Exciton Polarization Research Articles

Coherent effects in spectrally resolved pump-probe differential reflectivity measurements at exciton resonance in GaAs quantum wells

We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small $+ve$ and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}l0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small $+ve$ $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both $+ve$ and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large $+ve$ $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small $+ve$ delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.

Resonant Rayleigh scattering dynamics of excitons in single quantum wells

The resonant Rayleigh scattering dynamics of excitons in single GaAs quantum wells is investigated. The deviation of the measured intensity from the ideal ensemble average is analyzed as a function of the speckle ensemble size. The influence of the amplitude and correlation length of the exciton disorder potential is traced using a series of samples with varying inhomogeneous broadening and interface island sizes. The experimental data are compared with theoretical predictions using exciton states of spatially uncorrelated energies, as well as full calculations of the exciton polarization dynamics using a more realistic disorder potential including the formation of monolayer islands. Deviations from the dynamics of uncorrelated states are found at early times after excitation. They are reproduced by the calculations possessing a state correlation due to quantum mechanical level repulsion and a finite correlation length for the disorder potential. Additionally, the presence of a long-range disorder potential in the micrometer range is suggested. Changing the disorder potential by varying the island size influences the observed dynamics systematically according to the different disorder correlation lengths.

Simultaneous optical coherent control of excitonic and biexcitonic polarization in a ZnSe quantum well

The optical coherent-control technique is used to study biexcitonic effects in the four-wave-mixing signal of a ZnSe single quantum well. The signal is analyzed in both directions 2k1 − k2 and 2k2 − k1 which are not equivalent if a pulse pair is applied from direction k1 to achieve coherent control of the induced polarization. It is shown that the coherent control enables a selective enhancement or suppression of the contribution at the exciton and biexciton resonance to the signal, respectively, but only for certain sequences of the excitation pulses. Further, the suppression of exciton-biexciton beats in the signal as a function of tdel by a selective destruction of the biexciton polarization is demonstrated.

Electric-field-induced anisotropy of excitonic optical properties in semiconductor quantum dots

We report the anisotropic excitonic optical properties (polarization dependent photoemission and photoabsorption) induced by applying a lateral electric field in a single semiconductor quantum dot. The excitonic optical polarization characteristics are examined using theoretical calculation and optical measurement. The optical properties are numerically analyzed taking into account the quantum dot potential, electric field, and electron–hole Coulomb interaction. We evaluate the polarization properties from calculated exciton wave functions. The polarization properties depend strongly on the size of the quantum dots and the spatial symmetry of the hole part of the wave function. There is large electric-field-induced anisotropy in thin quantum dots to a larger lateral extent even where the polarization properties are completely isotropic without an electric field. We compare the theoretical results with experimental results for InGaAs quantum dots obtained using the microphotoluminescence technique. Qualitative agreement between the theoretical results and experimental ones is obtained.

Effect of the electric field on the luminescence of self-supporting porous silicon

The effect of the electric field on the emission spectra of self-supporting porous silicon is studied. A decrease in the luminescence intensity, proportional to the square of the electric field has been observed. The suppression of the luminescence intensity is explained within a theoretical model, which attributes the effect to the polarization of excitons localized within the Si crystallites.

Polarization-resolved electro-absorption in InAs/GaAs quantum dots in waveguide structures—modeling of size, shape and In-content

Integrating InAs self-assembled quantum dots into p–i–n (and n–i–p) waveguide structures allows for polarization resolved electro-absorption measurements of quantum dot single excitonic transitions. In this geometry, the field dependence of three electron heavy-hole and three electron light-hole transitions has been investigated. The light-hole ground state exciton is separated from the heavy-hole ground state transition by 160 meV . A zero field polarization of the heavy-hole excitons is found, which compensates at −75 kV/cm . The light hole excitons, however, do not indicate any dipole moment. In contrast to the heavy-hole transitions they show a strongly pronounced field dependence. Modeling these extensive results, the parameter space with respect to shape, size and In-content of the quantum dot turns out to be very narrow. As a key issue, the light-/heavy-hole splitting is strongly influenced by the biaxial strain, which in turn depends on the width/height ratio of the dot. The best agreement with the experimental data has been achieved by assuming a lens-shaped dot with a trumpet-shaped In-distribution.

Intraband polarization as the source of degenerate four-wave mixing signals in asymmetric semiconductor quantum well structures

We have developed a formalism for calculating the coherent response of asymmetric semiconductor quantum well structures to ultrashort optical pulses. We work in an excitonic basis and include exciton-exciton interactions via the long-wavelength portion of the excitonic intraband polarization. We apply this formalism to the calculation of degenerate four-wave mixing intensities of a biased semiconductor superlattice and find that many aspects of the four-wave mixing signals are most naturally interpreted as directly resulting from the scattering of excitons off of the intraband polarization grating. We furthermore develop an extremely accurate method of factoring the dynamical equations that does not suffer from the problem encountered by the semiconductor Bloch equations in the Hartree-Fock approximation.

