Theory of single-photon emission from neutral and charged excitons in a polarization-selective cavity

TL;DR

This work analyzes polarization-selective emission from neutral and charged excitons in elliptical microcavities to overcome the 0.5 polarization-efficiency limit in cross-polarized single-photon sources. By combining a three-level neutral-exciton model with two orthogonally polarized cavity modes and a rotation between exciton and cavity axes, solved numerically and analytically in the weak-coupling regime, it shows that near-unity polarized output is achievable when the cavity mode splitting Δ_cav is large and the exciton-state precession is driven by a nonzero fine-structure splitting Δ_{FSS}. The formalism is extended to trions, where the emission probabilities depend on the polarization-dependent Purcell factors, yielding similar expressions with potential high efficiency even without 45° alignment. The results provide explicit design rules for elliptical cavities to achieve high polarization-efficient, indistinguishable single-photon emission, with practical implications for scalable quantum photonic devices.

Abstract

Single-photon sources based on neutral or charged excitons in a semiconductor quantum dot are attractive resources for photonic quantum computers and simulators. To obtain indistinguishable photons, the source is pumped on resonance with polarized laser pulses, and the output is collected in orthogonal polarization. However, for sources featuring vertical emission of light, 50% of the emitted photons are unavoidably lost in this way. Here, we theoretically study the quantum dynamics of an exciton embedded in an asymmetric vertical cavity that favors emission in a specific polarization. We identify the configuration for optimal state initialization and demonstrate a path toward near-unity polarized efficiency. We also derive simple analytical formulas for the photon output in each polarization as a function of the Purcell-enhanced emission rates, which shed light on the physical mechanism behind our results.

Figures (6)

• Figure 1: (a) Energy levels of a neutral exciton with eigenstates $\ket{G}, \ket{V'}, \ket{H'}$ and fine structure splitting $\hbar \Delta_{\rm FSS}$, embedded in a cavity supporting two non-degenerate modes $H$ and $V$. (b) Energy spectrum of the cavity modes and of the emitter, showing the splitting $\hbar \Delta_{\rm cav}$ between cavity modes. The inset shows the splitting $\hbar \Delta_{\rm FSS}$ between exciton states, which is much smaller than $\hbar \Delta_{\rm cav}$. (c) Sketch of an elliptical micropillar supporting two non-degenerate cavity modes. (d) Exciton axes are rotated by an angle $\theta$ with respect to the cavity axes.
• Figure 2: (a--c) Polarized photon emission and exciton dynamics for a symmetric structure with degenerate cavity modes, $\hbar \Delta_{\rm cav} = 0$. Panels (a) and (b) show the number of photons emitted with vertical ($N_V$) and horizontal ($N_H$) polarization as a function of the rotation angle $\theta$ between cavity and exciton axes and of the FSS $\hbar \Delta_{\rm FSS}$. Panel (c) show the evolution of the emitter state population in time for $\theta = \pi/4$ and $\hbar \Delta_{\rm FSS} =$ 32.9µ, corresponding to the red cross in (a, b). (d--f) Same as in (a-c), with nonzero splitting $\hbar \Delta_{\rm cav} =$ 770µ between the cavity modes.
• Figure 3: Number of photons emitted with (a) $V$ and (b) $H$ polarization as a function of the cavity loss rate (identical for both polarizations) and of the cavity $V$-mode detuning, $\hbar \delta_V$. The $H$ cavity mode is on resonance with the $H$ exciton, i.e. $\hbar \delta_H = \frac{1}{2} \hbar \Delta_{\rm FSS}$, and the rotation angle is set to $\theta = \pi/4$. The FSS is $\hbar \Delta_{\rm FSS} =$ 39.5µ.
• Figure 4: Number of photons emitted in each polarization as a function of the FSS, calculated analytically with Eqs. \ref{['eq:NV']} and \ref{['eq:NH']}. We use $\hbar \Gamma_V =$ 0.66µ, corresponding to $(\Gamma_V)^{-1} =$ 1n, and three increasing values of the ratio $\Gamma_H / \Gamma_V$. The background emission rate $\Lambda$ is set to zero.
• Figure 5: (a) Sketch of the energy levels of a charged exciton with eigenstates $\ket{G_\pm}$ and $\ket{X_\pm}$ embedded in a cavity supporting two non-degenerate modes $H$ and $V$. (b) Optical selection rules for the charged exciton. Blue (orange) transitions are coupled to $H$-polarized ($V$-polarized) light. (c) Number of photons $N_H$ emitted with $H$ polarization as a function of the polarization-dependent Purcell factors, see Eq. \ref{['eq:N_j_Purcell']}. For the background emission factor we use $B = 0.5$.