Transport and quantum walk of nonclassical light in coupled waveguides

We study the transport and quantum walk of nonclassical light in an array of coupled waveguides which have properties like very low decoherence and thus making them ideal for storage of quantum information. We show how squeezing gets turned over from one waveguide to another. We further show how input nonclassical light can generate entanglement among different waveguides. Our results, which are valid for an arbitrary number of waveguides, involve both first quantization due to array structure and second quantization due to the quantum nature of fields and can also be used to discuss the Talbot effect in the quantum regime.

Figure 1

(Color online) Coupled waveguide array.

Figure 2

(Color online) Behavior of the normalized intensity as a function of $\tau$ $(\tau \equiv Jt∕\pi )$. The input is injected into the first waveguide and the number of waveguides in the system is $N=6$.

Figure 3

(Color online) Time evolution of the squeezing factor $s_j\left(q\right)$ as a function of $\tau$ $(\tau \equiv Jt∕\pi )$. The input is in the first waveguide and the number of waveguides in the system is $N=5$. The magnitude and the phase of the squeezing parameter are chosen as $r=0.7$ and $\varphi =0$, respectively.

Figure 4

(Color online) The top [bottom] part shows the variation of $s_j\left(q\right)$ $\left[s_j\left(p\right)\right]$ as a function of $\tau \equiv Jt∕\pi$ for $j=1,\dots ,5$, smeared out in the $j$ direction. The magnitude and the phase of the squeezing parameter are chosen as $r=0.7$ and $\varphi =0$, respectively. The number of waveguides in the system is $N=5$.

Figure 5

(Color online) The correlation function $M(j,k)$ as a function of $\tau$ $(\tau \equiv Jt∕\pi )$ for the case of six waveguides. The magnitude and the phase of the squeezing parameter are chosen as (a) $r=0.7$ and $\varphi =3\pi ∕2$ and (b) $r=0.6$ and $\varphi =\pi$, respectively.