Time-resolved charge fractionalization in inhomogeneous Luttinger liquids

The recent observation of charge fractionalization in single Tomanga-Luttinger liquids (TLLs) [Kamata et al., Nature Nanotech., 9 177 (2014)] opens new routes for a systematic investigation of this exotic quantum phenomenon. In this Letter we perform measurements on two adjacent TLLs and put forward an accurate theoretical framework to address the experiments. The theory is based on the plasmon scattering approach and can deal with injected charge pulses of arbitrary shape in TLL regions. We accurately reproduce and interpret the time-resolved multiple fractionalization events in both single and double TLLs. The effect of inter-correlations between the two TLLs is also discussed.