  Quantum state transfer is a very important process in building a quantum
network when information from flying Qubit is transferred to the stationary
Qubit in a node via a quantum state transfer. NV centers due to their long
coherence time and the presence of nearby $13_C$ nuclear spin is an excellent
candidate for multi-Qubit quantum memory. Here we propose a theoretical
description for such a quantum state transfer from a cavity to a nearest
neighbour $13_C$ nuclear spin of a single Nitrogen vacancy center in diamond;
it shows great potential in realizing scalable quantum networks and quantum
simulation. The full Hamiltonian was considered with the zeroth-order and
interaction terms in the Hamiltonian and the theory of effective hamiltonian
theory was applied. We study the time evolution of the combined cavity-$13_C$
state through analytical calculation and simulation using QuTip. Graphs for
state transfer and fidelity measurement are presented here. We show that our
theoretical description verifies a high fidelity quantum state transfer from
the cavity to $13_C$ center by choosing suitable system parameters.
