Four-wave mixing in coupled semiconductor quantum dots

Abstract

We present a theoretical analysis of four-wave mixing in coupled quantum dots subject to inhomogeneous broadening. For the biexciton transitions, a clear signature of interdot-coupling appears in the spectra. Few-particle states in optically excited semiconductor quantum dots [1 -3] have recently attracted enormous interest: on the one hand, they exhibit a number of atomic-like properties attributed to their zero-dimensional nature, such as ultranarrow emission peaks [4,5] or ultralong dephasing times [6]; on the other hand, the semiconductor compound gives rise to a number of novel features which lack atomic counterparts, among which multi-excitons [7 -10] and flexible interdot coupling [11,12] are the most prominent ones. Optical excitations in semiconductors quantum dots are composed of electron -hole pairs (excitons), which become profoundly renormalized because of the resulting mutual Coulomb interactions; indeed, such Coulomb-renormalization effects have been studied exhaustively in single-dot spectroscopy [13] and are at the heart of the celebrated quantum-dot-based single-photon sources [14,15]. In addition, advanced growth procedures now allow to vertically couple dots in a well-controlled manner, and to tune the coupling strength within a wide parameter range.This flexibility renders quantum dots as ideal candidates for novel (quantum) device applications. Proposals range from cellular automata [16] over storage devices [17,18] to possible registers for quantum computers [19]. Yet, such challenging future technology requires a detailed understanding of interdot couplings and of the resulting fewparticle states-issues which have only recently become subject of careful investigations. One of the crucial difficulties in these studies is the unavoidable inhomogeneous line broadening because of dot size fluctuations, inherent to any self-assembly growth procedure, which hinders the direct observation of interdot-coupling induced level splittings. Although the investigation of single quantum-dot molecules has been demonstrated and has given clear evidence of interdot coupling [11,12], the underlying analysis faces severe problems when the change of interdot coupling is accompanied by possible variations of the lateral confinement-a delicate problem in particular for the technologically highly relevant self-assembled dots.In this paper we present a theoretical analysis of fourwave mixing (FWM) [20] in an ensemble of inhomogeneously broadened coupled quantum dots, and we show that FWM spectra provide a sensitive measure of such pertinent interdot couplings. This finding rests on a number of nontrivial observations. Firstly, FWM is a technique particularly suited for the measurement of transport parameters independent of inhomogeneous broadening, e.g. exciton dephasing or biexciton binding [6,21,22]. Secondly, in the strong confinement regime the electron -hole tunneling 0038-1098/03/$ -see front matter q