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arXiv:0711.1848 · The Journal of Chemical Physics

A coherent nonlinear optical signal induced by electron correlations

Shaul Mukamel, Rafał Oszwałdowski, Lijun Yang

Published Dec 13, 2007• 45 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.2820379

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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.
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.
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)).
We propose a three-pulse coherent ultrafast optical technique that is particularly sensitive to two-exciton correlations. Two Liouville-space pathways for the density matrix contribute to this signal which reveals double quantum coherences when displayed as a two-dimensional correlation plot. Two-exciton couplings spread the cross peaks along both axes, creating 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, in which two-exciton couplings show up along a single axis and are highly congested.
Nonlinear optical signals in optically driven quantum systems can reveal coherences and thereby open up the possibility for manipulation of quantum states. While the limiting cases of ultrafast and continuous-wave excitation have been extensively studied, the time dynamics of finite pulses bear interesting phenomena. In this paper, we explore the nonlinear optical probe signals of a two-level system excited with a laser pulse of finite duration. In addition to the prominent Mollow peaks, the probe spectra feature several smaller peaks for certain time delays. Similar features have been recently observed for resonance fluorescence signals [K. Boos , ]. We discuss that the emergent phenomena can be explained by a combination of Mollow triplet physics and perturbed free induction decay effects, providing an insightful understanding of the underlying physics. Published by the American Physical Society 2024
Understanding the effect of strong laser pulses on the evolution of an atomic or molecular wave function is important in the context of coherent control in the strong-field regime, when power broadening and dynamic Stark shifts become comparable with or bigger than the bandwidth of the control field. We experimentally demonstrate the method of complete characterization of a complex-valued amplitude of a quantum state driven by a strong two-photon field. The method is based on coherent scattering of a weak probe pulse from the strong-field-induced atomic coherence, followed by the detection of the time- and frequency-resolved parametric four-wave-mixing signal. We show that the proposed technique corresponds to a cross-correlation frequency-resolved optical gating (XFROG) of the highly perturbed evolution of an atomic quantum state. Utilizing the XFROG retrieval algorithm, we determine both the amplitude and phase of an atomic wave function at any time moment throughout the interaction with the driving field. The direct retrieval of the time-dependent phase of the wave function, rather than the population dynamics only, enables us to observe the strong-field effects with arbitrary time and frequency resolution.
We show theoretically that a quantum system in a nonequilibrium state interacting with a set of laser pulses in a four-wave-mixing setup leads to signal emission in directions opposite to the ones usually considered. When combined with a pump mechanism which sets a time origin for the nonequilibrium state creation, this particular optical response can be utilized to directly follow decoherence processes in real time. By varying the time delays within the probe sequence, signals in these unconventional directions can also be used to detect two-dimensional spectra determined by the dynamics of up to three-quantum coherences, revealing energetical anharmonicities and environmental influences. As a numerical example, these findings are demonstrated by considering a model of vibrational decoherence of carbon monoxide after photolysis from a hemeprotein.