Entangled-photon generation from a quantum dot in a microcavity through pulsed laser irradiation

We theoretically investigate fast and highly efficient entangled-photon generation by irradiating a quantum dot (QD) embedded in a microcavity with short laser pulses. We evaluate the optimized width and field strength of the pulses for achieving a high population of an excited state as an entangled-photon source. We also calculate the emission time of the entangled photon pair as a function of the cavity quality factor $Q$. The shortest emission time reaches $3/\left(4g\right)$ under the condition $Q={\omega }_0/\left(4g\right)$, where $g$ is the coupling frequency between the cavity photon and excited states of the QD and ${\omega }_0$ is the excitation frequency of the QD. The QD-cavity system has a potential for fast and efficient generation of high-quality entangled-photon pairs.

Figure 1

Low-lying dressed states of the QD-cavity system. A triplet entangled-photon pair is generated by cascade transitions from $|T\pm \rangle$ to $|G\rangle$. A singlet pair is generated by cascade transitions from $|S\rangle$ to $|G\rangle$. “R-photon” and “L-photon” mean right- and left-circularly polarized photons, respectively.

Figure 2

Emission time $\tau$ of entangled photons accompanied by the transitions from $|S\rangle$ to $|G\rangle$ as a function of $Q$ factor. The shortest emission time $\tau =3/\left(4g\right)$ is realized at $Q={\omega }_0/\left(4g\right)$.

Figure 3

Schematic illustrations of the resonant excitation processes from $|G\rangle$ to $|S\rangle$ for ${\Omega }_R={\omega }_0-g$ and ${\Omega }_L={\omega }_0+g$. (a) When the two pulses are simultaneously irradiated, there are two resonant transition processes $|G\rangle \to |R-\rangle \to |S\rangle$ and $|G\rangle \to |L+\rangle \to |S\rangle$. (b) When the pulse with ${\Omega }_R$ is irradiated followed by the pulse with ${\Omega }_L$, the resonant transition process is only $|G\rangle \to |R-\rangle \to |S\rangle$.

Figure 4

Population of $|R-\rangle$ after irradiation from the first pulse with ${\Omega }_R={\omega }_0-g$ for (a) $\hslash g=$ 0.5, (c) 1, and (e) 5 meV as a function of the effective pulse intensity $V_R$ and the pulse width $P_R$. Populations of $|G\rangle$, $|R-\rangle$, $|R+\rangle$, and $|2R-\rangle$ under the $\pi$ pulse condition (dotted curves) for (b) $\hslash g=$ 0.5, (d) 1, and (f) 5 meV.

Figure 5

The population of $|S\rangle$ after irradiation from the second pulse with ${\Omega }_L={\omega }_0+g$ for $\hslash g=1$ meV as a function of the effective pulse intensity $V_L$ and the pulse width $P_L$. The initial population of $|R-\rangle$ after irradiation from the first pulse is 95.4% for $V_R=0.08$ meV and $P_R=18.12$ ps. Here, the maximum population of $|S\rangle$ is 91.8% for $V_L=0.12$ meV and $P_L=17.40$ ps.

Figure 6

Calculated degree of entanglement as a function of relative population of $|S\rangle$ under steady-state excitation.