Non-classical light state transfer in $su(2)$ resonator networks

TL;DR

This paper investigates quantum state transfer in $su(2)$ symmetric resonator networks using a normal mode approach, revealing conditions for full and partial transfer and providing insights into quantum state reconstruction times.

Contribution

It introduces a normal mode method to analyze quantum state transfer in $su(2)$ networks, including the $J_x$ lattice, and characterizes transfer times and phase shifts affecting state fidelity.

Findings

Full quantum state transfer occurs in networks of size $4n+1$.

Initial Fock state probabilities are conserved during transfer.

Partial transfer results from phase shifts in other network sizes.

Abstract

We use a normal mode approach to show full and partial state transfer in a class of coupled resonator networks with underlying $su(2)$ symmetry that includes the so-called $J_{x}$ photonic lattice. Our approach defines an auxiliary Hermitian coupling matrix describing the network that yields the normal modes of the system and its time evolution in terms of orthogonal polynomials. These results provide insight on the full quantum state reconstruction time in a general $su(2)$ network of any size and the full quantum transfer time in the $J_{x}$ network of size $4 n + 1$ with $n=1,2,3,\ldots$ In the latter, our approach shows that the Fock state probability distribution of the initial state is conserved but the amplitudes suffer a phase shift proportional to $\pi/2$ that results in partial quantum state transfer for any other network size.