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Few-cycle THz pulses are employed to resonantly access the internal fine structure of photogenerated excitons in semiconductors, on the femtosecond time scale. This technique allows us to gain novel insight into many-body effects of excitons and reveal key quantum optical processes. We discuss experiments that monitor the density-dependent re?normalization of the binding energy of a high-density exciton gas in GaAs/AlGaAs quantum wells close to the Mott transition. In a dilute ensemble of 3p excitons in Cu2O, stimulated THz emission from internal transitions to the energetically lower 2s state is observed at a photon energy of 6.6 meV, with a cross section of 10-14 cm2. Simultaneous interband excitation of both exciton levels drives quantum beats, which cause efficient THz emission at the difference frequency. By extending this principle to various other exciton resonances, we develop a novel way of mapping the fine structure by two-dimensional THz emission spectroscopy.

Excitons are of fundamental interest and of importance foropto-electronic applications of bulk and nano-structured semiconductors.This paper discusses the utilization of ultrafast terahertz (THz) pulsesfor the study of characteristic low-energy excitations of photoexcitedquasi 2D electron-hole (e-h) gases. Optical-pump THz-probe spectroscopyat 250-kHz repetition rate is employed to detect characteristic THzsignatures of excitons and unbound e-h pairs in GaAs quantum wells.Exciton and free-carrier densities are extracted from the data using atwo-component model. We report the detailed THz response and pairdensities for different photoexcitation energies resonant to heavy-holeexcitons, light-hole excitons, or the continuum of unbound pairs. Suchexperiments can provide quantitative insights into wavelength, time, andtemperature dependence of the low-energy response and composition ofoptically excited e-h gases in low-dimensionalsemiconductors.

We present a many-body theory of the non-linear optical response of the Quantum Hall system. This theory describes the role of the cold, strongly correlated, two-dimensional electron gas (2DEG) in the ultrafast dynamics. We discuss the manifestations of intraband and interband coherences induced by the collective 2DEG excitations in the coupled photocarrier-Quantum Hall system. We compare to transient three-pulse four-wave-mixing experiments.

Using the non linear optical technique of 3-pulse 4-wave mixing, we study the dynamics of the collective excitations of the quantum Hall system. We excite the system with 100 fs pulses propagating in directions k 1 and k 3 and then probe its time evolution with a delayed pulse k 2 . We measure the non-linear optical response from the lowest Landau level along the direction k 1 + k 2 − k 3 . As function of the time delay of pulse k 2 , this signal shows striking beats for short time delays (∼500 fs), followed by a rise (∼20 ps) and then a decay (∼100 ps). We identify the microscopic origin of this dynamics by extending the standard theory of ultra fast nonlinear optics to include the effects of the correlations.

We study the role of many-body correlations in the ultrafast dynamics of quantum well magnetoexcitons. In linear response, inter-Landau level transitions are suppressed if magnetic field is stronger than magnetoexciton binding energy. However, in nonlinear response, two-electron Auger processes remain unsuppressed even at very strong field. We show that Auger scattering plays a dominant role in the coherent exciton dynamics in strong magnetic field. We perform numerical calculations of four-wave-mixing (FWM) polarization which incorporate Auger processes nonperturbatively, and find a strong amplitude enhancement of the FWM signal accompanied with polarization oscillations at negative time delays. We identify these oscillations as quantum beats between dark two-exciton states related to each other via Auger processes.

Degenerate exciton systems have been produced in quasi–two-dimensional confined areas in semiconductor coupled quantum well structures. We observed contractions of clouds containing tens of thousands of excitons within areas as small as (10 μm) 2 near 10 kelvin. The spatial and energy distributions of optically active excitons were determined by measuring photoluminescence as a function of temperature and laser excitation and were used as thermodynamic quantities to construct the phase diagram of the exciton system, which demonstrates the existence of distinct phases. Understanding the formation mechanisms of these degenerate exciton systems can open new opportunities for the realization of Bose-Einstein condensation in the solid state.

We employ a novel, ultrafast terahertz probe to investigate the dynamical interplay of optically-induced excitons and unbound electron-hole pairs in GaAs quantum wells. Resonant creation of heavy-hole excitons induces a new low-energy oscillator linked to transitions between the internal exciton degrees of freedom. The time resolved terahertz optical conductivity is found to be a probe well suited for studies of fundamental processes such as formation, relaxation and ionization of excitons.

