非均匀磁场下可伸缩量子寄存器的反铁磁核自旋模型
Antiferromagnet-based nuclear spin model of scalable quantum register with inhomogeneous magnetic field
摘要：
作为一种可伸缩量子寄存器的核自旋模型，考虑了核自旋为1/2的磁性原子链替代核自旋自由易轴三维反铁磁体中的基本原子的一维链.在自旋波近似下（低温），考虑了非均匀外磁场，该磁场沿垂直于板平面的易磁化轴方向，沿核自旋链方向具有恒定梯度，导出了广义反铁磁哈密顿量.在弱梯度条件下，得到了反铁磁哈密顿量对角化幺正变换系数的渐近表达式，并由此求得了原子中超精细核电子耦合和反铁磁基态中虚自旋波传播引起的间接自旋间耦合的表达式.结果表明，非均匀磁场从本质上改变了间接自旋间耦合的特性。当两核自旋中点的局域场接近体反铁磁自旋翻转型量子相变的临界场或接近反铁磁共振时，间接相互作用随自旋间距的增大而增大，甚至振荡.因此，外部磁场、其梯度、微波频率和功率可以起到量子比特状态的控制参数的作用。最后计算了反铁磁基态中核自旋与虚自旋波相互作用引起的单、双量子比特态的退相干和纵向弛豫速率。
英文摘要：
As a nuclear spin model of scalable quantum register, the one-dimensional chain of the magnetic atoms with nuclear spins 1/2 substituting the basic atoms in the plate of nuclear spin free easy-axis 3D antiferromagnet is considered. It is formulated the generalized antiferromagnet Hamiltonian in spin-wave approximation (low temperatures) considering the inhomogeneous external magnetic field, which is directed along the easy axis normally to plane of the plate and has a constant gradient along the nuclear spin chain. Assuming a weak gradient, the asymptotic expression for coefficients of unitary transformations to the diagonal form of antiferromagnet Hamiltonian is found. With this result the expression for indirect interspin coupling, which is due to hyperfine nuclear electron coupling in atoms and the virtual spin wave propagation in antiferromagnet ground state, was evaluated. It is shown that the inhomogeneous magnetic field essentially modifies the characteristics of indirect interspin coupling. The indirect interaction essentially grows and even oscillates in relation to the interspin distance when the local field value in the middle point of two considered nuclear spin is close to the critical field for quantum phase transition of spin-flop type in bulk antiferromagnet or close to antiferromagnetic resonance. Thus, the external magnetic field, its gradient, microwave frequency and power can play the role of control parameters for qubit states. Finally, the one and two qubit states decoherence and longitudinal relaxation rate are caused by the interaction of nuclear spins with virtual spin waves in antiferromagnet ground state are calculated.
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