Exciton-exciton interaction and biexcitons in the presence of spin-polarized carriers

We present an absorption study of the neutral exciton, biexciton and positively charged exciton (trion) in a (Cd,Mn)Te quantum well under the influence of a femtosecond, circularly polarized, resonant pump pulse. By using spin-dependent selection rules in a quantum well containing a strongly diluted magnetic semiconductor, we could unambiguously separate the biexcitonic transitions from the charged exciton ones, and we report on their simultaneous observation for a well chosen configuration of the pump and probe polarization. The influence of the hole gas on the biexciton line is described. In a polarization such as the charged exciton line is not present in the transmission spectrum, the sum of the neutral exciton and biexciton intensities is conserved, whatever the density of preexisting holes. However, when both the charged exciton and the biexciton coexist, we observed some intensity stealing from the biexciton by the charged exciton.

Figure 1

Absorption transitions for different configurations of the circularly polarized pump (solid vertical lines) and probe pulses (dashed vertical line, observed transitions are indicated) in a magnetic field.

Figure 2

(Color online.) (a),(b) Transmission of the ${\sigma }^{+}$ (a) and ${\sigma }^{-}$ (b) polarized probe pulse 10 ns after the cross-polarized pump pulse (“negative delay”). (c),(f) Difference transmission spectra for zero delay (black solid lines), 2 ps positive delay (red dashed lines), and 4 ps positive delay (green dotted lines). The magnetic field was $B=0.5\mathrm{T}$, the hole density $p=0.5\times {10}^{10}{\mathrm{cm}}^{-2}$. Pump and probe polarizations are also indicated. Arrows denote the position of the neutral exciton and charged exciton lines at negative delays (which depends on the polarization of the pump due to heating of the Mn system, see text), and the biexciton energy at zero delay.

Figure 3

Transmission at negative delay, for a probe pulse polarized ${\sigma }^{-}$ (dashed line) or ${\sigma }^{+}$ (solid line), without applied field (center), or with a field of 1 T, with the pump pulse polarized ${\sigma }^{-}$ (bottom) or ${\sigma }^{+}$ (top).

Figure 4

Change of neutral exciton intensity and biexciton intensity. The applied field was 0.5 T. The hole density was $0.5\times {10}^{10}{\mathrm{cm}}^{-2}$ (black symbols), $1\times {10}^{10}{\mathrm{cm}}^{-2}$ (dark grey), or $4\times {10}^{10}{\mathrm{cm}}^{-2}$ (light grey). Full symbols mark ${\sigma }^{+}$ probe and open symbols ${\sigma }^{-}$ probe. Most of data are for cross-polarized configurations, but triangles which are for the $(+∕+)$ one. (a) Change of the exciton intensity (circles) and biexciton intensity (squares) as a function of the pump power absorbed in the neutral exciton creation process (or, equivalently, the neutral exciton density, upper scale). (b) Biexciton intensity versus the change of neutral exciton intensity. (c) Change of X intensity normalized to its intensity at negative delays, as a function of the neutral exciton density.