Quantum communication with quantum dot spins

Single electron spins in quantum dots are attractive for quantum communication because of their expected long coherence times. We propose a method to create entanglement between two remote spins based on the coincident detection of two photons emitted by the dots. Local nodes of two or more qubits can be realized using the dipole-dipole interaction between trions in neighboring dots and spectral addressing, allowing the realization of a quantum repeater. We have performed a detailed feasibility study of our proposal based on tight-binding calculations of quantum dot properties.

Figure 1

(a) Level scheme underlying entanglement creation, qubit measurement and two-qubit gates. The $\mid 1∕2⟩$ electron state is coupled to the ${\mid 3∕2⟩}_T$ trion state by ${\sigma }_{+}$ radiation propagating along the growth direction, while the $\mid -1∕2⟩$ electron state is coupled to the ${\mid -3∕2⟩}_T$ trion by ${\sigma }_{-}$ radiation. The other transitions, which have $\mid \Delta J\mid =2$, are strongly suppressed, cf. below. The photon energies are $E_{{\sigma }_{\pm }}=E_T\pm E_Z$, where $E_T$ is the trion energy in zero field and $E_Z=g_X{\mu }_{B}B$ is the Zeeman energy, with $g_X$ the $g$ factor of the exciton. (b) Outline of a single node. A stack of quantum dots (QD) is embedded in a waveguide. $L_1$ is a control beam addressing the transitions in (a), a perpendicular beam $L_2$ is required for one-qubit gates. The waveguide ensures efficient collection of the emitted photons.

Figure 2

Requirements imposed by spectral addressing. $G$ is the quantum dot ground state, $T_1$, $T_2$, etc., are the trion states. Zeeman sublevels are not shown, i.e., $G$ corresponds to the states $\mid \pm 1∕2⟩$ and $T_1$ to ${\mid \pm 3∕2⟩}_T$. Suppose that $A$ is the dot with the lowest energy for $T_1$, and $B$ another dot in the same node. When exciting the $G^B\to T_1^B$ transition, one must avoid exciting $G^A\to T_2^A$. This defines an energy window $E_W$ in which $T_1^B$ must lie. On the other hand, $T_1^B$ must be larger than $T_1^A$ by at least $E_S$ in order to avoid exciting $T_1^A$ while emitting a phonon.