Coherent control of biexcitonic polarization

Biexcitonic polarization excited in a ZnSe quantum well is coherently controlled with a pair of phase-locked laser pulses. The coherent control of this four-particle correlation is directly verified by observing a spectrally resolved four-wave-mixing signal in direction of the first order of diffraction of the pulse pair. By using polarization selection rules for the generation of biexcitons and changing the interpulse delay of the pulse pair the oscillations of the four-wave-mixing signal are studied at the energetic position of the excitonic as well as the biexcitonic resonance. The excitonic and biexcitonic signals exhibit a phase shift in dependence on the interpulse delay which clearly indicates the separate coherent control of the excitonic and biexcitonic polarization.

Excitonic polarization dephasing under strong resonant pulsed excitation in GaAs quantum wells

We study the coherent response of an optically dense exciton system in GaAs quantum wells (QWs). For this, we resonantly excite $1s$ heavy-hole excitons in the QWs at 8 K with subpicosecond laser pulses. The excitonic polarization is probed using time integrated (TI) degenerate four wave mixing (DFWM) measurements in self-diffraction geometry. The average power density ${(I}_{1})$ of the leading laser pulse is systematically increased to large values, keeping that of the delayed pulse small and fixed. The dephasing rate of the excitonic coherent polarization (determined by the rate of decrease of the TI-DFWM signal with delay between the exciting pulses) attains saturation at large ${I}_{1}$ after an initial rise at small ${I}_{1}.$ In comparison, the coherent polarization (as given by the DFWM signal at a fixed delay) increases initially with ${I}_{1},$ reaches a peak and then decreases at large ${I}_{1}.$

Biexcitonic effects in the coherent control of the excitonic polarization detected in six-wave-mixing signals

Coherently controlled six-wave-mixing experiments on a ZnSe single quantum well are performed with different polarizations of the excitation pulses to enable or disable the creation of a biexcitonic polarization. A significant contribution of the biexcitonic polarization and other two-pair correlations is observed in the signal which is mainly modulated with the exciton transition frequency. A microscopic theory based on the dynamics controlled truncation scheme including six-point correlations is able to reproduce the experimental results.

Theory of polaritons in bounded spatially dispersive media

In crystal optics with spatial dispersion there are two alternative approaches to the polariton problems starting from either mechanical excitons ~ME’s ! or Coulomb excitons ~CE’s !, respectively. The difference between them arises from the different treatment of that part of the polarized crystal unit interaction which is associated with the long-range curl-free proper crystal field, generated by fictitious charges of macroscopic dielectric polarization. In the case of the CE scheme the unperturbed ~by electromagnetic field! energy operator contains that part, while in the case of the ME scheme it does not. This is the peculiarity that makes their dispersion laws and all other characteristics, including the boundary conditions, essentially different. Both primary conceptions are equally used in theoretical research and have their own advantages and shortcomings. The agreement between those for infinite space has been proven by a lot of investigations, but solving the same problem for finite media has not been done. Moreover, the majority of papers in the field use the same boundary conditions for excitonic polarizations in both schemes. This makes them all true only for some particular cases but, certainly, the contradictions appearing should be eliminated. The aim of this paper is the critical analysis of the existing inconsistencies and the fitting of the solutions to the boundary-value problems for polaritons formed from those two different types of exciton states. Partially we fill the arised recess by making both approaches in line with the case of the N-exponential Frenkel exciton model, when describing the polarization of some bounded spatially dispersive dielectrics in the excitonic spectrum region. The light reflection coefficient is taken as the main quantity to be fitted in both of the above calculation schemes. This is possible only by including several exciton transport mechanisms at once ~that is, for N>2) and by using the concept of Pekar’s ‘‘missing’’ electromagnetic wave. With success in this particular case, we hope to induce further investigations in the area for other exitonic models and in a general enough case, such as the case for infinite media.

Coherent nonlinear optical response of single quantum dots studied by ultrafast near-field spectroscopy.

The nonlinear response of single GaAs quantum dots is studied in femtosecond near-field pump-probe experiments. At negative time delays, transient reflectivity spectra show pronounced oscillatory structure around the quantum dot exciton line, providing the first evidence for a perturbed free induction decay of the excitonic polarization. Phase-disturbing Coulomb interactions between the excitonic polarization and continuum excitations dominate the optical nonlinearity on ultrafast time scales. A theoretical analysis based on the semiconductor Bloch equations accounts for this behavior.

Suppressed Electron-Hole Exchange Spin Flip in Cavity Polaritons

We consider theoretically the spin relaxation of exciton–polaritons in semiconductor microcavities in the strong coupling regime. The dominant quantum well exciton polarization relaxation mechanism is typically due to the long-range intra-exciton electron–hole exchange. We estimate perturbatively the corresponding contribution for the lower polaritons as a function of the elastic scattering time in analogy to the Dyakonov-Perel model for electron spin relaxation. We find a strong suppression of the polariton spin flip rate due to the electron–hole exchange with respect to the quantum well exciton case.

