High-quality single photons from cavity-enhanced biexciton-to-exciton transition

Abstract

Resonant laser excitation of a two-level system with subsequent single-photon emission can be used to generate single photons with high indistinguishability or Hong-Ou-Mandel (HOM) visibility. However, spectral overlap between excitation laser and emitted photons generally poses significant challenges. Furthermore, emitter re-excitation intrinsically limits achievable single-photon purity. Established solutions mitigate these issues at significant cost to source efficiency and with increased source complexity. This motivates the use of few-level systems with spectral separation of excitation and emission pathways. One option is a three-level cascade. However, without targeted lifetime engineering of emitting states, the cascade naturally limits achievable photon indistinguishability. Here we study a semiconductor quantum dot with resonant and selective cavity-enhancement of biexciton-to-exciton transition. Following resonant two-photon excitation of the biexciton state, we collect the emitted single photon with the cavity. This approach circumvents emitter re-excitation and naturally introduces spectral separation of excitation laser and emitted single photon. Supported by first experimental results, we demonstrate theoretically that with selective Purcell enhancement, the observed quality quantifiers of single-photon emission (purity, equivalently $g^{(2)}(0)$, and HOM visibility $\mathcal{V}$, equivalently indistinguishability) are competitive with respect to high-quality deterministic quantum-dot single-photon sources. This is already achieved without systematic optimization or targeted system engineering, which firmly places the reported approach as a viable route to the next generation of highest-quality quantum-dot based deterministic single-photon sources.

Figures (8)

