Line shape of time-resolved four-wave mixing

Wegener, Martin; Chemla, D. S.; Schmitt‐Rink, S.; Schäfer, Wilfried

doi:10.1103/physreva.42.5675

Cited by 355 publications

(195 citation statements)

References 27 publications

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“…2), but was shown to be independent of t d , in contrast to the behaviour expected for the photon echo signal from inhomogeneous systems 14 . The time-integrated signal at negative time delays, and the delayed peak in the time-resolved signals were explained in terms of local ®elds resulting from Coulomb interactions 19 . A more detailed discussion of the physical origins of these effects is given in the next section.…”

Section: Nonlinear Optical Response Of Semiconductorsmentioning

confidence: 99%

Many-body and correlation effects in semiconductors

Chemla

Shah²

2001

Nature

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335

304

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Solids consist of 10 22 ±10 23 particles per cubic centimetre, interacting through in®nite-range Coulomb interactions. The linear response of a solid to a weak external perturbation is well described by the concept of non-interacting`quasiparticles' ®rst introduced by Landau. But interactions between quasiparticles can be substantial in dense systems. For example, studies over the past decade have shown that Coulomb correlations between quasiparticles dominate the nonlinear optical response of semiconductors, in marked contrast to the behaviour of atomic systems. These Coulomb correlations and other many-body interactions are important not only for semiconductors, but also for all condensed-matter systems.O ne of the most fascinating properties of quantum mechanical systems is that they can be in entangled states, that is, a coherent superposition of eigenstates unknown in classical systems. Entangled states have been observed in atomic physics, but they remain elusive in condensed matter. The primary dif®culty is that they survive only as long as the coherence is maintained, and numerous processes conspire to produce decoherence, dephasing and relaxation on an extremely short timescale (,10 -12 s) in condensed matter, which is typically composed of 10 22 ±10 23 particles cmthat interact through the in®nite-range Coulomb force. The complexity of the problem makes any theoretical approach extremely dif®cult. About ®ve decades ago, Landau proposed that real particles, strongly interacting among themselves but evolving in the real vacuum, be mapped onto`quasiparticles' . The quasiparticles arè dressed' by a part of the interaction, and are relatively long-lived excitations of the many-body system evolving in a`new vacuum' that consists of the`rest' of the many-body system and the part of the Coulomb interaction not accounted for in the quasiparticles. The quasiparticles are complex objects (Cooper pairs in a superconductor, excitons in a semiconductor, and so forth), and the new vacuum itself can be structured (it can have an antiferromagnetic order in the copper oxides) and dynamical (it can sustain phonons and magnons). For many solids, the concept of quasiparticles has been very useful for describing the ground state and small departures from it, that is, the most basic excitation and the linear response to weak external perturbations. However, the part of the Coulomb forces not accounted for in the formation of quasiparticles leads to interactions between these quasiparticles, inducing nonlinearities and destroying their phase coherence. Scientists interested in the linear response of a many-body system like to call these interactions`residual' . They are, however, not small, as shown below. They are residual only in the sense that we do not know (yet) how to treat them correctly. Understanding the in¯u-ence of these many-body interactions and Coulomb correlations is one of the central challenges of condensed-matter physics. Semiconductors form an ideal laboratory for quantitatively investigating the role of Co...

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Section: Nonlinear Optical Response Of Semiconductorsmentioning

confidence: 99%

Many-body and correlation effects in semiconductors

Chemla

Shah²

2001

Nature

Self Cite

335

304

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“…The first and most prominent was a signal for the ''wrong'' time delay in a two-pulse TFWM experiment. Theoretically, such signals could arise from several effects including local fields (3,4), biexcitons (5), excitation-induced dephasing (6, 7), or excitation-induced shift (8). Time resolving the signal also provided evidence for many-body contributions (9,10), although it did not resolve the ambiguity regarding the underlying phenomena.…”

mentioning

confidence: 99%

Polarization-dependent optical 2D Fourier transform spectroscopy of semiconductors

