Proposed entanglement beam splitter using a quantum-dot spin in a double-sided optical microcavity

We propose an entanglement beam splitter (EBS) using a quantum-dot spin in a double-sided optical microcavity. In contrast to the conventional optical beam splitter, the EBS can directly split a photon-spin product state into two constituent entangled states via transmission and reflection with high fidelity and high efficiency (up to 100 percent). This device is based on giant optical circular birefringence induced by a single spin as a result of cavity quantum electrodynamics and the spin-selection rule of trion transition (Pauli blocking). The EBS is robust and it is immune to the fine-structure splitting in a realistic quantum dot. This quantum device can be used for deterministically creating photon-spin, photon-photon, and spin-spin entanglements as well as a single-shot quantum nondemolition measurement of a single spin. Therefore, the EBS can find wide applications in quantum information science and technology.

Figure 1

(a) A charged QD inside a micropillar microcavity with circular cross-section. (b) Energy levels and spin-selection rules for the optical transitions of $X^{-}$ (see text).

Figure 2

(Color online) (a) Calculated transmission (solid curves) and reflection (dotted curves) spectra vs the normalized frequency detuning for different coupling strength $g$. (b) The entanglement fidelity vs the frequency detuning in the strong-coupling regime ($g=2.4\kappa$ is taken). Solid curve for $F^t\left(\omega \right)$ and dotted curve for $F^r\left(\omega \right)$. (c) Transmittance $\left|t\left({\omega }_0\right)\right|$ (solid curve) and reflectance $\left|r\left({\omega }_0\right)\right|$ (dotted curve) vs the normalized coupling strength. (d) The entanglement fidelity vs the normalized coupling strength. (e) Transmittance $\left|t_0\left({\omega }_0\right)\right|$ (solid curve) and reflectance $\left|r_0\left({\omega }_0\right)\right|$ (dotted curve) vs the normalized side leakage rate. (f) The entanglement fidelity vs the normalized side leakage rate. Solid curve for $F^t\left({\omega }_0\right)$ and dotted curve for $F^r\left({\omega }_0\right)$. ${\omega }_c={\omega }_{X^{-}}={\omega }_0$ and $\gamma =0.1\kappa$ are taken for (a)–(f) and ${\kappa }_s=0$ for (a)–(d).

Figure 3

The proposed photon-spin entanglement beam splitter. A photon-spin product state can be split into two constituent photon-spin entangled states: one in the transmission port and another in the reflection port. Note that the single photon is either transmitted or reflected, so this entanglement beam splitter is deterministic.

Figure 4

Schematic of a photon-spin interface. It also works in the reflection geometry (not shown here). (a) State transfer from a photon to a spin. (b) State transfer from a spin to a photon. PBS, D1 and D2 (photon detectors), and $\lambda /4$ (quarter-wave plate).

Figure 5

An EBS-based scheme to entangle independent photons by measuring the spin states. The two photons can be (a) both transmitted, (b) both reflected, or (c) one transmitted and another reflected.