Phonon‐induced damping of Rabi oscillations in semiconductor quantum dots

Abstract

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

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