  Exciton, trion and electron spin dynamics in a 20 nm wide modulation-doped
GaAs single quantum well are investigated using resonant ultrafast two-color
Kerr rotation spectroscopy. Excitons and trions are selectively detected by
resonant probe pulses while their relative spectral weight is controlled by
adjusting the gate voltage which tunes the carrier density. Tuning the carrier
density markedly influences the spin decay time of the two dimensional electron
gas. The spin decay time can be enhanced by a factor of 3 at an intermediate
carrier concentration in the quantum well, where excitons and trions coexist in
the system. In addition, we explore the capability to tune the g-factor of the
electron gas via the carrier density.
