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Symmetry effects in optical properties of single semiconductor quantum dots

Abstract : The aim of this work was to investigate the symmetry effects in optical properties of single semiconductor quantum dots (QDs). The main goal was to find new technologies which would allow us to modify those properties in a controllable way. Especially it was important to test different external perturbations restoring the spin degeneracy of the system what is a prerequisite for the achievement of photon entanglement in a QD emission. Although the polarization-entanglement in biexciton-exciton cascade have been recently demonstrated [1, 2], a reliable technique enabling such a control over QD anisotropy remains highly demanded. If QD anisotropy (measured as fine structure splitting of an excitonic line in photoluminescence (FSS) is larger then the natural linewidth, the rate of entangled photon pairs collected after post-selection gets dramatically reduced [2]. Different strategies for restoring higher symmetry were tested, either by influencing material properties of heterostructures (annealing or strain engineering [3, 4]) or by applying external perturbations compensating the native asymmetry: in-plane electric field [7], uniaxial strain [5], and in-plane magnetic field [6, 8] were tried. The last-mentioned method has given the most satisfactory results so far in GaAs-based self-assembled QDs [6].
We have examined two different pathways consisting in applying external perturbations of specific symmetry, namely an electric field applied parallel to one of the symmetry axes of the QD, and an in-plane magnetic field. In both cases, our experimental results indicate that the FSS in a single QD can be tuned significantly and canceled.
Chapter 1 (Introduction: quantum dots for entangled photon emission) contains short introduction into the subject { description of structural properties of quantum dots and discussion about the relations between the symmetry of dots and the properties of emitted photons. We put emphasis on the explanation of the origin of fine structure splitting in the excitonic spectra.
Next Chapter 2 (Samples and Experimental setups) presents the preparation of experiments (from the description of investigated samples, through technological processing (preparation of field-effect structures), and it ends up with showing the experimental techniques enabling studies on single quantum dots.
Chapter 3 (Influence of electric field on quantum dots) reports the experimental results and the discussion of the influence of electric field on the optical properties of quantum dots. The splitting in the spectra is related with anisotropic exchange interaction between electron and hole, which form an exciton. Because of the character of this interaction, the electric ¯eld seems to be a very good candidate as a perturbation to modify it. If applied in the QD plane it should affect the symmetry of the wavefunctions for single carriers and depending on the direction (with respect to QD anisotropy) it should either increase or decrease the splitting in spectra. Thanks to the preparation of field-effective structures on III-V materials (n-Schottky, Schottky-Schottky) it was possible to apply an in-plane electric field. We obtained systematical changes of FSS for individual quantum dots with applied field [7]. The observed FSS changes with the applied voltage result always from both effects: the expected symmetry modification of the wavefunctions and the diminution of the overlap of single carriers wavefunctions. The latter effect always leads to the reduction of the exchange interaction. In order to estimated this contribution from the separation of the interacting carriers, we performed measurements for structures with the field applied in the growth direction. In this vertical configuration the field should not modify strongly the symmetry of the wavefunctions, and the changes in the FSS should be influenced mostly by the spatial separation of an electron and a hole. Observed changes in FSS for vertical field were a few times weaker than those for in-plane configuration, what confirm our explanation how the electric field acts on QDs [9]. From additional tests on the excitonic complexes we gained the knowledge about precise spatial alignment of electrons and holes in a QD, we were thus able to estimate the permanent vertical dipole [9]. The studies of the influence of electric field on QDs made of II-VI materials were limited to the studies of local electric fields. These investigations were used to identify different transitions from the same QD [11]. Charge fluctuations in the QD vicinity may produce non-controlled changes in the excitonic splitting [10]. Therefore it is important to study the mechanisms which produce the fluctuations in order to find the conditions under which they are statistically negligible. Nevertheless the FSS changes in electric field are significant, and for samples with electro-optical devices embedding InAs/GaAs QDs in their intrinsic region they were comparable with Stark shift, but the application of this method