Dynamics of Inter-Landau-Level Excitations of a Two-Dimensional Electron Gas in the Quantum Hall Regime

The femtosecond inter-Landau-level dynamics of a two-dimensional electron gas in a large magnetic field is investigated by degenerate four-wave mixing on modulation doped quantum wells. We observe a large transfer of oscillator strength to the lowest Landau level, and unusual dynamics due to Coulomb correlation. We interpret the effects using a model based on shakeup of the electron gas.

Figure 1

Spectrally resolved FWM signal at $B=8\mathrm{T}$ for laser exciting an equal number of $e\text{−}h$ pairs into both Landau levels 0 and 1, for (a) the MDQWs, and (b) the undoped QWs. The back screens show the laser and absorption spectra.

Figure 2

FWM vs time delay $\Delta t$ for the MDQWs at $B=8\mathrm{T}$. The solid curve is the signal from LL0 and the dashed curve is from LL1. The laser is tuned to excite LL1 (60:1 over LL0), and the signals have been normalized for clarity. The decay time for both curves is $\approx 0.25\mathrm{p}\mathrm{s}$. The rise time for the LL1 signal is $0.13\mathrm{p}\mathrm{s}$, as expected from mean-field theory, while for LL0 it is $0.27\mathrm{p}\mathrm{s}$. The inset shows the SR-FWM signal at $\Delta t=0\mathrm{p}\mathrm{s}$ for this excitation from both the doped (solid) and undoped (dashed) QWs.

Figure 3

Model calculation of the FWM profile vs time delay $\Delta t$. The inset shows a FWM process which involves the excitation and destruction of a MP. We photoexcite an $X$ state (a) which scatters with the 2DEG (b) and then is deexcited (c), leaving the 2DEG in an excited state (the VB states are strongly mixed by the magnetic field, allowing this transition [17]). The process is reversed in panels (d)–(f). Note that the excitation shown in (b) does not exist in undoped QWs, and we call this state $Y$. The upper graph shows the signal vs $\Delta t$ at the LL0 energy, and the lower one the signal at the LL1 energy, when only mean-field $X$-$X$ interactions are in the model without the 2DEG (dotted line), when we add only the $X$-$X$ interactions (dashed line), and when we also add MP scattering processes such as those described in the inset (solid line).