Electron-phonon interaction is a major source of optical dephasing in semiconductor quantum dots. Within a density matrix theory the electron-phonon interaction is considered up to the second order of a correlation expansion, allowing the calculation of the quantum kinetic dephasing dynamics of optically induced nonlinearities in GaAs quantum dots for arbitrary pulse strengths and shapes. We find Rabi oscillations renormalized and a damping that depends on the input pulse strength, a behavior not known from exponential dephasing mechanisms.

We investigate the optical properties of a Coulomb-coupled double-quantum dot system excited by coherent light pulses. Basic effects of Coulomb coupling regarding linear and nonlinear optical processes are discussed. By numerically solving the Heisenberg equation of motion we are able to present the temporal evolution of the system's density matrix for a wide range of coupling parameters. The two main coupling effects in dipole approximation, biexcitonic shift and Förster energy transfer, are investigated and their qualitative and quantitative influence on absorption spectra, Rabi oscillations, and single-and two-pulse excitation is discussed. We present simulated differential transmission spectra to allow for comparison with recent experimental studies.

The phonon-induced dephasing dynamics of semiconductor quantum dots during nonlinear optical excitation is studied using quantum kinetic equations. We find that despite the decoherence process Rabi oscillations occur even for relatively long pulse durations and that their signatures in pump-probe experiments only get suppressed for high input pulse areas.1 General remarks Rabi oscillations are the results of the coherent interplay of level occupation filling and the optical polarization dynamics during nonlinear optical excitation and have been studied extensively in both atoms [1,2] and semiconductor structures like bulk material [3,4] and quantum wells [5]. In atomic systems radiation damping limits the Rabi flopping process by energy and phase relaxation. Similarly, in bulk semiconductors electron-electron and electron-phonon scattering lead to simultaneous energy and phase relaxation due to a continuous density of states [6]. This situation is different in semiconductor quantum dots, which like atoms exhibit well isolated energy levels, often with a larger separation than the typical phonon energies. Therefore energy-conserving scattering events yielding simultaneous phase relaxation are strongly reduced. Instead, quantum kinetic processes which make use of the energy uncertainty lead to pure dephasing, i.e. phase relaxation without energy relaxation [7][8][9][10].In this work, we present a theory in the nonlinear optical regime describing the dephasing dynamics of electronic excitations in semiconductor quantum dots coupled to acoustic phonons. This allows us to study phenomena related to Rabi flopping in GaAs semiconductor quantum dots. Indications of Rabi flopping have been experimentally observed in semiconductor quantum dots [11,12]. Also, the dephasing dynamics after excitation with nonlinear d-pulses has been investigated theoretically [13].2 The model system In order to describe our system a Hamiltonian is introduced which consists of the quasi-free energy of electrons and phonons, the interaction with the electromagnetic field, and the coupling of electrons and phonons:Here, the energy E l , the creation (a þ l ) and annihilation (a l ) operators of an electron in level l have been defined. The quantum dot transition dipole moment M lm couples the electronic system to the external light field EðtÞ. Acoustic phonons with kinetic energy hw q ¼ c LA jqj and creation (b þ Àq ) and

ErratumLight propagation-and many-particle-induced non-Lorentzian lineshapes in semiconductor nanooptics [phys. stat. sol. (b) 234, 155 (2002)]

Dedicated to Professor Dr. Roland Zimmermann on the occasion of his 60th birthdayThe occurrence of non-Lorentzian lineshapes is analyzed for a variety of nanooptical semiconductor systems such as quantum wells and quantum dots. Their origin is traced back to light-matter interaction (light propagation) and many-particle correlations (electron-electron and electronphonon interaction). 157

status solidi www.pss-b.com physica basic solid state physics Ne w I m p a ct Fa c t o r 2 0 0 9

We investigate the effect of the Coulomb interaction on the applicability of quantum gates on a system of two Coulombcoupled quantum dots. We calculate the fidelity for a single-and a two-qubit gate and the creation of Bell states in the system. The influence of radiative damping is also studied. We find that the application of quantum gates based on the Coulomb interaction leads to significant input state-dependent errors which strongly depend on the Coulomb coupling strength. By optimizing the Coulomb matrix elements via the material and the external field parameters, error rates in the range of 10 À3 can be reached. Radiative dephasing is a more serious problem and typically leads to larger errors on the order of 10 À2 for the considered gates. In the specific case of the generation of a maximally entangled Bell state, error rates in the range of 10 À3can be achieved even in the presence of radiative dephasing.

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