Phase cycling for optical two-dimensional Fourier-transform spectroscopy*

Phase-cycling has been implemented in optical two-dimensional Fourier-transform spectroscopy to extract signals from quantum wells and quantum dots and to eliminate noise such as pump scatter co-propagating with the four-wave mixing signal. Experiments using actively phase-stabilized interferometers to cycle the excitation pulse optical phases suffer from partial noise cancellation because excitation and phase-control laser wavelengths are incommensurate. To obtain full noise elimination, we have incorporated liquid crystal variable retarders capable of imposing a $\pi $ phase shift for wavelengths 650-950 nm. We present non-rephasing spectra of potassium vapor contained in a $\sim $20 $\mu $m transmission cell and show that this phase cycling method removes all noise from pump scatter while drastically reducing the data acquisition time compared to mechanical phase-delay techniques.