Tailoring photonic entanglement in high-dimensional Hilbert spaces

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.

Figure 1

Schematic of the experiment. See text for details.

Figure 2

Two-photon interference visibility for different dimensions $d$. The solid line is a sinusoidal fit from which we can deduce the net visibility of the fringes. The level of accidental coincidence is indicated by the straight line.

Figure 3

Two-photon interference visibility as a function of the dimension of the Hilbert space. The black circles are experimental points. The solid line is a fit with Eq. (4).

Figure 4

Visibility of the interference fringes as function of the mean number of pairs per pulse $\mu$, for $d=20$.