Coherent coupling of individual quantum dots measured with phase-referenced two-dimensional spectroscopy: photon echo versus double quantum coherence

We employ two-dimensional (2D) coherent, nonlinear spectroscopy to investigate couplings within individual InAs quantum dots (QD) and QD molecules. Swapping pulse ordering in a two-beam sequence permits to distinguish between rephasing and non-rephasing four-wave mixing (FWM) configurations. We emphasize the non-rephasing case, allowing to monitor two-photon coherence dynamics. Respective Fourier transform yields a double quantum 2D FWM map, which is corroborated with its single quantum counterpart, originating from the rephasing sequence. We introduce referencing of the FWM phase with the one carried by the driving pulses, overcoming the necessity of its active-stabilization, as required in 2D spectroscopy. Combining single and double quantum 2D FWM, provides a pertinent tool in detecting and ascertaining coherent coupling mechanisms between individual quantum systems, as exemplified experimentally.