We review recent investigations of the femtosecond non-linear optical response of the two-dimensional electron gas (2DEG) in the quantum Hall effect regime. We find that the time and frequency profile of the four-wave-mixing non-linear optical spectrum is strongly influenced by Coulomb correlations between the photoexcited electron–hole pairs and the 2DEG collective excitations. We discuss experimental and theoretical results showing non-Markovian memory effects in the polarization dephasing, and an optically induced time-dependent coupling between the two lowest Landau level magnetoexcitons.

Using time resolved four-wave-mixing (FWM) spectroscopy and many-body theory we investigate the role of non-instantaneous collective and correlation effects in the dynamics of the cold two dimensional electron gas (2DEG) in large magnetic fields. We find a strong non-Markovian magnetoexciton dephasing and a strong time-dependent Coulomb coupling between the Landau levels (LL), governed by the dynamics of the inter-LL magnetoplasmon (MP) excitations. Our results show that ultrafast spectroscopy is a powerful tool for studying collective and strong correlation effects on the nanoscale.

An exciton is an electron-hole bound pair in a semiconductor. In the low-density limit, it is a composite Bose quasi-particle, akin to the hydrogen atom. Just as in dilute atomic gases, reducing the temperature or increasing the exciton density increases the occupation numbers of the low-energy states leading to quantum degeneracy and eventually to Bose-Einstein condensation (BEC). Because the exciton mass is small--even smaller than the free electron mass--exciton BEC should occur at temperatures of about 1 K, many orders of magnitude higher than for atoms. However, it is in practice difficult to reach BEC conditions, as the temperature of excitons can considerably exceed that of the semiconductor lattice. The search for exciton BEC has concentrated on long-lived excitons: the exciton lifetime against electron-hole recombination therefore should exceed the characteristic timescale for the cooling of initially hot photo-generated excitons. Until now, all experiments on atom condensation were performed on atomic gases confined in the potential traps. Inspired by these experiments, and using specially designed semiconductor nanostructures, we have collected quasi-two-dimensional excitons in an in-plane potential trap. Our photoluminescence measurements show that the quasi-two-dimensional excitons indeed condense at the bottom of the traps, giving rise to a statistically degenerate Bose gas.

We present evidence from both linear and nonlinear optical spectroscopy for the existence of distinct exciton types at the charge-transfer gap of Sr 2 CuO 2 Cl 2 , which are linked by strong, phonon-mediated coupling. We show how several basic optical properties of this material depend on these excitations.

▪ Abstract We outline recent developments in biological single-molecule fluorescence detection with particular emphasis on observations by ratiometric fluorescence resonance energy transfer (FRET) of biomolecules freely diffusing in solution. Single-molecule-diffusion methodologies were developed to minimize perturbations introduced by interactions between molecules and surfaces. Confocal microscopy is used in combination with sensitive detectors to observe bursts of photons from fluorescently labeled biomolecules as they diffuse through the focal volume. These bursts are analyzed to extract ratiometric observables such as FRET efficiency and polarization anisotropy. We describe the development of single-molecule FRET methodology and its application to the observation of the Förster distance dependence and the study of protein folding and polymer physics problems. Finally, we discuss future advances in data acquisition and analysis techniques that can provide a more complete picture of the accessible molecular information.

We present single-pair fluorescence resonance energy transfer (spFRET) observations of individual opening and closing events of surface-immobilized DNA hairpins. Two glass-surface immobilization strategies employing the biotin-streptavidin interaction and a third covalent immobilization strategy involving formation of a disulfide bond to a thiol-derivatized glass surface are described and evaluated. Results from image and time-trace data from surface-immobilized molecules are compared with those from freely diffusing molecules, which are unperturbed by surface interactions. Using a simple two-state model to analyze the open and closed time distributions for immobilized hairpins, we calculate the lifetimes of the two states. For hairpins with a loop size of 40 adenosines and a stem size of either seven or nine bases, the respective closed-state lifetimes are 45 +/- 2.4 and 103 +/- 6.0 ms, while the respective open-state lifetimes are 133 +/- 5.5 and 142 +/- 22 ms. These results show that the open state of the hairpin is favored over the closed state of the hairpin under these conditions, consistent with previous diffusion fluorescence correlation spectroscopy (FCS) experiments on poly(A)-loop hairpins. The measured open-state lifetime is about 30 times longer than the calculated 3 ms open-state lifetime for both hairpins based on a closing rate scaling factor derived from a previous FCS study for hairpins in diffusion with 12-30 thymidines in their loops. As predicted, the closed-state lifetime is dependent on the stem length and is independent of the loop characteristics. Our findings indicate that current models should consider sequence dependence in calculating ssDNA thermostability. The surface immobilization chemistries and other experimental techniques described here should prove useful for studies of single-molecule populations and dynamics.