• Figure 1: (a) Schematics of quantum-dot-cavity system for single-photon generation from biexciton. Considered electronic states are ground state, $|\text{G}\rangle$, two exciton states, $|\text{X}_\text{H}\rangle$ and $|\text{X}_\text{V}\rangle$, and biexciton state, $|\text{XX}\rangle$, with biexciton binding energy $E_\text{bind}$. Electronic transitions couple to linearly polarized cavity modes with angular frequencies $\omega_{\text{H}}$ and $\omega_{\text{V}}$. The (bi-)exciton decays with rate $1/\tau_{\text{X}}$ ($1/\tau_{\text{XX}}$), which is inverse to its lifetime. Single-photon generation occurs in the H-polarization channel with H-cavity mode tuned to the XX-$\text{X}_\text{H}$ transition. The V-cavity mode (not shown) is spectrally detuned to favor emission into the H-cavity mode. In our simulations, biexciton initialization with two-photon excitation (TPE) proceeds via the V-polarization channel. Energy differences shown are not to scale. (b) Calculated cavity emission spectrum for $E_\text{bind}=2.9\meV$ and $T=4.2\K$, normalized to the main cavity peak. The inset shows the side peak at $\text{X}_\text{H}$-G transition frequency. (c) Achievable photon indistinguishability for different biexciton-exciton lifetime ratios for an ideal three-level model (Eq. \ref{['LimitOnI']}, adapted from Schoell_2020Simon_2005). This result also applies to our Purcell-enhanced case, as explicitly derived in Appendices \ref{['AppX:ExpansionOfCrux']} and \ref{['AppX:ConnectionToExp']}, and to the experimental situation with a tunable cavity Baltisberger_2025, as further detailed in Appendix \ref{['AppX:ConnectionToExp']}. The black cross marks the lifetime ratio for the naturally decaying QD and the orange cross for the Purcell-enhanced XX-X transition for the parameters of the present paper.
• Figure 2: Influence of biexciton binding energy and phonons on single-photon emission. For H-mode cavity photons we show (a) photon indistinguishability $\mathcal{I}_{\text{H}}$ (green), (b) single-photon purity $P_{\text{H}}$ (red), (c) emission $\mathcal{P}_{\text{H}}$ (blue) for $T=4.2\K$ (solid lines), $T=0\K$ (dashed-dotted lines), and $T=0\K$ without phonon interactions (dotted lines) for initially excited biexciton and empty cavity. To demonstrate insensitivity of single-photon indistinguishability and purity to resonant two-photon excitation (TPE) of the biexciton, corresponding data points are included as orange stars for pulse length $\sigma=5\ps$ and pulse area $\Omega_0=5.2\pi$ at $T=4.2\K$ (results are insensitive to TPE pulse length; pulse parameters given in Appendix \ref{['AppX:Theory']}, Table \ref{['Tab1']}). Results of experimental realization Baltisberger_2025 are shown as purple diamonds with error bars in (a,b). Panel (c) includes the analytical approximation for the relevant phonon-mediated QD-cavity coupling (light gray) Roy_2011 for the X-G transition, $\Gamma^{\text{Cav,}4.2\K}_{\text{X}_{\text{H}}\to\text{G}}$ (solid line), and for the XX-X transition $\Gamma^{\text{Cav,}4.2\K}_{\text{XX}\to\text{X}_{\text{H}}}$ (single dot). Detuning between X-G transition and cavity changes with biexciton binding energy as $\hbar\Delta_{\text{Cav,X}_{\text{H}}\to\text{G}} = -E_\text{bind}-E_\text{fss} \approx -E_\text{bind}$.
• Figure 3: Influence of QD-cavity coupling and cavity loss on single-photon emission. Shown are photon indistinguishability $\mathcal{I}_{\text{H}}$ (green), single-photon purity $P_{\text{H}}$ (red), and emission $\mathcal{P}_{\text{H}}$ (blue) at $T=4.2\K$ and $E_\text{bind}=2.9\meV$. (a,b) Influence of QD-cavity coupling for (a) fixed cavity loss $\kappa=4.97\cdot \left. g\right|_{\hbar g=20.8\mu\eV}$ and (b) cavity loss that scales with QD-cavity coupling as $\kappa=4.97\cdot\tilde{g}_{T}$ ($\tilde{g}=\tilde{g}_T=\langle B \rangle_T g$). (c) Influence of cavity loss for fixed QD-cavity coupling $\hbar g=20.8\mu\eV$. Results shown are for initially excited biexciton and empty cavity. Corresponding results for $T=0\K$ are given in Appendix \ref{['AppX:DiffTemp']}.
• Figure 4: Influence of QD-cavity coupling on single-photon emission for different temperatures and phonon models for fixed cavity loss. Presented is an extended and rearranged version of Fig. \ref{['Fig3']}⁠ (a). Shown are (a) indistinguishability $\mathcal{I}_{\text{H}}$ (green), (b) purity $P_{\text{H}}$ (red), and (c) emission $\mathcal{P}_{\text{H}}$ (blue) at $T=4.2\K$ (solid lines), $T=0\K$ (dashed-dotted lines), and $T=0\K$ without phonons (dotted lines) for $E_\text{bind}=2.9\meV$. Panel (a) includes the analytical approximation of the indistinguishability $\mathcal{I}_{{\rm Purcell}}^{0\,{\rm K}}$ at $T=0\K$ (dark gray line, Eq. \ref{['LimitOnI']} with Eq. \ref{['Eq:FullDecayRates']}), valid for weak coupling ($g \ll \kappa/4$, black dashed vertical line) in the Purcell regime, as clarified in Appendices \ref{['AppX:ExpansionOfCrux']} and \ref{['AppX:ConnectionToExp']}. Results for fixed cavity loss $\kappa=4.97\cdot \left. g\right|_{\hbar g=20.8\mu\eV}$ and initially excited biexciton and empty cavity. Results of experimental realization Baltisberger_2025 are shown as purple diamonds with error bars in (a,b).
• Figure 5: Influence of QD-cavity coupling on single-photon emission for different temperatures and phonon models for scaled cavity loss. Presented is an extended and rearranged version of Fig. \ref{['Fig3']}⁠ (b). Shown are (a) indistinguishability $\mathcal{I}_{\text{H}}$ (green), (b) purity $P_{\text{H}}$ (red), and (c) emission $\mathcal{P}_{\text{H}}$ (blue) at $T=4.2\K$ (solid lines), $T=0\K$ (dashed-dotted lines), and $T=0\K$ without phonons (dotted lines) for $E_\text{bind}=2.9\meV$. Cavity loss scales with QD-cavity coupling, as $\kappa=4.97\cdot\tilde{g}_T$ ($\tilde{g}=\tilde{g}_T=\langle B \rangle_T g$). Results for initially excited biexciton and empty cavity. Results of experimental realization Baltisberger_2025 are shown as purple diamonds with error bars in (a,b).