Dispersion sensitivity of amplitude and phase modulated time-energy entangled photons

We demonstrate spectral amplitude and phase modulation of time-energy entangled photon pairs by means of a spatial light modulator (SLM) [1]. Coincidences are detected by sum frequency generation in a nonlinear crystal which has been applied in several experiments as an ultrafast coincidence detection method to temporally resolve entangled photons on a timescale of fs [2,3]. By taking into account the properties of the detection crystal, we derive an expression for the up-converted frequency signal in the form of a second-order correlation function G⁽¹⁾ [3]. This detection scheme is in contrast to a perfect coincidence detection described by the fourth-order correlation function G⁽²⁾. However, in former two photon shaping experiments [1,2] the detected signal was compared to simulations based on G⁽²⁾. We investigate here under which conditions the G⁽²⁾ ceases to provide an accurate description of the measurements.