The pump-and-probe response of a ZnSe quantum well is investigated. In this particular sample the binding energy far exceeds both the exciton damping and the inhomogeneous broadening. A comparison between experimental data and model calculations shows that with co-circularly polarized beams the nonlinear mean-field contributions dominate those induced by four-particle correlations. In contrast, only the four-particle correlations contribute to the signal in counter-circular configuration. For this configuration, the exciton–biexciton interaction dominates the response for resonant excitation of the exciton. The occurrence of exciton–biexciton transitions leads to a renormalization of the period of coherent oscillations at negative pulse delay.

An optical ruler based on ultrahigh-resolution colocalization of single fluorescent probes is described in this paper. It relies on the use of two unique families of fluorophores, namely energy-transfer fluorescent beads (TransFluoSpheres) and semiconductor nanocrystal quantum dots, that can be excited by a single laser wavelength but emit at different wavelengths. A multicolor sample-scanning confocal microscope was constructed that allows one to image each fluorescent light emitter, free of chromatic aberrations, by scanning the sample with nanometer scale steps with a piezo-scanner. The resulting spots are accurately localized by fitting them to the known shape of the excitation point-spread function of the microscope. We present results of two-dimensional colocalization of TransFluoSpheres (40 nm in diameter) and of nanocrystals (3–10 nm in diameter) and demonstrate distance-measurement accuracy of better than 10 nm using conventional far-field optics. This ruler bridges the gap between fluorescence resonance energy transfer, near- and far-field imaging, spanning a range of a few nanometers to tens of micrometers.

Combining linear polarization excitation and magnetic-field breaking of chiral symmetry of optical transitions in Group-III-V semiconductors, we use resonant degenerate four-wave mixing to observe effects beyond the time-dependent Hartree-Fock theory that are not seen by other techniques. (c) 2000 The American Physical Society.

The optical third-order nonlinearity of a ZnSe-based microcavity is investigated by the pump-and-probe method. In the specially designed non-monolithic sample the biexciton binding energy exceeds all damping constants and the normal-mode splitting between exciton and cavity photon. For counter-circular polarized beams the nonlinear response exhibits strong oscillatory structures in the spectral vicinity of the polariton–biexciton transition. Comparison to model calculations shows that in this case the coherent nonlinearity is completely dominated by biexciton–exciton interactions beyond the Hartree–Fock approximation.

We report single-molecule folding studies of a small, single-domain protein, chymotrypsin inhibitor 2 (CI2). CI2 is an excellent model system for protein folding studies and has been extensively studied, both experimentally (at the ensemble level) and theoretically. Conformationally assisted ligation methodology was used to synthesize the proteins and site-specifically label them with donor and acceptor dyes. Folded and denatured subpopulations were observed by fluorescence resonance energy transfer (FRET) measurements on freely diffusing single protein molecules. Properties of these subpopulations were directly monitored as a function of guanidinium chloride concentration. It is shown that new information about different aspects of the protein folding reaction can be extracted from such subpopulation properties. Shifts in the mean transfer efficiencies are discussed, FRET efficiency distributions are translated into potentials, and denaturation curves are directly plotted from the areas of the FRET peaks. Changes in stability caused by mutation also are measured by comparing pseudo wild-type CI2 with a destabilized mutant (K17G). Current limitations and future possibilities and prospects for single-pair FRET protein folding investigations are discussed.

