Dephasing in Quantum Dots

Coherent light-matter interaction in semiconductor quantum dots (QD's) is receiving increasing attention due to possible solid-state implementations in the emerging field of quantum information processing.

Beside its fundamental interest, the knowledge of the dephasing time, inversely proportional to the homogeneous broadening, of an excitonic transition in a QD is of crucial importance for these applications. The dephasing time sets the time scale during which the coherence of the excitonic transition is preserved and therefore operations based on coherent-light matter interaction can occur. Moreover, it is strictly related to intrinsic mechanisms such as radiative processes, carrier-phonon scattering and carrier-carrier scattering. Its study is a direct probe of those carrier dynamics which ultimately are limiting the high-speed performances of QD-based lasers/amplifiers.

Among the physical mechanisms responsible for the dephasing of the excitonic polarisation the interaction of excitons with phonons is a topic intensively discussed in the literature. Using a sensitive four-wave mixing technique in heterodyne detection we measured a non-exponential decay of the optically-driven polarisation in epitaxially-grown InGaAs/GaAs QD's at low temperatures, consisting of a fast initial decay over a few picoseconds followed by a long exponential decay over several hundreds picoseconds eventually limited by the radiative lifetime in the few nanosecond range [1,6,7]. The corresponding non-Lorentzian homogeneous lineshape in spectral domain has stimulated a number of theoretical works and is interpreted in terms of a narrow zero-phonon line (ZPL) superimposed to a broad band from exciton-acoustic phonon interactions due to the local character of the electronic excitations in QD's giving rise to a local lattice distortion [4]. A clear understanding of the physical processes governing this unusual dephasing is of fundamental interest and of key importance to predict and control the decoherence for applications of QD's in quantum computing.

Activities

We have revealed theoretically the key fundamental mechanisms of the phonon induced dephasing in QDs [8,9,13,14,16], which differ considerably for acoustical and optical phonons. Depending on the energy distance between exciton levels in a QD the acoustic-phonon induced dephasing can be dominated either by real acoustic phonon-assisted transitions (which change the level occupation numbers), or by virtual transitions (leading to pure dephasing). For the ground exciton state in a single QD, virtual processes are usually the major mechanism of the dephasing, since the energy distance to higher confined states is much larger than the typical energy of acoustic phonons coupled to the QD. In the absorption spectrum, the pure dephasing manifests itself as a broad band of phonon satellites and a narrow ZPL with a temperature dependent width.

Dephasing induced by dispersionless optical phonon is of quite different nature: It is a cumulative effect of the full excitonic spectrum. Each individual line being coupled to the LO phonon produces an everlasting mixed state showing no dephasing, as it is well known from the literature. Practically, only taking into account in the calculation the full spectrum including exciton levels in the wetting-layer continuum, one can predict spectral broadening and temperature dependent dephasing.

We have also succeeded to incorporate these microscopic mechanisms of the dephasing into the theory of nonlinear optical response including calculation of the measured four-wave mixing signal in individual QDs and QD ensembles [11,12]. This is one of our current active research directions.

The phonon-assisted relaxation between fine-structure states is another important dephasing mechanism, which gains importance with decreasing size of the QD and correspondingly increasing energy splitting of the states. This leads to a dephasing which is not radiatively limited in typical colloidal quantum dots. Engineering the fine-structure to avoid this effect is an active research direction.