Perfect transfer of path-entangled photons in $J_x$ photonic lattices

We demonstrate that perfect transfer of path-entangled photons as well as of single-photon states is possible in a certain class of spin inspired optical systems—the so-called $J_x$ photonic lattices. In these fully integrable optical arrangements, perfect cyclic transitions from correlated states to totally anticorrelated states can naturally occur. Moreover we show that the bunching and antibunching response of path-entangled photons can be preengineered at will in such coupled optical arrangements. We elucidate these effects via pertinent examples.

Figure 1

(a) Schematic of a spin chain containing $N$ spin $1/2$ particles with hopping rate $J_n$ between nearest neighbors. The $n$th particle has been flipped from its ground state $|{\downarrow }_n\rangle$ to the state $|{\uparrow }_n\rangle$. (b) In the optical domain this spin system can be represented by photons being launched into the first waveguide element of an array of $N$ optical waveguides with evanescent nearest-neighbor coupling $J_n$.

Figure 2

Analytical eigenvector density ${\Psi }_m={\left|\langle u^{\left(m\right)}|u^{\left(m\right)}\rangle \right|}^2$. Label $m$ represents the eigenvector number and $n$ the corresponding components. Note that unlike standard angular momentum notation we have displaced the origin of $m$, $n$ from $-j$ to 1.

Figure 3

Probability evolution when light is launched into the (a) first, (b) second, (c) eighth, and (d) 17th waveguide. In both lattices the intensity revival distance is at $z=2\pi$.

Figure 4

(a)–(c) Upper row shows the calculated quantum correlation maps when the correlated input state $|{\psi }_C\rangle$ is coupled into a $J_x$ photonic lattice. (d)–(f) Similarly, bottom row depicts the correlation evolution for the anticorrelated input state $|{\psi }_A\rangle$.

Figure 5

(a) Theoretical average particle number at waveguide $m$, $\langle n_m\left(Z\right)\rangle$, of two single photons simultaneously launched into the first and last waveguides. The blue line indicates the distance $Z=\pi /2$, where the correlation matrix is obtained. (b), (c) Calculated correlation map ${\Gamma }_{m,n}$: As the particles approach the “collision region” $\left(Z=\pi /2\right)$, the coincidence rate vanishes for the particular combinations $\left(n-m\right)=\mathrm{odd}$, whereas for fermions it vanishes when $\left(n-m\right)=\mathrm{even}$.

Figure 6

Wave packet dynamics: evolution of a discrete Gaussian beam in a $J_x$ waveguide array. The blue arrow indicates the waveguide where the wave packet is initially centered.

Figure 7

Left column depicts the calculated intensity propagation when light is launched into (a) the first and 31st sites, (c) the first, 16th, and 31st sites, (e) the first, fifth, tenth, 16th, 22nd, 27th, and 31st sites, (g) every other site $\left(n=\mathrm{odd}\right)$, and (i) every site. In all the cases we have considered unitary input intensities at every excited waveguide. Right column shows the intensity distributions at $Z=\frac{\pi }{2}$ for each case.