Modified Spontaneous Emission and Qubit Entanglement from Dipole-Coupled Quantum Dots in a Photonic Crystal Nanocavity

The modified spontaneous emission dynamics of two photon-coupled quantum dots in a planar-photonic crystal are theoretically investigated. Based on a photon Green function technique for quantizing the electromagnetic fields in arbitrary surroundings, pronounced vacuum Rabi oscillations and dipole-dipole interactions are self-consistently incorporated and are shown to result in a high degree of quantum-bit entanglement. Quantum dots with different optical dipole moments are also found to yield a very rich display of quantum dynamics and offer several advantages over coupling identical atoms.

Figure 1

Simple schematic of a semiconductor PPC nanocavity. The holes represent etched air holes, and a deliberate missing hole forms a defect nanocavity; two quantum dots (QDs) are embedded near a field antinode that contains one electron-hole pair in the spectral region of interest. In reality, of course, the PPC contains many more holes.

Figure 2

(a) Upper decay of the quantum dots $a$ (solid curve) and $b$ (dashed curve), and the entanglement (chain curve); the dotted curve shows $E$ with slightly different QD positions in the cavity (see text). (b) As in (a) but with $d_a=1.6d_b$. (c) As in (b) but with QD $b$ initially excited; the dotted curve shows $E$ with 0.1 meV detuning between the QDs. (d) Corresponding first-order quantum correlation function for nominal cases in Fig. 2a, 2b, 2c shown, respectively, by the solid, dashed, and chain curve.

Figure 3

(a) Upper decay of the entangled quantum dots $a$ (solid curve) and $b$ (dashed curve), and the entanglement $E$ (chain curve); the QDs are detuned by 0.1 meV. (b) As in (a) but with $d_a=1.6d_b$ and no detuning between the dots. (c) Equal dipole moment QDs in a reduced $Q$ cavity (factor of 10 smaller than the above). (d) As in (c) but with $d_a=1.3d_b$; the dotted curve shows $E$ with 0.1 meV detuning between the QDs.