ar X iv : 1 40 6 . 42 52 v 1 [ qu an t - ph ] 1 7 Ju n 20 14 Time - frequency quantum process tomography of para - metric down - conversion

Parametric down-conversion (PDC) is the established standard for the practical generation of a multiplicity of quantum optical states. These include two-mode squeezed vacuum1, heralded non-Gaussian states2–6 and entangled photon pairs7, 8. Detailed theoretical studies provide insight into the time-frequency (TF) structure of PDC, which are governed by the complex-valued joint spectral amplitude (JSA) function9–11. However in experiments, the TF structure of PDC is mostly characterised by intensity measurements12–15that forbid access to the important phase of the JSA16. In this paper, we present an amplitude-sensitive quantum process tomography technique that combines methods from ultrafast optics and classical three-wave mixing. Our approach facilitates a direct and phase-sensitive time-frequency tomography of PDC with high spectral resolution and excellent signal-to-noise ratio. This is important for all quantum optical applications, which rely on engineered parametric processes and base on minute knowledge of the quantum wave-function for the generation of tailored photonic quantum states.