Tailoring photonic entanglement in high-dimensional Hilbert spaces

Abstract

We present an experiment where two photonic systems of arbitrary dimensions can be entangled. The method is based on spontaneous parametric down-conversion with trains of $d$ pump pulses with a fixed phase relation, generated by a mode-locked laser. This leads to a photon pair created in a coherent superposition of $d$ discrete emission times, given by the successive laser pulses. Entanglement is shown by performing a two-photon interference experiment and by observing the visibility of the interference fringes increasing as a function of the dimension $d$. Factors limiting the visibility, such as the presence of multiple pairs in one train, are discussed.