The antiferromagnet-based nuclear spin quantum register in inhomogeneous magnetic field

As a large-scale quantum register, the one-dimensional chain of the magnetic atoms with nuclear spins 1/2 in thin plate of nuclear spin-free easy-axis 3D antiferromagnet is considered. The external magnetic field is directed along the easy axis, normally to the plate surface and has a week constant gradient along the nuclear spin chain. The expression for indirect inter-spin coupling, which is due to hyperfine nuclear electron coupling in atoms and spin-wave propagation in antiferromagnet, was evaluated. It was shown that near critical point of spin-flop quantum phase transition in antiferromagnet indirect nuclear spin coupling in inhomogeneous external magnetic field might have both long-range damping and oscillating dependence from interspin distance. The external magnetic field and its gradient play the role of control parameters.