Photon correlation spectroscopy of a single quantum dot

We report photon correlation measurements that allow us to observe unique signatures of biexcitons in a single self-assembled InAs quantum dot. Photon correlation measurements of biexciton emission exhibit both bunching and antibunching under continuous-wave excitation while only antibunching is observed under pulsed excitation. Cross-correlation between biexciton and single-exciton peaks reveal highly asymmetric features, demonstrating that biexciton and exciton emissions have strong correlations due to cascaded emission. The anticipated correlation between the polarization of exciton and biexciton emissions however, is absent under our excitation conditions. Photon correlation measurements also provide evidence for the identification of the charged exciton emission.

Nonlinear optical response of highly energetic excitons in GaAs: Microscopic electrodynamics at semiconductor interfaces

A spectroscopic investigation of bound electron-hole pairs in GaAs propagating with large center-of-mass momentum is presented. The approach is based on transmission experiments exploiting the coupling of excitonic polarization to the electromagnetic field of femtosecond laser pulses. The dispersion relations of the coherent excitations are determined up to excess energies of 300 meV above the band edge. A surprisingly low Frohlich coupling of light-hole excitons is observed in excellent agreement with theoretical simulations. The influence of different phonon scattering processes on the excitonic damping is discussed. The interaction dynamics of excitonic wave packets with nonthermal carrier distributions is analyzed with femtosecond time resolution. A theoretical model based on the exciton-polariton concept including additional boundary conditions reproduces our experimental results. The observations in extremely thin samples show deviations from our phenomenological model. This finding is important for a detailed understanding of the microscopic polarizability near semiconductor surfaces.

Neutral and Charged Exciton Photoluminescence in a Magnetic Field Studied for Different Electron Concentrations and g-Factors

We report on the measurements of charged (X—) and neutral (X) exciton cw photoluminescence (PL) in a magnetic field as a function of the electron concentration and carrier g-factors. We observe a strong influence of both of these parameters on the circular polarization degree of PL in remotely doped Cd1—xMnxTe/Cd1—yMgyTe quantum wells (QWs). To explain these polarization properties, the processes that lead to a dynamical equilibrium among trions, excitons and electron gas must be taken into account. This is in contrast to absorption experiments where the polarization of charged excitons is governed only by the occupation of spin-split conduction band states. We develop a rate equation model involving characteristic times as obtained from time resolved experiments. The model is capable to describe adequately our PL polarization results.

Neutral and Charged Exciton Photoluminescence in a Magnetic Field Studied for Different Electron Concentrations and g-Factors

We report on the measurements of charged (X-) and neutral (X) exciton cw photoluminescence (PL) in a magnetic field as a function of the electron concentration and carrier g-factors. We observe a strong influence of both of these parameters on the circular polarization degree of PL in remotely doped Cd 1-x Mn x Te/Cd 1-y Mg y Te quantum wells (QWs). To explain these polarization properties, the processes that lead to a dynamical equilibrium among trions, excitons and electron gas must be taken into account. This is in contrast to absorption experiments where the polarization of charged excitons is governed only by the occupation of spin-split conduction band states. We develop a rate equation model involving characteristic times as obtained from time resolved experiments. The model is capable to describe adequately our PL polarization results.

Coherent nonlinear pulse propagation on a free-exciton resonance in a semiconductor

The coherent exciton-light coupling in pulse propagation experiments on the A-exciton resonance in bulk CdSe is investigated over a broad intensity range. At low light intensities, polariton propagation beats due to interference between excited states on both polariton branches are observed. In an intermediate intensity regime, the temporal polariton beating is suppressed in consequence of exciton-exciton interaction. At the highest light intensities, self-induced transmission and multiple pulse breakup are identified as a signature for carrier density Rabi flopping. Exciton-phonon scattering is shown to gradually eliminate coherent nonlinear propagation effects due to enhanced dephasing of the excitonic polarization. Calculations using the semiconductor Maxwell-Bloch equations are in qualitative agreement with the experimental data.

Bose condensation of cavity polaritons beyond the linear regime: The thermal equilibrium of a model microcavity

We consider a generalization of the Dicke model. This model describes localized, physically separated, saturable excitations, such as excitons bound on impurities, coupled to a single long-lived mode of an optical cavity. We consider the thermal equilibrium of this model at a fixed total number of excitons and photons. We find a phase in which both the cavity field and the excitonic polarization are coherent. This phase corresponds to a Bose condensate of cavity polaritons, generalized to allow for the fermionic internal structure of the excitons. It is separated from the normal state by an unusual reentrant phase boundary. We calculate the excitation energies of the model, and hence the optical absorption spectra of the cavity. In the condensed phase the absorption spectrum is gapped. The presence of this gap distinguishes the polariton condensate from the normal state and from a conventional laser, even when the inhomogeneous linewidth of the excitons is so large that there is no observable polariton splitting in the normal state.

Transient coherent emission from anisotropic semiconductors studied with phase-locked pulse pairs

The coherent emission in the direction of the reflection has been investigated under the Brewster angle of incidence by using phase-locked pulse pairs to excite resonantly the excitons in the anisotropic crystal GaSe. The interferogram of the reflected pulse has a long tail corresponding to the free induction decay signal. We also observed the phase difference between the coherent emission from the Γ 4 and Γ 6 excitonic polarizations in the direction of the reflection.