Quantum entanglement between a hole spin confined to a semiconductor quantum dot and a photon

Abstract

We demonstrate quantum entanglement between a single hole spin confined to a positively charged semiconductor quantum dot (QD) and a photon spontaneously emitted from the matter’s excited state. The QD system is in the Voigt geometry with two ground hole spin states and two excited trion states. We consider the light-matter coupling initially prepared in one of the ground hole spin states. For very weak Rabi frequencies, the spin-flip process transfers most of the population to another hole spin state, leading to the disentanglement between the single photon and single QD hole spin. A maximum entanglement is achieved by increasing the intensity of Rabi frequencies. In this case, the population almost equally distributes among all the bare quantum states. Our results may pave the way toward creating a scalable QD quantum computing architecture relying on the photon as flying qubits to mediate entanglement between distant nodes of a QD network.

Appendix

As an example, we calculate the term $H_{14}$ in Eq. (9). From Eqs. (2), (6) and (7), one can evaluate the Hamiltonian term

$$ \begin{aligned} V_{14} & = - 1{|}{\varvec{\mu}}{|}4.{\varvec{E}}\left( t \right) = - \frac{\wp }{2\sqrt 2 }\left( {E_{x} \left( t \right)e^{ - i\omega t} + E_{x}^{*} \left( t \right)e^{i\omega t} } \right) \\ & = \frac{\hbar }{2}\left( {\Omega_{x} \left( t \right)e^{ - i\omega t} + \Omega_{x}^{*} \left( t \right)e^{i\omega t} } \right), \\ \end{aligned} $$

where $\Omega_{x} \equiv \frac{{\wp E_{x} }}{\hbar \surd 2}$ and $\Omega_{y} \equiv \frac{{i\wp E_{y} }}{\hbar \surd 2}$ are the Rabi frequencies along the x- and y-axis.

Thus,

$$ H_{14} = V_{14} e^{ - i\omega t} = \frac{\hbar }{2}\left( {\Omega_{x} \left( t \right)e^{ - 2i\omega t} + \Omega_{x}^{*} \left( t \right)} \right). $$

(A1)

According to the RWA, we can neglect terms that oscillate at 2ω, as they will average out to zero, while the other terms remain unchanged. Therefore,$H_{14} = \frac{\hbar }{2} \Omega_{x}^{*} \left( t \right)$. Similarly, the other terms of Eq. (9) can be obtained.