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Accounts of Chemical Research

Coherent Multidimensional Optical Probes for Electron Correlations and Exciton Dynamics: From NMR to X-rays

Shaul Mukamel, Darius Abramavičius, Lijun Yang, Wei Zhuang, Igor V. Schweigert, Dmitri V. Voronine

Published Mar 26, 2009• 97 citations
Publisher

Abstract

Over the past 15 years, researchers have extended the multidimensional techniques which originated with NMR in the 1970s to infrared and visible coherent spectroscopy. These advances have dramatically enhanced the temporal resolution from the microsecond to the femtosecond regime. NMR spectroscopists have developed principles for the design of pulse sequences that enhance selected spectral features and reveal desired dynamical events. Extending these principles to the optical regime offers numerous opportunities for narrowing the line shapes in specific directions, unraveling weak cross-peaks from otherwise congested spectra, and controlling the interferences between quantum pathways. We can achieve these enhancements by shaping the spectral and temporal profiles of the pulses. Pulse polarization shaping may lead to unique probes of time-dependent chirality. In this Account, we compare two types of signals. The first, the photon echo, is generated in the direction -k(1) + k(2) + k(3), and the second, double quantum coherence, is detected at +k(1) + k(2) - k(3). Here k(1), k(2), and k(3) are the wave vectors of the three incoming pulses in chronological order. We illustrate the novel information extracted from these signals by simulations of three physical systems. In the first system, spectra of GaAs semiconductor quantum wells provide a direct look at many-body electron correlation effects. We directly observe specific projections of the many-electron wave function, which we can use to test the quality of various levels of computational techniques for electronic structure. Secondly, the spectra of photosynthetic aggregates reveal couplings between chromophores, quantum coherence signatures of chromophore entanglement, and energy-transfer pathways. Using some fundamental symmetries of pulse polarization configurations of nonlinear signals, we can construct superpositions of signals designed to better distinguish among various coherent and incoherent exciton transport pathways and amplify subtle variations among different species of the Fenna-Matthews-Olson (FMO) antenna complex. Both of the first two applications require femtosecond pulses of light in the visible range. The third application demonstrates how resonant core spectroscopy may be used to generate core excitations that are highly localized at selected atoms. Such signals can monitor the motions of valence electron wavepackets in real space with atomic spatial resolution. These future X-ray applications will require attosecond bright X-ray sources, which are currently being developed in several labs. Common principles underlie these techniques in coherent spectroscopy for spins, valence electrons, and core electronic excitations, spanning frequencies from radiowaves to hard X-rays.

