Extracting double-quantum coherence in two-dimensional electronic spectroscopy under pump-probe geometry

Optical two-dimensional (2D) spectroscopy under pump-probe geometry has achieved significant successes in one-quantum research. However, due to the typical phase matching condition, its implementation on the measurement of double-quantum (2Q) coherence have been limited for long, until recently Farrell and Zanni realized detecting 2Q signal with a permuted--pump--probe pulse sequence in 2D infrared spectroscopy. Here, we promote this technique to 2D electronic spectroscopy. Using this pulse sequence, both the 2Q and zero-quantum (0Q) signal will be detected. We present that with the propagation phase of the probe pulse and by applying a rotating frame, the 2Q and 0Q coherence exhibit distinct effective oscillation frequencies during the scanned interval. These frequencies may share the same sign. We propose that 2Q and 0Q coherence could be separated onto different spectra using phase cycling techniques and causality enforcement. Our experimental demonstration on measuring the electronic 2Q coherence of rubidium atoms yields broadband spectra. Notably, we simultaneously observe not only the doubly excited state of an individual rubidium atom but also the collective resonances of dipole-dipole interactions of both $D_{1}$ and $D_{2}$ lines.