Graphene-based qubits in quantum communications

We explore the potential application of graphene-based qubits in photonic quantum communications. In particular, the valley pair qubit in double quantum dots of gapped graphene is investigated as a quantum memory in the implementation of quantum repeaters. For the application envisioned here, our work extends the recent study of the qubit [Wu et al., arXiv:1104.0443; Phys. Rev. B 84, 195463 (2011)] to the case where the qubit is placed in an in-plane magnetic field configuration. It develops, for the configuration, a method of qubit manipulation, based on a unique ac electric field-induced, valley-orbit interaction-derived mechanism in gapped graphene. It also studies the optical response of graphene quantum dots in the configuration, in terms of valley excitation with respect to photonic polarization, and illustrates faithful photon ↔ valley quantum state transfers. This work suggests the interesting prospect of an all-graphene approach for the solid state components of a quantum network, e.g., quantum computers and quantum memories in communications.

Figure 1

(a) The DQD structure of a valley pair qubit. The QDs are electrostatically defined, for example, by back gates (not shown in the figure). Gate $V_c$ is used to tune the potential barrier and also generate a linear term (in $x$) in the QD confinement potential. The coupling between the two QDs is characterized by the tunneling amplitude $t_{d-d}$, and may be controlled by $V_c$ or the back gates. Gates $V_{\mathrm{L}}$ and $V_{\mathrm{R}}$ are ac biases. (b) A static in-plane magnetic field is applied to freeze the electron spin, leaving only the valley degree of freedom for qubit implementation. (c) Valley singlet ($z_S$) / triplet ($z_{T0}$, z${}_{T+}$, z${}_{T-}$) states constitute the low-energy sector of the two-electron states, with the singlet-triplet splitting being given by $J$.

Figure 2

Single qubit manipulation, with the initial qubit state, e.g., $|zs\rangle$. One may apply the alternating sequence $R_x\left({\theta }_x\right)\to R_z({\theta }_z=\pi )\to R_x\left(-{\theta }_x\right)\to R_z({\theta }_z=\pi )\to ...R_z\left({\theta }_z^{\left(\mathrm{target}\right)}+\pi /2\right)$ and manipulate the initial state into a target state (${\theta }_z^{\left(\mathrm{target}\right)}$ $=$ target state longitude).

Figure 3

Approximate selection rule of optical excitation in gapped graphene.

Figure 4

The quantum state transfer from a photon qubit to a valley pair qubit. Dashed circles are quantum dots, black dots are the electrons, and white dots are the holes. Double arrows indicate resonance between states. For simplicity, in the state Φ${}_2$ plotted here, we show the approximate polarization only, for the photon emitted by the exciton, as determined by the approximate selection rule in Eq. (1).