon Echo (GRAPE) spectroscopy, largely eliminates phase errors while reducing the acquisition time by orders of magnitude. By incorporating a spatiotemporal encoding of the nonlinear polarization along the excitation frequency axis of the 2D spectrum, GRAPE spectroscopy achieves no loss in signal while simultaneously reducing overall noise. Here, we describe the principles of GRAPE spectroscopy and discuss associated experimental considerations.