Dynamics of the collective excitations of the quantum Hall system

Using the non linear optical technique of 3-pulse 4-wave mixing, we study the dynamics of the collective excitations of the quantum Hall system. We excite the system with 100 fs pulses propagating in directions k1 and k3 and then probe its time evolution with a delayed pulse k2. We measure the non-linear optical response from the lowest Landau level along the direction k1+k2−k3. As function of the time delay of pulse k2, this signal shows striking beats for short time delays (∼500 fs), followed by a rise (∼20 ps) and then a decay (∼100 ps). We identify the microscopic origin of this dynamics by extending the standard theory of ultra fast nonlinear optics to include the effects of the correlations.