The large dielectric constant and small effective mass in a semiconductor allows a description of its electronic states in terms of envelope wavefunctions whose energy, time, and length scales are mesoscopic, i.e., halfway between those of atomic and those of condensed matter systems. This property makes it possible to demonstrate and investigate many quantum mechanical, many-body, and quantum kinetic phenomena with tabletop experiments that would be nearly impossible in other systems. This, along with the ability to custom-design semiconductor nanostructures, makes semiconductors an ideal laboratory for experimental investigations. We present an overview of some of the most exciting results obtained in semiconductors in recent years using the technique of ultrafast nonlinear optical spectrocopy. These results show that Coulomb correlation plays a major role in semiconductors and makes them behave more like a strongly interacting system than like an atomic system. The results provide insights into the physics of strongly interacting systems that are relevant to other condensed matter systems, but not easily accessible in other materials.

We study theoretically the coherent nonlinear optical response of doped semiconductors with partially occupied subbands. When the Fermi energy of an occupied subband approaches the exciton level of an upper subband, the absorption spectrum acquires a characteristic double-peak shape originating from the interference between the Fermi-edge singularity and the exciton resonance. We demonstrate that, for the off-resonant pump excitation, the pump/probe spectrum undergoes a dramatic transformation in the coherent regime, with a strong time-dependent exchange of oscillator strength between Fermi edge singularity and exciton peaks. We show that this effect originates from the many-body electron-hole correlations which determine the dynamical response of the Fermi see. To calculate the nonlinear absorption spectrum, we use the coupled cluster method combined with time-dependent Schrieffer-Wolff transformation. Possible experimental applications are discussed., 13 pages including 1 figures

By means of degenerate four-wave mixing (FWM), we investigate the quantum coherence of electron–hole pairs in the presence of a two-dimensional electron gas in modulation-doped GaAs–AlGaAs quantum wells in the regime of the integer quantum-Hall effect. We observe large jumps in the decay time of the FWM signal at even Landau level filling factors. The main features of the experimental observations can be qualitatively reproduced by a model which takes into account the number of unoccupied states within the highest partially occupied Landau level. Furthermore, we observe quantum beats between up to three different Landau level transitions.

Mean-field, Hartree-Fock theory has been successful in explaining many nonlinear optical experiments in semiconductors. But recently experiments have shown important cases where the mean-field theory (the semiconductor Bloch equations) fails. One such case is bulk GaAs in a strong magnetic field. Here the exciton-exciton interaction can be tuned by varying the magnetic field, providing an excellent method for studying the transition from a regime where mean-field theory is valid to a regime where exciton-exciton correlations must be taken into account. We perform ultrafast time-resolved four-wave mixing on bulk GaAs in a magnetic field, and compare our experimental results with theoretical calculations which go beyond Hartree-Fock theory. We find excellent qualitative agreement. Furthermore, because of the strong correlations that are present, GaAs in a magnetic field presents an excellent opportunity to study the exciton-exciton correlations themselves. We investigate the coherence of the exciton-exciton correlations as the temperature and free-carrier density are varied, and find a surprising sensitivity of the exciton-exciton correlation coherence to these parameters.

Polarization spectroscopy of single fluorescent molecules is used to probe their rotational dynamics. When a molecule is immobilized on a dry surface, its in-plane dipole orientation is precisely determined by utilizing its transition dipole moment. An angular offset between the absorption and the emission dipoles was detected from a single fluorophore revealing its binding geometry to the surface. In an aqueous environment, DNA-tethered fluorophores display dynamics that are well-described by a hindered rotational diffusion model. A detailed description of the model is given, including calculations to estimate depolarization effects resulting from the high numerical aperture objective used to collect fluorescence photons. Protein-conjugated fluorophores display very distinct dynamics with continuous evolution of the rotational profile, possibly reflecting fluctuations in the polypeptide chain. When protein-conjugated fluorophores are allowed to freely diffuse in solution, it is possible to determine the ...

The concept of ratiometric identification and separation of sub-populations of single biomolecules which are labeled with individual fluorophores and are freely diffusing (or flowing) through the laser excitation volume is introduced. The efficacy of the scheme versus the signal and noise level is considered and a general theoretical framework and data analysis schemes are introduced. Experimental results that demonstrate distributions of single molecule fluorescence polarization anisotropy (smFPA) and single pair fluorescence resonance energy transfer (spFRET) in solution are presented. Ultimate resolution for identifying molecular observables such as conformational states, degree of freedom of motion and spectral distribution are discussed.

