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. Our 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 For any other network sizes, 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.
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