Dynamics of the fractional quantum Hall edge probed by stroboscope measurements of trions

By using observations from pump-probe stroboscopic confocal microscopy and spectroscopy, we demonstrate the dynamics of trions and the fractional quantum Hall edge on the order of $∼ 1$ ps. The propagation of the quantum Hall edge state excited by a voltage pulse is detected as a temporal change in reflectance in the downstream edge probed by optical pulses synchronized with the voltage pulse. The temporal resolution of such stroboscopic pump-probe measurements is as fast as the duration time of the probe pulse (⁠ $∼ 1$ ps). This ultra-fast stroboscope measurement enables us to distinguish between the normal mode of edge excitation, known as the edge magneto-plasmon or charge density wave, and other high-energy non-linear excitations. This is the only experimental method available to study the ultra-fast dynamics of quantum Hall edges and makes it possible to derive the metric tensor $g μ ν$ of the $( 1 + 1 ) = 2$-dimensional curved spacetime in quantum universe and black hole analogs implemented in the quantum Hall edge.