Biological molecules together with available labeling chemistries provide an ideal setting to investigate the interaction between two closely spaced dye molecules. The photo-excitation of a donor molecule can be non-radiatively transferred to a near-by acceptor molecule via the induced-dipole–induced-dipole interaction in a distance-dependent manner. In this work, we further elaborate on single-molecule fluorescence resonance energy transfer measurements between two dye molecules attached to a single protein – staphylococcal nuclease molecules [T. Ha, A.Y. Ting, J. Liang, W.B. Caldwell, A.A. Deniz, D.S. Chemla, P.G. Schultz, S. Weiss, Proc. Natl. Acad. Sci. USA 96 (1999) 893–898]. Temporal fluctuations in the energy transfer signal include: (1) reversible transitions to dark states; (2) irreversible photodestruction; (3) intersystem crossing to and from the triplet state; (4) spectral fluctuations; (5) rotational dynamics of the dyes; and (6) distance changes between the two dyes. To extract biologically relevant information from such measurements, an experimental strategy and data analysis schemes are developed. First, abrupt photophysical events, such as (1)–(3) are identified and removed from the data. The remaining slow, gradual fluctuations in the energy transfer signal are due to spectral shifts, rotational dynamics and distance changes of the dyes. Direct measurements of each dye's spectral fluctuation and rotational dynamics indicate that these, by themselves, cannot fully account for the observed energy transfer fluctuations. It is therefore concluded that inter-dye distance changes must be present as well. The distance and orientational dynamics are shown to be dependent on the binding of the active-site inhibitor (deoxythymidine diphosphate) to the protein. The inhibitor most probably affects the protein's stability and the dye–protein interaction, possibly by amplifying the motion of the linker arm between the fluorophore and the protein.

Fourier transform spectral interferometry is applied to measure both amplitude and phase of the electric field in different types of semiconductor nanostructures, thus determining the real and imaginary parts of the dielectric function. The importance of measuring the phase is shown and discussed in three studies. First, the phase measurement is used to access directly the refractive index across excitonic resonances in bulk GaAs and AlGaAs-GaAs quantum wells, with unprecedented resolution. Second, we measure the density dependence of the full dielectric function across a Fano resonance in bulk GaAs and show that this allows us to obtain some information on the collisional broadening of the usually hidden linewidth of the coupled exciton/continuum. Third, the phase is studied in a complex heterostructure, a semiconductor microcavity. We investigate and discuss the effect of the cavity detuning and of the excitation density.

Photon bursts from single diffusing donor-acceptor labeled macromolecules were used to measure intramolecular distances and identify subpopulations of freely diffusing macromolecules in a heterogeneous ensemble. By using DNA as a rigid spacer, a series of constructs with varying intramolecular donor-acceptor spacings were used to measure the mean and distribution width of fluorescence resonance energy transfer (FRET) efficiencies as a function of distance. The mean single-pair FRET efficiencies qualitatively follow the distance dependence predicted by Förster theory. Possible contributions to the widths of the FRET efficiency distributions are discussed, and potential applications in the study of biopolymer conformational dynamics are suggested. The ability to measure intramolecular (and intermolecular) distances for single molecules implies the ability to distinguish and monitor subpopulations of molecules in a mixture with different distances or conformational states. This is demonstrated by monitoring substrate and product subpopulations before and after a restriction endonuclease cleavage reaction. Distance measurements at single-molecule resolution also should facilitate the study of complex reactions such as biopolymer folding. To this end, the denaturation of a DNA hairpin was examined by using single-pair FRET.