DOI
10.1021/ar800258z

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Over the past 15 years, researchers have extended the multidimensional techniques which originated with NMR in the 1970s to infrared and visible coherent spectroscopy. These advances have dramatically enhanced the temporal resolution from the microsecond to the femtosecond regime. NMR spectroscopists have developed principles for the design of pulse sequences that enhance selected spectral features and reveal desired dynamical events. Extending these principles to the optical regime offers numerous opportunities for narrowing the line shapes in specific directions, unraveling weak cross-peaks from otherwise congested spectra, and controlling the interferences between quantum pathways. We can achieve these enhancements by shaping the spectral and temporal profiles of the pulses. Pulse polarization shaping may lead to unique probes of time-dependent chirality. In this Account, we compare two types of signals. The first, the photon echo, is generated in the direction -k(1) + k(2) + k(3), and the second, double quantum coherence, is detected at +k(1) + k(2) - k(3). Here k(1), k(2), and k(3) are the wave vectors of the three incoming pulses in chronological order. We illustrate the novel information extracted from these signals by simulations of three physical systems. In the first system, spectra of GaAs semiconductor quantum wells provide a direct look at many-body electron correlation effects. We directly observe specific projections of the many-electron wave function, which we can use to test the quality of various levels of computational techniques for electronic structure. Secondly, the spectra of photosynthetic aggregates reveal couplings between chromophores, quantum coherence signatures of chromophore entanglement, and energy-transfer pathways. Using some fundamental symmetries of pulse polarization configurations of nonlinear signals, we can construct superpositions of signals designed to better distinguish among various coherent and incoherent exciton transport pathways and amplify subtle variations among different species of the Fenna-Matthews-Olson (FMO) antenna complex. Both of the first two applications require femtosecond pulses of light in the visible range. The third application demonstrates how resonant core spectroscopy may be used to generate core excitations that are highly localized at selected atoms. Such signals can monitor the motions of valence electron wavepackets in real space with atomic spatial resolution. These future X-ray applications will require attosecond bright X-ray sources, which are currently being developed in several labs. Common principles underlie these techniques in coherent spectroscopy for spins, valence electrons, and core electronic excitations, spanning frequencies from radiowaves to hard X-rays.
Heteronuclear multi-quantum spectroscopy is a powerful part of the NMR toolbox, commonly used to identify specific sequences of atoms in complex pulse sequences designed to determine the structure of complex molecules, including proteins. Optical coherent multidimensional spectroscopy (CMDS) is analogous to multidimensional NMR and many of the techniques of NMR have been adapted for application in the optical regime. This has been highly successful, with CMDS being used to understand energy transfer in photosynthesis and many body effects in semiconductor nanostructures amongst many other scientific breakthroughs. Experimental challenges have, however, prevented the translation of heteronuclear multi-quantum NMR to the optical regime, where capabilities to isolate signals in otherwise congested spectra, reduce acquisition times and enable more incisive probes of multi-particle correlations and complex electronic systems would have great benefit. Here we utilise a diffraction based pulseshaper to impose the two key avenues of selectivity required for the analogue of heteronuclear multi-quantum spectrocopy, - control of the individual pulse spectra, and control of the order and timing of interactions - while maintaining phase-locked excitation pulses. We utilise this approach to isolate the 2-quantum signal from a mixed two exciton state in a semiconductor coupled quantum well. The removal of other overlapping peaks allows analysis of the relevant peak shape and thus details of interactions with the environment and other carriers. An alternative pulse ordering also identifies a 2-quantum state associated only with a GaAs defect, the signature of which would otherwise be confused with other interaction induced effects. The experimental approach described here provides access to crucial details of excitonic interactions, which are important in a range of material systems
Multidimensional analysis of coherent signals is commonly used in nuclear magnetic resonance to study correlations among spins. These techniques were recently extended to the femtosecond regime and applied to chemical, biological and semiconductor systems. In this work, we apply a two-dimensional correlation spectroscopy technique which employs double-quantum-coherence to investigate many-body effects in a semiconductor quantum well. The signal is detected along the direction k(1)+ k(2)- k(3), where k(1), k(2) and k(3) are the pulse wave vectors in chronological order. We show that this signal is particularly sensitive to many-body correlations which are missed by time-dependent Hartree-Fock approximation. The correlation energy of two-exciton can be probed with a very high resolution arising from a two-dimensional correlation spectrum, where two-exciton couplings spread the cross peaks along both axes of the 2D spectrum to create a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo (-k(1)+ k(2)+ k(3)).
Nonlinear spectroscopic techniques using entangled photon pairs can provide an opportunity to exploit non-classical correlations encoded in two-photon wavefunctions to manipulate two-exciton wavefunctions. We propose an entangled photon pair-enhanced multidimensional spectroscopic technique that is sensitive to exciton-exciton interactions and correlations at the femtosecond timescale. Simulations for a dissipative system, namely, the photosynthetic aggregate reveal the superior ability of entangled photon pairs, compared to both transform-limited and frequency-chirped laser pulses, to manipulate excited-state absorption pathways. The corresponding spectral features in the two-dimensional spectrogram are interpreted in terms of one- and two-exciton resonances. The signal scales linearly with the incoming intensity of the photon sources. We show that classifying these resonances using entangled photon source in the perturbative limit allow for probing exciton correlations at the natural energy scale. These insights can be used to explore multi-exciton dynamics in molecular systems using multiphoton entanglement.
The correlated behavior of electrons determines the structure and optical properties of molecules, semiconductors, and other systems. Valuable information on these correlations is provided by measuring the response to femtosecond laser pulses, which probe the very short time period during which the excited particles remain correlated. The interpretation of four-wave-mixing techniques, commonly used to study the energy levels and dynamics of many-electron systems, is complicated by many competing effects and overlapping resonances. Here we propose a coherent optical technique, specifically designed to provide a background-free probe for electronic correlations in many-electron systems. The proposed signal pulse is generated only when the electrons are correlated, which gives rise to an extraordinary sensitivity. The peak pattern in two-dimensional plots, obtained by displaying the signal versus two frequencies conjugated to two pulse delays, provides a direct visualization and specific signatures of the many-electron wave functions.
The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.
New generations of ultrashort and intense laser pulses as well ashigh power synchrotron radiation sources and x-ray free electronlasers have promoted fast developments in nonlinear optics andx-ray spectroscopy.The new experimental achievements and the appearance of varieties of novelnonlinear phenomena call for further development of theories. The objective of this thesis is to develop and apply thetheories to explain existing experimental data and to suggest new experiments. The first part of the thesis is devoted to nonlinear propagation of optical pulses. It is shown that the vibrational levels can be selectively populated by varying the duration, shape and intensity of the pump pulse. We obtained a strict analytical solution for the resonant two-photon interaction in a multilevel system beyond rotating wave approximation. Simulations show that the polarization anisotropy of the two-photon excitation affects strongly the anisotropy of photobleaching.The two-photon area theorem is reformulated with taking into account the dynamical Stark shift and the contribution from the permanent dipole moments. In general the dynamical Stark shift does not allow complete population of the excited state, but it can be compensated by detunings in atoms. A dynamical theory of the sequential two-photon absorption of microsecond pulses is developed to explore the role of transverse inhomogeneity of the light beam on optical limiting properties. The propagation of ultrashort laser pulses in nondipolar and dipolar media is investigated with special attention to the generation of superfluorescence and supercontinuum and the formation of attosecond pulses. The second part of the thesis addresses the interaction of molecules with x-ray radiation. We explore here the role of nuclear dynamics in resonant Auger scattering. Multimode simulations of the Auger spectra of ethylene molecule explain the main spectral features of the experimental spectra and show that the spectral profiles are formed mainly due to six vibrational modes. We predict the Doppler splitting of the atomic peak in resonant Auger scattering from SF6 molecule for circularly polarized x-rays. This effect is confirmed by the recent experiment. A new scheme of x-ray pump-probe spectroscopy, namely, resonant inelastic x-ray scattering accompanied by core-hole hopping induced by strong laser fields is suggested. The laser-induced promotion of core holes opens the symmetry forbidden scattering channels and gives rise to new spectral lines in the x-ray scattering spectrum. The strength of the symmetry forbidden lines becomes strong when the time of Rabi flopping is shorter than the lifetime of the core-excited state. We study the role of propagation of femtosecond x-ray free-electron pulses on the Auger process. Simulations show that there exists a strong competition between Auger decay and stimulated emission. The Auger yield and Auger branching ratio are strongly suppressed in the course of pulse propagation.