Quantum interface between light and nuclear spins in quantum dots

The coherent coupling of flying photonic qubits to stationary matter-based qubits is an essential building block for quantum-communication networks. We show how such a quantum interface can be realized between a traveling-wave optical field and the polarized nuclear spins in a singly charged quantum dot strongly coupled to a high-finesse optical cavity. By adiabatically eliminating the electron a direct effective coupling is achieved. Depending on the laser field applied, interactions that enable either write-in or read-out are obtained.

Figure 1

(Color online) (a) Singly charged QD coupled to high-Q optical cavity. (b) Level scheme of the QD. Optical and hyperfine transitions.

Figure 2

(Color online) Evolution of the two-photon Fock state ${\psi }_{20}$ under the full Hamiltonian $H^{\prime }$ (solid lines) and Hamiltonian $H_{\text{bs}}$ ($\times$, dashed and dotted lines), where the trion and the electronic spin-up state have been eliminated.

Figure 3

(Color online) Average fidelity for the mapping of coherent states to the nuclei via teleportation (after complete decay of the cavity) plotted as a function of the interaction time $t_{\text{off}}$ for different values of $g/\gamma =1$, 10, and 100 (solid, dash-dotted, and dashed). All fidelities converge to 1 as $gt\to \infty$.

Figure 4

(Color online) Level scheme of the QD (a) electronic and trion states split in an external magnetic field in growth direction. They are coupled by a ${\sigma }^{-}$-polarized laser and a ${\sigma }^{+}$-polarized cavity field with frequencies ${\omega }_l$ and ${\omega }_c$, respectively. (b) Additional to the setting in (a), a microwave field resonant with the splitting of the trion states in the magnetic field $\left({\omega }_{\Uparrow }-{\omega }_{\Downarrow }={\omega }_{mw}\right)$ mixes the trion states. Laser and cavity couple both electronic states to the trion states $|+⟩$ and $|-⟩$.

Figure 5

(Color online) Performance of the quantum interface for the maximally entangled input state ${\psi }_{in}\propto {\sum }_{k=1}^2{|k⟩}_R{|k⟩}_c$ (subscript $c$ indicates the cavity). The red solid curve shows the fidelity $F_{\text{bs}}$ of ${\psi }_{in}$ evolved under $H_{\text{bs}}$ with the ideal target state $|{\psi }_{map}⟩\propto {\sum }_{k=1}^2{\left(-1\right)}^{lk}{\left(i\right)}^k{|k⟩}_R{|k⟩}_n$ (subscript $n$ indicates the nuclei) for $gtϵ\left[l\pi ,\left(l+1\right)\pi \right]$, where $l$ takes into account the phases acquired during mapping, see text. The blue solid curve shows the fidelity ${\tilde{F}}_{\text{bs}}$ with $|{\tilde{\psi }}_{map}⟩\propto {\sum }_{k=1}^2{\left(-1\right)}^{lk}{|k⟩}_R{|k⟩}_c$ for $gtϵ\left[\frac{2l+1}{2}\pi ,\frac{2l+3}{2}\pi \right]$. Dashed curves depict the same fidelities for evolution under $H^{\prime }$ (denoted by $F_{H^{\prime }}/{\tilde{F}}_{H^{\prime }}$). (Parameters chosen as in the text.)