2 two-dimensional electron gas density in the QWs does not exceed 10 10 cm − 2 in absence of optical excitation. This structure was selected on purpose because of pro- nounced carrier localization at cryogenic temperatures $^{9}$. The structure was optically characterized measuring the photoluminescence (PL) spectra [Fig. 1(a)]. In the PL spectrum two emission lines separated by 1.4 meV are observed which we attribute to exciton (X) and nega- tively charged trion (T) recombination $^{9}$. Their full width at half maximum of 1 meV is caused by trion and exciton localization on alloy and QW width fluctuations. direct optical access to the sample. When using this mil- liKelvin inserts we tried to minimize the laser power as much as possible to avoid overheating of the sample. Figure 1(b) shows Faraday rotation and ellipticity sig- nals obtained in the nondegenerate regime at B = 0 . 5 T. The pump energy was approximately tuned to the exci- ton resonance and the signal was probed at a different energy close to the trion resonance. The Faraday rota- tion and ellipticity signals are similar to each other and contain a fast decaying part with a decay time of 360 ps, which is the typical recombination time for excitons and trions in these QWs. Therefore we assign this component to the spin dynamics of photogenerated carriers $^{15,20}$. Ad- ditionally a long-lived component can be seen at times exceeding 1 ns, which is even found at delays of about 13 ns, i.e. shortly before the next pump pulse arrival, as shown in the inset of Fig. 1(b). The long-lived signal is caused by generation of spin coherence for the resident electrons and its decay is solely controlled by the electron spin dephasing time, which may be as long as 55 ns in the studied structure $^{9}$. The scenarios of spin coherence generation for the res- ident electrons in quantum wells have been considered in Ref. 20. As a rule, the spin orientation of resident car- riers involves either direct trion formation or trion for- mation from a spin oriented exciton generated by the pump. The trion formation is accompanied by capture of a resident electron with defined spin orientation, which results in polarization of the resident electron ensemble. Another mechanism can become involved for resonant ex- citon excitation: due to the exchange scattering between a resident electron and the electron from a photocreated exciton the resident carriers can become spin polarized. We demonstrate below in Sec. IV that these two mech- anisms can be equally important under resonant exciton excitation. In our pump-probe setup, we used one (degener- ate regime) or two (nondegenerate regime) synchronized Ti:Sapphire lasers, each with pulse duration of 5 ps and pulse repetition period of 13.2 ns corresponding to a rep- etition frequency of 75.6 MHz. The laser wavelength was tuned in resonance with either the QW exciton or trion transitions. The circular polarization of the pump beam was modulated at 50 kHz by an elasto-optical modula- tor. The excitation density was kept close to the lowest possible limit at 0.5 W/cm $^{2}$. A sensitive balanced pho- todiode scheme was used for recording the Faraday rota- tion and ellipticity signals. The sample was mounted in a cryostat with a split-coil superconducting magnet which allowed us to perform experiments in the Voigt config- uration with the magnetic field B ‖ x oriented in the quantum well plane perpendicular to the light propaga- tion direction (coinciding with the structure growth axis, denoted as z -axis). The sample temperature was var- ied from 0.34 K to 80 K. For milliKelvin measurements the cryostat had a $^{3}$He inset, instead of a $^{4}$He variable temperature inset. The sample was then in contact with $^{3}$He in the inset, whose temperature could be changed between 0.3 and 100 K. Windows on the $^{3}$He inset allow Now we turn to the spectral dependencies of the long- lived oscillations in the Faraday rotation and ellipticity signals, which are shown in Fig. 2. The experimental data measured at relatively large positive pump-probe delay of 2 ns and a small negative delay (shortly before pump pule arrival) are given in panels (a) and (b), re- spectively. The Faraday rotation and ellipticity signals obviously demonstrate quite different spectral behaviors. The maximum of the ellipticity signal and the zero of the FR signal are close to the trion resonance energy. Also, there is an extra feature in the ellipticity signal around the exciton resonance. The Faraday rotation, F , and ellipticity, E , of the probe pulse are proportional to the imaginary and real parts of the difference of quantum well transmission co- efficients for σ + and σ − polarizations, t ± , respectively. Taking into account that for the relatively thin quantum FIG. 1: (Color online) (a) Photoluminescence spectrum of the (In,Ga)As/GaAs QWs studied experimentally (black line). Filled contour represents the spectrum of the excitation laser used in the Faraday rotation and ellipticity experiments. (b) Time-resolved Faraday rotation and ellipticity signals mea- sured in nondegenerate regime (pump at 1.4395 eV, probe at 1.4382 eV). Signals are vertically shifted for clarity. T = 1 . 6 K. Inset: Long-lived parts of the signals shortly before pump pulse arrival. III. DETECTION OF FARADAY ROTATION AND ELLIPTICITY SIGNALS