Quantum entanglement of anisotropic magnetic nanodots

Anisotropic magnetic nanodots are promising physical realizations of qubits for quantum computing at finite temperature owing to their well-separated low-lying energy levels and scalability. The entanglement of two interacting magnetic nanodots is investigated and shown both analytically and numerically to be resonantly dependent on their interaction strength and on differences in their properties. These results provide criteria for fabricating and coupling magnetic nanodots so that their low-lying eigenstates can be significantly entangled.

Figure 1

Schematic of the low-lying basis states of two inequivalent nanodots coupled by (a) ferromagnetic and (b) antiferromagnetic couplings. The arrows denote single-dot spins; the $\mid S_z\mid =S$ states and $\mid S_z\mid =S-1$ states are denoted by ∣0⟩ and ∣1⟩, respectively.

Figure 2

Energy eigenstates of two interacting magnetic nanodots, considering, respectively, only the two and four lowest-energy levels in each dot. Curves in bold represent energy eigenvalues occurring in both the two- and four-level approximations; curves of regular thickness correspond to those occurring only in the four-level approximation. The fixed parameters are $S_0=S_0^{\prime }=1$, $N=1000$, $N^{\prime }=1100$, and $K_u=50\mathrm{K}$.

Figure 3

Concurrence of the lowest-lying entangled states as a function of the anisotropy $K_u^{\prime }$ of the second dot. The solid and dashed curves denote the concurrence $C$ for the cases of FM and AFM couplings, respectively, for several values of $\mid J\mid$: (1) $0.005\mathrm{K}$, (2) $0.01\mathrm{K}$, (3) $0.025\mathrm{K}$, (4) $0.05\mathrm{K}$, and (5) $0.1\mathrm{K}$. The fixed parameters are $S_0=S_0^{\prime }=1$, $N=1000$, $N^{\prime }=1100$, and $K_u=50\mathrm{K}$. A resonancelike behavior of concurrence is seen for small values of $J$ for the case of FM coupling, in contrast to the case of AFM coupling.