is limited by the intensity reduction (due to electron-hole separation and carriers escape out of a dot) and strong line broadening (spectral diffusion of the lines induced by local field fluctuations). Thus electric field enabled us to cancel FSS only for QDs with small native splitting. Second investigated perturbation used to influence the spin degeneracy, was in-plane magnetic field. Experimental results and theoretical model are presented in Chapter 4 (Influence of magnetic field on quantum dots). This method of FSS control seems to be very promising especially for II-VI QDs, since the technology of electric field-effect structure for these materials is not well established. We observed that an in-plane magnetic field modifies the fine-structure splitting of the excitonic emission of CdTe/ZnTe quantum dots depending on the field direction and amplitude. For the field applied obliquely to the QD anisotropy we noticed rotation of emission polarization. We observed strong coupling between "bright" and "dark" states, that became optically active due to field-induced mixing in this configuration and they appeared in the spectra at around 1meV below the excitonic doublet. The results were discussed in terms of an effective spin Hamiltonian derived for the exciton ground state. Full hole basis (including light-hole states) was taken into account in the calculations in order to explain all observations [8]. The presented experimental results are in qualitative (polarization rotation) and rough quantitative (splitting variation) agreement with the model based on a Zeeman spin Hamiltonian. It turned out that it is important to take into account not only the direction of the field with respect to QD anisotropy axes, but also with respect to the main crystallographic direction of the host lattice. These studies showed how magnetic field can be used to cancel FSS, and additionally they revealed such information about quantum dots as { g-factors for electrons and holes. Additional studies of the perpendicular configuration of the field allowed to get effective excitonic g-factors and to estimate the field range for which Zeeman splitting determines the optical properties of the emission.
The studies of spin coherence in the excitonic state are summarized in Chapter 5 (Towards entanglement). Cancellation of FSS in electrically-driven structures was measured in optical pumping experiment. A circularly polarized and quasi-resonant (~2LO-phonons above the excitonic transition) excitation induces an optical orientation of exciton spin. For an anisotropic QD it manifests itself in the experiment as an increase of the linear polarization degree under corresponding linear excitation, while for an isotropic dot circular σ+ or σ- excitation amounts to optical preparation of the exciton in one of the spin states |±1>. As a result, measuring the PL circular polarization provides a very sensitive probe of the excitonic system in the perspective of entangled photon emission. By electrically driving FSS across zero, we have been able to strongly increase the circular polarization to 70%. Remarkably, from the width of this circular polarization resonance we could also deduce the homogeneous linewidth of the excitonic transition. This technique may be used to test the preparation of the excitonic states for entangled emission. An accompanying e®ect under resonant excitation is conversion of polarization (enhancement of circular polarization under linear polarization and vice versa). These phenomena were investigated under 1LO-phonon excitation. Both,
linear-to-circular and circular-to-linear conversion was observed. The results were described using density matrix formalism.
Last Chapter 6 (Conclusions) shows the summary of the work. The obtained experimental results confirm that the external perturbations like electric and magnetic fields can be used to modify the optical properties of semiconductor quantum dots in a controllable way. Detailed studies of perturbation direction with respect to QDs eigenaxes allowed to understand how these fields act on the excitonic transitions from single quantum dots. Control of exchange interaction in QDs gives the possibility to restore high symmetry of the system and to obtain entangled photon emission. The studies of FSS strength and spin coherence are prerequisites for full understanding of excitonic emission from quantum dots.

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[5] S. Seidl et al., Appl. Phys. Lett., 88:203113, 2006.
[6] R. M. Stevenson et al., Phys. Rev. B, 73:033306, 2006.
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[8] K. Kowalik et al., Phys. Rev. B, 75:195340, 2007.
[9] K. Kowalik et al., Phys. Stat. Sol. (c), 3:3890, 2006.
[10] K. Kowalik et al., Phys. Stat. Sol. (c), 3:865, 2006.
[11] A. Kudelski et al., J. Lumin., 112:127, 2005.
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Katarzyna Kowalik. Symmetry effects in optical properties of single semiconductor quantum dots. Condensed Matter [cond-mat]. Université Pierre et Marie Curie - Paris VI, 2007. English. ⟨tel-00288343⟩

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