Figure 1

(a) The energy levels of the Hamiltonian given by Eq. (3). (b) The EoF (dotted lines) and quantum discord (full lines) of the state $\rho$ given by Eq. (4). When the temperature increases from 0 to 2 K, the EoF vanishes while the discord remains positive. The sudden changes of the discord correspond to the level crossings shown in (a).Reuse & Permissions

Figure 2

(a) Energy level diagram of the P:Si system. There are four Zeeman product states which are labeled states 1–4, where the left and the right $\uparrow$ ($\downarrow$) stands for the $\pm 1/2$ states of electron and nuclear spins, respectively. EPR and NMR transitions are indicated by two-way arrows. (b) Experimental results of the relaxation time measurements. The curve labeled $T_{1e}$ is collected from the echo-detected inversion recovery experiment (the related time axis is the bottom one), from which $T_{1e}$ is obtained. The curve labeled $T_{2d}$ is the electron spin echo decay through the Hahn echo sequence, from which $T_{2e}$ is obtained. The curve labeled $T_{2n}^{*}$ is the results of the nuclear spin FID with pulse sequence (${\pi }_{2,4}-\pi /2_{1,2}-\tau -\pi /2_{1,2}-$echo, $\tau$ a variable), which is used to calculate $T_{2n}^{*}$. Note that the time axis for the $T_{2e}$ and $T_{2n}^{*}$ curves is the top one. The inset shows the decay of ${\rho }_{23}$, where the time scale is nanosecond. The experimental data (black circles) were fitted with a damped exponential function (gray line) of the form $y=y_0+A{e}^{-{\left(\frac{t}{t_c}\right)}^2}$. (c) Diagram of the experimental pulse sequences. We use upper (lower) pulse sequence to generate the state $\rho$, in the case of $c_z>0$ ($c_z<0$). ${\theta }_{2,4}$ (${180}_{1,3}$) is a MW1(MW2) pulse to rotate the electron spin by $\theta$ ($\pi$). ${90}_{1,2(3,4)}$ stands for a $\pi /2$ RF1(RF2) pulse. The tomography procession is composed of a readout pulse sequence and electron spin echo detection.Reuse & Permissions

Figure 3

(a) The readout of ${\rho }_{23}$. I${}_{+x}-$I${}_{-x}$ (circles, in red) and I${}_{+y}-$I${}_{-y}$(triangles, in green) are plotted. Sine functions(dashed lines) are fitted to the experimental data. The $x$ axis is the rotation angle $\phi$ and the $y$ axis is the amplitude of the echo in unit of $\epsilon$. The results give both real and imaginary parts of ${\rho }_{23}$. (b) The reconstructed deviation density matrix $\delta \rho =\rho -\frac{1}{4}\mathbb{1}$ in unit of $\epsilon$, when $c_x=c_y=-0.0044$ and $c_z=-0.0008$.Reuse & Permissions

Figure 4

The behavior of quantum correlations when $\Delta$ varies. The $x$ axis is the tuning parameter $\Delta$ and the $y$ axis is quantum discord. The circles are experimental data of quantum discord derived from the reconstructed density matrices (Ref. 37), which agree with the solid lines calculated using Eq. (2). The deviation between the experimental data and the theoretical prediction is due to the imperfection of the pulses.Reuse & Permissions