Multiphoton path-entanglement generation by concurrent parametric down-conversion in a single ${\chi }^{\left(2\right)}$ nonlinear photonic crystal

We propose a two-dimensional ${\chi }^{\left(2\right)}$ nonlinear photonic crystal capable of satisfying quasi-phase-matching conditions for two or three parametric down-conversions simultaneously. Seeded by a two-mode coherent state, this crystal can produce two-, three-, four-, or five-photon path-entangled states, provided the corresponding number photons are produced, i.e., in a postselection-free way. In particular, up to five-photon NOON state can be generated, which enables phase supersensitive measurements at the Heisenberg limit. The concurrent multiple quasi-phase-matchings provided by the nonlinear photonic crystal open up a way to integrated quantum light sources.

Figure 1

(a) Schematic of a 2D ${\chi }^{\left(2\right)}$ NPC with a rectangular inverted domain structure. (b) Reciprocal lattice of the crystal. Thick gray arrows represent pump, signal, and idler wave vectors. Thin black arrows represent reciprocal vectors of the crystal. (c) Transverse pattern of the parametric light in the Fourier plane.

Figure 2

(a) Schematic of the reciprocal lattice of a 2D ${\chi }^{\left(2\right)}$ NPC with a square inverted domain structure. Thick gray arrows represent pump, signal, and idler wave vectors. Thin black arrows represent reciprocal vectors of the crystal. (b) Transverse pattern of the parametric light in the Fourier plane.

Figure 3

Scheme for path-entanglement generation from a single NPC.