To study the effects of confinement by quantum-well potential discontinuities on ultrafast carrier dynamics, we performed pump-broadband probe studies of a series of In{sub 0.47}Ga{sub 0.53}As quantum wells excited 30 meV above the band edge. Our measurements show that the rate of carrier thermalization is well width independent; however, the rate of carrier cooling to the band edge is strongly influenced by confinement. This influence has two separate physical origins. First, the dimensionality dependence of the density of states results in a larger proportion of thermalized electrons that can emit LO phonons in three dimensions than in two. Second, modification of the phonon density of states by the ionic mass discontinuity at the well boundaries may reduce the electron{endash}LO-phonon coupling. {copyright} {ital 1998} {ital The American Physical Society}

We report direct investigations of the coherence of four-particle (exciton-exciton) correlations by ultrafast four-wave mixing experiments. We determine the sensitivity of the coherence of the four-particle correlations to temperature and excitation density, comparing it to the coherence of the two-particle correlations. We discuss our results in terms of numerical solutions of the general kinetic equations, treating the four-particle correlations in the second order Born approximation. We introduce a simple model deduced from these kinetic equations that provides an intuitive interpretation of our results. {copyright} {ital 1998} {ital The American Physical Society}

We extended the sensitivity of fluorescence polarization anisotropy measurements to the single molecule level by studying the polarization response of single fluorophores rapidly rotating in liquid. Comparison with a simple model calculation allows us to obtain information on the hindered motion as well as on the rotational diffusion in the presence of specific molecular interactions. We also observed rotational jumps between surface-bound and unbound states and show that they are, similar to jumps to long dark states, photoactivated.

We study the effects of photocarrier density on a magnetically induced Fano resonance in GaAs, using a combined phase-amplitude transmission spectroscopy technique. By comparing our results to an extension of the Fano model we measure the relative contributions of two, usually undistinguished, effects of the photocarriers: the screening of the inter-Landau-level Coulomb coupling, and the induced collisional broadening of the coupled discrete-state/continuum natural linewidth.

Recent experiments on fs time-resolved coherent wave mixing under a high magnetic field have revealed a new regime at low excitation densities which is not in accordance with the semiconductor Bloch equations. We present a theory of coherently driven biexcitons in a strong magnetic field, which — due to the restriction of excitonic degrees of freedom — results in a strong enhancement of Coulomb correlation effects. The theory describes most of the observed features. Especially, the slow rising time of the time-integrated four-wave mixing signal is shown to result from biexcitonic correlation. The same interaction effects yield a strong dependence of the oscillator strength of the heavy- (hh) and light-hole (lh) excitons on the time delay between the two pulses.

Στην παρούσα διατριβή μελετάμε μία θεωρία για την υπερταχή μη γραμμική οπτική απόκριση του κβαντικού συστήματος Hall. Η θεωρία μας επικεντρώνεται στο ρόλο των συλλογικών διεγέρσεων χαμηλής ενέργειας του κρύου, ισχυρά συσχετισμένου, διδιάστατου ηλεκτρονικού αερίου (2ΔΗΑ) που υπάρχει στη θεμελιώδη κατάσταση του συστήματος. Η θεωρία μας λαμβάνει υπόψη τις ηλεκτρονικές συσχετίσεις της θεμελιώδους κατάστασης και τις επιδράσεις ανταλλαγών και αλληλεπιδράσεων Pauli μεταξύ των φωτοδιεγερμένων ηλεκτρονίων και των συλλογικών διεγέρσεων του ηλεκτρονικού αερίου. Ο φορμαλισμός μας περιγράφει τόσο την αρχική χρονική περίοδο όπου υπάρχει συμφωνία φάσης και κατά την οποία η δυναμική καθορίζεται από πολώσεις και κβαντομηχανικές συμφωνίες φάσης του 2ΔΗΑ και των φωτοδιεγερμένων εξιτονίων, όσο και την ακόλουθη περίοδο όπου η συμφωνία φάσης έχει χαθεί και η οποία κυριαρχείται από τη δυναμική των πληθυσμών. Συζητάμε, επίσης, πώς εκδηλώνονται, τόσο εντός μίας ενεργειακής ζώνης όσο και μεταξύ διαφορετικών ενεργειακών ζωνών, οι συμφωνίες φάσης οι οποίες δημιουργούνται από τις συλλογικές διεγέρσεις του 2ΔΗΑ στο συζευγμένο σύστημα φωτοφορέων - κβαντικού συστήματος Hall και συγκρίνουμε με πειράματα μίξης τεσσάρων κυμάτων με τρεις παροδικούς παλμούς. Επιπλέον, εφαρμόζουμε τη θεωρία μας στην περίπτωση ενός κβαντικού πηγαδιού χωρίς δότες μέσα σε μαγνητικό πεδίο και περιγράφουμε την εκεί δημιουργία συμφωνιών φάσης εντός της ίδιας ενεργειακής ζώνης και μεταξύ διαφορετικών ζωνών που παράγονται από τους φωτοδιεγερμένους φορείς.

