Swing-up dynamics in quantum emitter cavity systems: Near ideal single photons and entangled photon pairs

In the SUPER scheme (Swing-UP of the quantum EmitteR population), excitation of a quantum emitter is achieved with two off-resonant, red-detuned laser pulses. This allows the generation of high-quality single photons without the need of complex laser stray light suppression or careful spectral filtering. In the present work, we extend this promising method to quantum emitters, specifically semiconductor quantum dots, inside a resonant optical cavity. A significant advantage of the SUPER scheme is identified in that it eliminates re-excitation of the quantum emitter by suppressing photon emission during the excitation cycle. This, in turn, leads to almost ideal single-photon purity, overcoming a major factor typically limiting the quality of photons generated with quantum emitters in high-quality cavities. We further find that for cavity-mediated biexciton emission of degenerate photon pairs, the SUPER scheme leads to near-perfect biexciton initialization with very high values of polarization entanglement of emitted photon pairs.

Figure 1

Schematics of quantum dot cavity system. Electronic states considered are ground state, $|\text{G}\rangle$, two exciton states, $|{\text{X}}_{\text{H}}\rangle$ and $|{\text{X}}_{\text{V}}\rangle$, with fine structure splitting $E_{\text{fsp}}$, and biexciton state, $|\text{B}\rangle$, with binding energy $E_{\text{bind}}$. Electronic transitions are coupled to linearly polarized cavity modes with frequencies ${\omega }_{\text{H}}$ and ${\omega }_{\text{V}}$, with coupling strength $g$ and cavity photon loss $\kappa$. Spectra of the two red-detuned pulses of the SUPER scheme with H polarization at $\hslash {\omega }_1$ and $\hslash {\omega }_2$ and exciton emission are indicated. Energy differences shown are not to scale.

Figure 2

Dynamics of SUPER excitation. Populations of H exciton (green), biexciton (blue), and H cavity mode (red). (a) and (b) Excitation of H exciton with cavity at $\mathrm{X}\to \mathrm{G}$ transitions for $E_{\text{bind}}=3\mathrm{m}\mathrm{eV}$. Laser parameters as in first set of Table 1. (c) and (d) Excitation of biexciton with cavity at two-photon $\mathrm{B}\to \mathrm{G}$ transition with $E_{\text{bind}}=1\mathrm{m}\mathrm{eV}$. Laser parameters as in fourth set of Table 1. (a) and (c) show the initial excitation period, (b) and (d) show time evolution up to $300\mathrm{p}\mathrm{s}$. The laser pulses are $3\mathrm{p}\mathrm{s}$ long, centered at $10\mathrm{p}\mathrm{s}$. Cavity coupling is $g=66\mu \mathrm{eV}$, cavity loss $\hslash \kappa =g$. Insets in (b) and (d) show normalized H mode emission spectra $S_{\text{H}}\left(\omega \right)$ with frequencies relative to cavity frequency ${\omega }_{\text{H}}$.

Figure 3

Single-photon generation. Quality measures for photons emitted from the H polarization cavity mode for a cavity resonant with the $\mathrm{X}\to \mathrm{G}$ transition. Excitation with the SUPER scheme (red; first set of Table 1) or with a resonant Gaussian $\pi$-pulse (green; width $\sigma =3.5\mathrm{ps}$), respectively, for two different QD-cavity couplings $g=20\mu \mathrm{e}\mathrm{V}$ (solid lines) and $g=66\mu \mathrm{e}\mathrm{V}$ (dotted). Shown are (a) emission probability ${\mathcal{P}}_{\text{H}}$, (b) photon purity $P_{\text{H}}$, and (c) photon indistinguishability ${\mathcal{I}}_{\text{H}}$.

Figure 4

Polarization entangled photon pairs for cavity resonant with degenerate $\mathrm{B}\to \mathrm{G}$ two-photon transition for $g=66\mu \mathrm{e}\mathrm{V}$. Shown are biexciton excitation with the SUPER scheme (red; fourth set of Table 1), with a resonant Gaussian pulse (green; pulse area $\mathrm{\Omega }=3.3\pi$, width $\sigma =3\mathrm{ps}$, $\hslash \omega =\frac{E_{\text{B}}}{2}$), and for initially excited biexciton (blue). Shown are (a) emission probabilities ${\mathcal{P}}_{\text{H,V}}$ of photons from H (points) and V (squares) mode, respectively, and (b) concurrence $\mathcal{C}$.