Figure 1

(a) Energy level diagram of the two photon transition $5S\to 5D$ in atomic Rb. Wavelengths shorter than 761 nm are blocked as they spectrally overlap the $5S\to 7S$ transition. (b) Outline of the experimental setup. (c) Schematic description of the noninterfering paths induced by two photons of parallel polarization and by two photon of orthogonal polarizations. (d) Schematic description of interfering paths induced by pairs of photons with parallel polarizations.Reuse & Permissions

Figure 2

TPA measurement for polarization and phase spectral manipulations. The TPA is measured for: (a) polarization-only filter as a function of the polarization step position (solid line). (b) phase-only filter as a function of a $\pi$ step position (dashed line), and with a constant polarization step located at 788 nm (solid line). Inset: Schematic drawing of the spectral polarization of the electric field.Reuse & Permissions

Figure 3

TPA measurement (left panel) and calculated result (right panel) as a function of the polarization step position (along the vertical direction) and the $\pi$ phase step position (along the horizontal direction). In region I we control the transitions induced by photon pairs with orthogonal polarizations, corresponding to $|f,F^{\prime \prime },M\pm 1⟩$ states. In regions II and III we control the transitions induced by photon pairs with parallel polarization, corresponding to $|f,F^{\prime \prime },M,M\pm 2⟩$ states. The measurement and calculated images are inverted, due to the symmetry about half of the two photon transition frequency.Reuse & Permissions

Figure 4

TPA population measurement for a constant spectral polarization function and a variable phase step, setting a relative phase between the $E_x{E}_x$ and the $E_y{E}_y$ terms. The signal is measured as a function of the relative phase for the $5S\to 5D$ transition (solid line) and for the $5S\to 7S$ transition (dashed line). Inset: Schematic drawing of the spectral polarization and phase of the electric field used in the experiment.Reuse & Permissions