Laser-induced fluorescence (LIF) from single molecules at room temperature displays rich dynamics of reversible and irreversible transitions within the photodestruction lifetime of the molecule. In contrast to ensemble studies, these transitions are directly resolved when the fluorescence signal is monitored in time. We present a strategy and describe the instrumentation needed for spectroscopic studies on a large number of individual molecules. It is based on a computer controlled optical system which automatically and rapidly positions single molecules in the excitation volume of a confocal microscope and subsequently performs spectroscopic measurements. Examples for such spectroscopies are presented.

The optical absorption of quantum-well wires is studied theoretically. A single quantum-well wire is treated by means of the subband expansion which allows us to classify the optical transitions. The accuracy of this approximation for quantitative predictions is examined. For the first time, optical spectra of quantum-well-wire arrays are calculated, including Coulomb interaction and continuum states. The absorption shows Fano resonances and features of above-barrier excitons. As the band offsets increase, we observe a transition to decoupled quantum-well wires.

Optical spectra of type-II superlattices are presented, including Coulomb interaction and continuum states. We clarify the relative importance of above- and below-barrier transitions. By gradually increasing the band-gap modulation, we visualize the transition from a bulk semiconductor to a type-I or type-II superlattice. We show that transitions that dominate the spectrum of a type-II superlattice are absent in the spectrum of a type-I superlattice and vice versa. The interplay of size and Landau quantization in the optical absorption is studied for both a type-I superlattice and a type-II superlattice in a perpendicular magnetic field. {copyright} {ital 1997} {ital The American Physical Society}

To study the effects of confinement by quantum-well potential discontinuities on excitonic dephasing, we performed a spectrally and temporally resolved study of band-edge four wave mixing emission from a series of In{sub 1{minus}x}Ga{sub x}As quantum wells. Our measurements reveal an array of dynamics as we move from the three-dimensional to the two-dimensional limit. Spectral resolution allows us to resolve a slowly dephasing excitonic contribution in bulk In{sub 1-x}Ga{sub x}As. In measurements on quantum-well samples of intermediate width, we find no change of the dephasing time as the quantum-well width becomes smaller than the bulk Bohr diameter. This indicates that the dominant dephasing mechanism in this regime is scattering by alloy disorder and interface roughness. For quantum-well widths below 200 {Angstrom} we observe a substantial increase of the dephasing time. Spectral resolution allows us to associate the slow dephasing in this regime with localized excitons. {copyright} {ital 1997} {ital The American Physical Society}

We present investigations of fs time resolved coherent wave mixing under high magnetic field. Our experiments reveal a new regime at high magnetic field and low excitation density dominated by the Coulomb interaction. This regime is inconsistent with the semiconductor Bloch equations. A model which includes exciton-exciton correlation successfully describes many features of this regime. {copyright} {ital 1997} {ital The American Physical Society}

We observed and made unambiguous distinctions between abrupt photophysical events of single molecules: a rotational jump of a single dipole, a transition to a dark state (reversible and irreversible photobleaching), and a spectral jump. The study was performed in the far field by modulating the excitation polarization and monitoring the fluorescence in time. This technique also allowed us to measure the in-plane dipole orientation of stationary single molecular dipoles with subdegree accuracy and to resolve desorption and readsorption of fluorophores from and onto a glass surface. In one case, clear evidence was obtained for rapid rotation of the dipole after a desorption process. {copyright} {ital 1996 The American Physical Society.}

We describe a highly efficient, general-purpose, and easy-to-use method of calculating the optical absorption of semiconductor microstructures. The linear optical susceptibility is obtained by the numerical evaluation of the polarization in real space and real time, using finite differences and the leap-frog scheme. Numerical effort and storage scale as O(N), where N is the number of base elements. The algorithm is suitable for large-scale quantum systems. For illustration, we apply this method to quantum wells in a perpendicular magnetic field, flat quantum dots, superlattices, coupled multiple quantum wells, and excitons on rough interfaces. \textcopyright{} 1996 The American Physical Society.

