Biexciton and spin dephasing effects in quantum dots embedded in a glass matrix proved by four-wave mixing and pump-and-probe spectroscopy V. D. Kulakovskii, 1,2 K. Babocsi, 1 M. Schmitt, 1 N. A. Gippius, 3 and W. Kiefer 1 1 Universita ¨t Wu ¨rzburg, Am Hubland, D-97074 Wu ¨rzburg, Germany 2 Institute of Solid State Physics, RAS, 142432 Chernogolovka, Russia 3 General Physics Institute, RAS, Moscow, Russia ~Received 11 June 2002; revised manuscript received 4 December 2002; published 13 March 2003! The polarization properties of time-integrated four-wave mixing ~FWM! and pump-and-probe transmission ~PPT! signal spectroscopy were investigated for a system of excitons confined in CdSSe quantum dots ~QD’s! embedded in a glass matrix. A strong FWM signal was observed by scattering s 2 circularly polarized light on the population grating created by two s 1 pulses ~forbidden geometry according to the noninteracting oscilla- tor’s model!. A similar depolarization effect is observed in the PPT studies: the difference in the signals in the s 1 s 1 and s 1 s 2 geometries decays for delay times of about 5 ps. No marked scattering is observed if the population grating is created by two pulses of opposite ( s 1 and s 2 ) polarizations. We demonstrate that these facts are associated to a strong exciton-exciton coupling in the QD and to the inhomogeneous spin dephasing of the QD excitons due to a random exchange splitting of the J 51 exciton state, originating from the lowered QD symmetry. DOI: 10.1103/PhysRevB.67.113303 PACS number~s!: 78.47.1p, 42.65.2k Nanocrystals of semiconductor materials raised high in- terest in the last decade. 1–7 Excitons confined in all spatial dimensions are interesting not only because of their highly enhanced optical nonlinearities but also because they are known as prototypical systems for investigating the physics of quantum confinement. In the II–VI compounds CdS and CdSe, the range of currently accessible sizes allows one to study how the electron wave functions and their coupling to lattice vibrations change as the number of atoms increases from a few hundred to many thousands. Recent interest in manipulating semiconductor spins for applications ranging from spintronics to quantum computation 8 is based on the ability to control and maintain the spin coherence of the system. An experimental investigation of quantum dot ~QD! systems is usually complicated by issues such as the disper- sion of the QD size present in the sample because of the extreme sensitivity of the exciton energy to the QD size. In this paper we present pump-probe transmission ~PPT! and three-pulse fs photon-echo measurements performed on CdSSe nanocrystals embedded in a glass matrix. The latter technique avoids the issue of inhomogeneous broadening of the oscillator energies because the integrated photon-echo signal reflects the average properties of the QD’s within the inhomogeneous distribution. 9 Much attention is paid to po- larization properties of the signal recorded for either time- integrated ~TI! four-wave mixing ~FWM! or PPT spectros- copy at the energy of 1 s excitons ~X! confined in QD’s. The TI-FWM selection rules for the system of noninter- acting oscillators predict a nonzero signal only for the pulses of the same polarization. 9 In contrast, the experiment shows a strong signal also for the scattering of s 2 polarized light on the population grating created by two s 1 beams. A simi- lar depolarization effect has been observed in the PPT signal. The depolarization observed earlier in FWM and PPT studies of an exciton system in quantum wells has been shown as due to an influence of the X-X coupling. 9–12 A qualitative distinction of the exciton system in the QD structure ~an inhomogeneous broadening of an exciton level, a negligible Coulomb interaction between X ’s belonging to different dots and a very strong interaction between two X ’s in one dot! results in a qualitatively different time behavior of the FWM signal observed in QD structures. The QD system studied here consists of CdS 0.6 Se 0.3 QDs embedded in a glass matrix ~commercially available Shott filter glass, namely, OG550!. The QD diameter is 9.1 nm with a size distribution of about 15%. 13 The sample was mounted in an optical cryostat and kept at a temperature of 10 K. In the TI-FWM studies, three 80-fs laser pulses with the wave vectors k 1 , k 2 , and k 3 ( 52k 2 ) have been used for excitation. A FWM signal is created in the direction k s 52k 1 1k 2 1k 3 determined by the phase matching condi- tion. All three pulses have the angle of incidence of about 5° and the same frequency lying in the range of the inhomoge- neously broadened 1 s 2X transitions as shown in Fig. 1. The FIG. 1. Absorption spectra recorded at 10 K for the 9.1 nm CdSSe QD embedded in a glass matrix. PHYSICAL REVIEW B 67, 113303 ~2003! 0163-1829/2003/67~11!/113303~4!/$20.00 ©2003 The American Physical Society 67 113303-1