Pseudoentanglement of Spin States in the Multilevel ${}^{15}\mathrm{N}@{\mathrm{C}}_{60}$ System

We have prepared combined electron and nuclear spin pseudoentangled states ${\Psi }_{27}^{\pm }$ and ${\Phi }_{18}^{\pm }$ out of the total number of eight quantum states in the multilevel quantum system of a nitrogen atom with electron spin $3/2$ and nuclear spin $1/2$ encaged in the endohedral fullerene ${}^{15}\mathrm{N}@{\mathrm{C}}_{60}$. Density matrix tomography was applied to verify the degree of entanglement.

Figure 1

Level diagram of the eight spin states of ${}^{15}\mathrm{N}@{\mathrm{C}}_{60}$. Allowed transitions (solid lines) and forbidden transitions between selected entangled states (dashed lines) are indicated.

Figure 2

Pictorial representation of the initial density matrix ${\rho }_{(-+)}$ (left) and the density matrix of the entangled state ${\rho }_{{\Psi }^{(-)}}$ (right) of the fictitious two-qubit sublevel states $|\pm \pm ⟩$ as defined in the text. For details on the values displayed see Eq. (5) and the corresponding text.

Figure 3

Phase interferograms (left) and corresponding spectra (right) for the entangled states with phase incrementation frequencies ${\nu }_1=2.0\mathrm{M}\mathrm{H}\mathrm{z}$ and ${\nu }_2=1.0\mathrm{M}\mathrm{H}\mathrm{z}$ as discussed in the text. (a) ${\nu }_1=0$, ${\nu }_2=1.0\mathrm{M}\mathrm{H}\mathrm{z}$; (b) $3{\nu }_1=6.0\mathrm{M}\mathrm{H}\mathrm{z}$, ${\nu }_2=0$; (c) $3{\nu }_1-{\nu }_2=5.0\mathrm{M}\mathrm{H}\mathrm{z}$ as expected for ${\rho }_{{\Psi }^{(-)}}$; (d) $3{\nu }_1+{\nu }_2=7.0\mathrm{M}\mathrm{H}\mathrm{z}$ as expected for ${\rho }_{{\Phi }^{(+)}}$. See text for additional lines.