Zhang

Кузнецова

Meier

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

118

113

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Optical 2D Fourier transform spectroscopy (2DFTS) provides insight into the many-body interactions in direct gap semiconductors by separating the contributions to the coherent nonlinear optical response. We demonstrate these features of optical 2DFTS by studying the heavy-hole and light-hole excitonic resonances in a gallium arsenide quantum well at low temperature. Varying the polarization of the incident beams exploits selection rules to achieve further separation. Calculations using a full many-body theory agree well with experimental results and unambiguously demonstrate the dominance of many-body physics.excitons ͉ many-body effects ͉ ultrafast O ptical excitation of a direct gap semiconductor, such as gallium arsenide (GaAs), produces electron-hole pairs. The Coulomb attraction between the electron and hole can result in a bound state, known as an exciton, with a hydrogenic wavefunction for the relative coordinate. Excitons have a large oscillator strength because of the proximity of the electron and hole and thus can dominate the absorption spectrum close to the fundamental band gap. In GaAs heterostructures, the exciton binding energy is of order 10 meV; thus, excitonic resonances appear only at low temperatures. Excitons and unbound electron-hole pairs exhibit dynamics on a femtosecond-to-picosecond time scale. These timescales, combined with the strong interaction with light, make ultrafast spectroscopy an ideal tool for studying carrier dynamics in semiconductors.Over the last two decades, excitonic resonances in semiconductors have been studied extensively by using ultrafast spectroscopy, primarily transient four-wave-mixing (TFWM) (1, 2). The measurements clearly showed signatures of many-body effects. The first and most prominent was a signal for the ''wrong'' time delay in a two-pulse TFWM experiment. Theoretically, such signals could arise from several effects including local fields (3, 4), biexcitons (5), excitation-induced dephasing (6, 7), or excitation-induced shift (8). Time resolving the signal also provided evidence for many-body contributions (9, 10), although it did not resolve the ambiguity regarding the underlying phenomena.Recent results using optical 2D Fourier transform spectroscopy (2DFTS) to study the exciton resonances have shown that much more information is obtained, promising a more stringent test of the theory (11). 2DFTS traces its roots to NMR (12). Recently, there has been significant progress in translating multidimensional NMR techniques into the infrared and optical domains for the study of vibrations (13) and electronic excitations (14-16) in molecules. Although the usefulness of adding a second dimension was recognized in TWFM studies of semiconductors (17-20), only the intensity of the emitted signal, not the phase-resolved electric field, was measured. The transient absorption experiments clearly show that detecting only the real part of the emitted field is advantageous (21, 22), but the effects of inhomogeneous broadening cannot be removed. 2DFTS combines the best...

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“…Phase-coherent nonlinear spectroscopic measurements such as four-wave-mixing are sensitive to the changes that occur when excitons interact through Coulomb forces [5] or local fields [6]. Early nonlinear 'self-diffraction' measurements revealed a signal at 'negative' delays due to many-body interactions (MBIs) [6][7][8], but since the exciton coherence frequencies could not be correlated with the emitted coherence frequencies, the contributions due to MBIs such as excitationinduced dephasing (EID) [9], excitation-induced energy shift (EIS) [10], and local field effects (LFEs) [6] could not be distinguished. EID and EIS result in density-dependent collisional broadening and renormalization of the exciton energy, respectively.…”

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confidence: 99%

Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy

et al. 2011

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We use fifth-order two-dimensional electronic spectroscopy to measure coherent four-particle dynamics in a semiconductor nanostructure. By using optical polarization control in two-quantum measurements enabled by the COLBERT spectrometer, we separate coherent signals due to bound biexcitons and unbound two-exciton correlations. The rephasing nature of the measurement allows us to separate homogeneous from inhomogeneous contributions to the two-quantum lineshapes. We find that, unlike the bound biexciton state, the energy of the unbound pair and its homogeneous linewidth depend on the laser fluence. Simulations using an extended phenomenological model help determine the primary interaction mechanism that leads to the formation of the unbound exciton pair; the model also indicates that seventh-order interactions contribute to the measured spectra under high pulse fluences.

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Line shape of time-resolved four-wave mixing

Cited by 355 publications

References 27 publications

Many-body and correlation effects in semiconductors

Many-body and correlation effects in semiconductors

Polarization-dependent optical 2D Fourier transform spectroscopy of semiconductors

Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy

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