Generating photon-encoded $W$ states in multiport waveguide-array systems

We propose a versatile approach for generating multipartite $W$ states in predesigned on-chip multiport photonic lattices. It is shown that is possible to produce photon-encoded $W$ states where exactly one photon is coherently “shared” among $N$ optical modes by judiciously adjusting the coupling coefficients involved in one-dimensional arrays of evanescently coupled single-mode waveguides. Two-dimensional waveguide configurations are also investigated as possible avenues to produce $W$ states with equal probability amplitudes and equal relative phases.

Figure 1

Planar 1D waveguide array of $N$identical waveguides, $\xi$ is the normalized propagation distance, and ${\kappa }_{m,n}$ represents the coupling coefficients between elements $m$ and $n$.

Figure 2

(a) Probability evolution corresponding to a single photon propagating through a planar 1D waveguide array of five elements. The coupling parameter used is ${\kappa }_1=1.618$. (b) Output probability at a normalized propagation distance of $\xi =0.861$.

Figure 3

Transverse view of a ring configuration of $N$ identical single-mode waveguides, $C$ is the coupling strength between the external guides, $\kappa$ is the coupling between the external guides and the central element, and $a_n^{†}$'s are the creation operators at the $n$th waveguide.

Figure 4

Top: Transverse view of the probability distributions corresponding to a single photon propagating through a ring configuration of waveguides with seven elements. Bottom: Theoretical evolution of the probability of detecting the photon at the blue line (lower): external waveguides and at the red line (upper) central waveguide.

Figure 5

Top: Transverse view of the probability distributions corresponding to a single photon propagating through a ring configuration of waveguides with seven elements. Bottom: Theoretical evolution of the probability of detecting the photon at the blue line (lower): external waveguides and at the red line (upper): central waveguide.