Tailoring the correlation and anticorrelation behavior of path-entangled photons in Glauber-Fock oscillator lattices

We demonstrate that single-photon as well as biphoton revivals are possible in a new class of dynamic optical systems—the so-called Glauber-Fock oscillator lattices. In these arrays, both Bloch-like oscillations and dynamic delocalization can occur which can be described in closed form. The bunching and antibunching response of path-entangled photons can be pre-engineered in such coupled optical arrangements, and the emulation of fermionic behavior in this family of lattices is also considered. We elucidate these effects via pertinent examples.

Figure 1

Bloch-like oscillation for a single photon propagating through Glauber-Fock oscillator lattices. The red arrow indicates the site where the photon is being launched. The lattice parameters used are ${\kappa }_0=1$, and $\lambda =1/2$, $\lambda =4/5$ for (a) and (b), respectively.

Figure 2

Evolution of the probability distributions for single photons propagating through this Glauber-Fock oscillator lattices with $\lambda =1$ and $\varpi =3/4$ for (a), and $\varpi =2/3$ for (b). Dashed lines show the evolution of ${\left|B\left(Z\right)\right|}^2$ along $Z$, predicting the corresponding revival distance at $8\pi$ and $6\pi$, respectively.

Figure 3

Theoretical evolution of the probability of having one photon at waveguide $n$ when launched at channel 0, $P_{n,0}\left(Z\right)=\langle a_n^{†}{a}_n\rangle$, under the resonance condition.

Figure 4

Left column shows the quantum correlation maps when the input state $|{\psi }_C\rangle$ is coupled into a modulated-tilted Glauber-Fock oscillator array $(\lambda =1/2,\varpi =3/4)$. Similarly, the right column depicts the correlation evolution for the input state $|{\psi }_A\rangle$.

Figure 5

Correlation matrices at $Z=15\pi$ for the initial states (a) $|{\psi }_C\rangle$, (b) $|{\psi }_A\rangle$ and (c) $|{\psi }_F\rangle$.