Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices

We demonstrate a general method of engineering the joint quantum state of photon pairs produced in spontaneous parametric down-conversion. The method makes use of a superlattice structure of nonlinear and linear materials, in conjunction with a broadband pump, to manipulate the group delays of the signal and idler photons relative to the pump pulse, and realizes photon pairs described by a joint spectral amplitude with arbitrary degree of entanglement. This method of group-delay engineering has the potential of synthesizing a broad range of states including factorizable states crucial for quantum networking and states optimized for Hong-Ou-Mandel interferometry. Experimental results for the latter case are presented, illustrating the principles of this approach.

Figure 1

Nonlinear crystal superlattice, pumped by an ultrashort pulse, yielding an arbitrary degree of entanglement. Sections of nonlinear material, length L (shaded) are separated by sections of linear material, length h (light).

Figure 2

Density plots of: (a) single crystal segment PMF exhibiting lack of symmetry, (b) BBO-quartz-BBO superlattice contribution to the PMF, (c) pump envelope function, (d) JSI symmetrized by the superlattice. (e) Time (with respect to pump pulse) at which signal-idler generated halfway through the first crystal traverse each point of two crystal segments. (f) Same as before for a BBO-quartz-BBO superlattice; signal-idler walk-off is limited to its single crystal value.

Figure 3

$\mathrm{BBO}1/\mathrm{BBO}2$: $250\mu \mathrm{m}$ BBO crystals, QTZ: 1.53 mm quartz spacer, MO: $16\times$ microscope objective, $\mathrm{BP}1/\mathrm{BP}2$: bandpass filters of 40 nm width, $\mathrm{APD}1/\mathrm{APD}2$: avalanche photo diodes. Labels for other components are defined in the text.

Figure 4

HOM interference curves, normalized to a unit background to suppress source brightness variation resulting from realignment for each experiment. (a) single crystal segment. (b) Two crystal segments in sequence, exhibiting reduced visibility and broadening. (c) BBO-quartz-BBO superlattice exhibiting restoration of visibility. (d) BBO-quartz-BBO with quartz rotated by 90°; visibility no longer restored.