Polaron dephasing processes are investigated in InAs/GaAs dots using far-infrared transient four wave mixing (FWM) spectroscopy. We observe an oscillatory behaviour in the FWM signal shortly (< 5 ps) after resonant excitation of the lowest energy conduction band transition due to coherent acoustic phonon generation. The subsequent single exponential decay yields long intraband dephasing times of 90 ps. We find excellent agreement between our measured and calculated FWM dynamics, and show that both real and virtual acoustic phonon processes are necessary to explain the temperature dependence of the polarization decay. PACS numbers: 78.67.Hc, 78.47.+p, 42.50.Md, 71.38.-k The strong spatial confinement of carriers in semiconductor quantum dots (QDs) leads to striking differences in the carrier-phonon interaction compared with systems of higher dimensionality. In particular, the discrete energy level s tructure in QDs results in long exciton and electron dephasing times [1, 2, 3, 4], making these semiconductor nanostructures highly attractive for implementation in quantum information processing applications. The study of dephasing mechanisms in QDs is commonly carried out using transient four wave mixing (FWM) spectroscopy. Using resonant interband excitation, FWM measurements have revealed the absorption lineshape of single QDs to consist of a narrow zero phonon line (ZPL) and an acoustic phonon-related broadband centred at the same energy. The only intraband FWM study [5] involved resonant excitation of high energy transitions in th e valence band of p-doped QDs yielding dephasing times ∼ 15 ps. However it was not possible to determine the dephasing mechanisms in this case. Intraband studies of the well-resolved lowest energy conduction band electron transitions in InAs/GaAs QDs have provided deep insight into the electron-phonon interaction and carrier relaxation processes in n-doped samples. Clear evidence of strong coupling between electrons and phonons, resulting in polaron formation, has been demonstrated using magneto-transmission measurements [6]. Ultrafast studies [7, 8] of polaron decay have shown that the previously assumed ’phonon bottleneck’ picture is not valid. Compared with semiconductor quantum wells, the intraband population relaxation time in QDs is long (∼ 50 ps) suggesting relatively long dephasing times. However there have been no reports of direct dephasing measurements to date. In the present letter we present the first investigations of i ntraband dephasing in n-doped QDs using degenerate FWM. Our calculations of the absorption lineshape in this case sh ow marked differences in comparison with the interband absorption [9]. The intraband lineshape consists of peaked acoustic phonon sidebands separated by ∼ 1.5 meV from the ZPL, which corresponds to phonons with wavelength close to the dot size, and is reminiscent of the lineshape associated wit h impurity-bound electron transitions [10]. Using pulse durations short enough to excite both the ZPL and acoustic phonon sidebands we find damped oscillations in the FWM signal, indicative of coherent acoustic phonon generation, followed by a single exponential decay. In contrast with the interband case, where the origin of the strong temperature dependence of the excitonic linewidth is still subject to debate, the simple 3 -level structure of the lowest energy conduction band states in InAs QDs permits an accurate simulation of the temperature dependence of the FWM signal. The excellent agreement found between experiment and theory, shows that virtual transitions between the p-states is the dominant dephasing mechanism at high temperature. At low temperature, we have measured an intersublevel dephasing time of T2 ∼ 90 ps. It is also interesting to compare our results with previous intraband dephasing measurements in higher dimensional (quantum well) systems [11]. Here phonon-mediated processes are not significant with the intraband dephasing instead determined by electronelectron interactions, yielding typical dephasing times ∼ 0.3 ps which are approximately 2 orders of magnitude faster than for the QD samples studied here. The relatively long intraband dephasing time in QDs is key to the efficient operation of new types of mid-infrared QD-based devices, such as intersublevel polaron lasers [12] and may be relevant for potential device applications such as qubits for quantum information processors [13]. The investigated samples were grown on (100) GaAs substrates by molecular beam epitaxy in the Stranski-Krastranow mode. They comprise 80 layers of InAs self-assembled QDs separated by 50 nm wide GaAs barriers, thus preventing both structural and electronic coupling between QD layers. The polaron transitions were studied between s-like ground (s) and p-like first excited ( p) states within the conduction band. To populate the s state, the samples were delta-doped with Si 2 nm below each QD layer. The doping density was controlled in such a way that the average doping did not exceed 1 electron per dot (see Ref. [14] for more details). Absorp
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