We present investigations of the temporal evolution of phase and amplitude of coherent emission of GaAs/GaAlAs quantum well structures, excited by ultrashort laser pulses. We find that the coherent light emitted by excitons or by electron-hole pairs exhibits a complex phase behavior, which depends critically on the intensity and the central frequency of the exciting pulses. We observe nonlinear shifts of the instantaneous frequency within one ultrashort pulsed emission. We also discuss the theoretical interpretation the experiments. Although it is clear that non-local Coulomb correlation and non-Markovian dephasing processes are responsible for the observations, quantitative theories are not available presently. Therefore our experiments, point the need for theoretical refinements of nonlinear optical processes in semiconductors.

We investigate the ultrashort coherent dynamics of one-dimensional Fano andvLorentzian magnetoexcitons in GaAs using temporally and spectrally resolved four-wave mixing (FWM). The dephasing time of a Fano resonance is intrinsically limited by the coupling between discrete states and continua which is responsible for Fano interference. In contrast, the coherent emission from Lorentzian magnetoexcitons dephases solely due to quasi-particle scattering, dominated by exciton-exciton scattering at low temperatures. We find a very fast decay of the time-integrated FWM signal from Fano magnetoexciton resonances. This decay is not due to dephasing. The quenching of the FWM signal for non-overlapping excitation pulses is the result of quantum interference. This destructive quantum interference is not observed for purely Lorentzian dynamics. For the simultaneous excitation of Lorentzian and Fano magnetoexciton resonances, destructive quantum interference also quenches the coherent emission from Lorentzian magnetoexcitons due to quantum mechanical coupling between the different resonances.

Single-molecule detection and spectroscopy by laser induced fluorescence offer many applications to life sciences. We review recent techniques and experiments based on the detection and spectroscopy of two near-by molecules. The spectroscopic signature of the light emitted from the two molecules can be used to measure the distance, orientation and relative dynamics between biological macromolecules.

Using transient four-wave mixing spectroscopy, we study the ultrafast nonlinear optical response of magnetoexcitons in GaAs at 1.6 K. By spectrally and temporally resolving the coherent emission, we measure the magnetic field dependence of Coulomb interactions between magnetoexcitons. Contrary to experiments performed in quantum wells, these interactions persist for field strengths up to 10 T.

We study the dynamics of coherent emission of a semiconductor within the framework of the semiconductor Bloch equations, both in the time domain and in real space for various excitation conditions. We find that the spatial properties of the four-wave-mixing (FWM) response reflect the well-known temporal dynamics. For excitation high above the band edge, the FWM signal is emitted as a photon echo. This photon echo from continuum states of a semiconductor has the same dynamical properties as a photon echo from inhomogeneously broadened uncoupled two-level systems. However, unlike the case of two-level atoms, the polarization of the photon echo from the semiconductor continuum extends over macroscopic distances in real space. The implications of the large spatial extent of the photon echo polarization are discussed. In particular, we show that, in spite of the macroscopic size of the photon echo polarization, the wavelength of the exciting light can still be neglected.

By spectrally resolving the transient four-wave mixing (FWM) signal and the differential transmission signal arising from electron-hole pairs optically excited into the continuum of a GaAs/AlGaAs quantum well structure, we directly measure the dynamics of the quantum coherence among such interacting carriers. We observe a dynamic blue-shift of the coherent FWM emission spectrum with respect to the excitation laser pulse. We interpret our results in terms of dynamic Coulomb correlation effects arising in non-equilibrium degenerate electron-hole systems.

The coherent dynamics of Fano resonances in GaAs are studied under magnetic field using femtosecond four-wave mixing (FWM). In this system Coulomb coupling between magnetoexciton and continuum states gives rise to Fano interference. By time-resolving the FWM signal it is shown that dephasing or the coherent emission from a Fano resonance is dominated by the coupling to the continuum. Unlike Lorentzian resonances, the decay of the time-integrated FWM signal is not related to dephasing. This surprising behavior is due to the interplay between Fano interference and Coulomb correlation in a semiconductor