Perfect transfer of multiple excitations in quantum networks

We present a general formalism to the problem of perfect state transfer (PST), where the state involves multiple excitations of the quantum network. A key feature of our formalism is that it allows for inclusion of nontrivial interactions between the excitations. Hence, it is perfectly suited to addressing the problem of PST in the context of various types of physical realizations. The general formalism is also flexible enough to account for situations where multiple excitations are “focused” onto the same site.

Figure 1

A permutation of block-diagonal form.

Figure 2

Plots of the probability of finding an excitation at each node as a function of time for a network of $M=5$ sites. Both plots correspond to the parameters $W=0.035672$, $J_{1,2}=3.15891$, and $J_{2,3}=3.84084$. In plot (a), the initial state $|1,\mu ;2,\nu \rangle$ is transferred to $|4,\mu ;5,\nu \rangle$, while in (b) the initial state $|1,\mu ;4,\nu \rangle$ is transferred to $|2,\mu ;5,\nu \rangle$.

Figure 3

Plot of the probability of transfer as a function of time for a centrosymmetric network with $M=5$ sites, and spatially dependent couplings of the form given by (11), with $J=\pi$. The parameters used are those given in Table . The solid line shows the probability of finding the system in the state $|4,\nu ;5,\mu \rangle$, when it was initially prepared in the state $|1,\mu ;2,\nu \rangle$. The dotted line shows the probability of finding the system in the state $|3,\nu ;4,\mu \rangle$, when it was initially prepared in the state $|2,\mu ;3,\nu \rangle$.