Hidden anisotropy controls spin-photon entanglement in a charged quantum dot

TL;DR

This work reveals that hidden anisotropy in singly charged quantum dots—manifested as an off‑diagonal hole g‑tensor and misaligned hole precession axis—significantly shapes spin–photon entanglement used to generate multiphoton cluster states. By combining theory with time‑resolved photoluminescence and cross‑polarized g^{(2)} measurements, the authors show that entanglement fidelity is highly sensitive to excitation polarization and to the direction of the in‑plane magnetic field, with a maximum time‑filtered fidelity around 0.94 and a maximum concurrence near 0.88. The results identify precise conditions (polarization angle φ and field orientation α) that maximize entanglement, and quantify how symmetry (D_{2d}, C_{2v}, Cs) dictates optimal settings. These findings provide practical guidelines for robust, high‑fidelity spin–photon entanglement in charged QDs, advancing deterministic multiphoton cluster‑state generation for optical quantum networks.

Abstract

Photon entanglement is indispensable for optical quantum technologies. Measurement-based optical quantum computing and all-optical quantum networks rely on multiphoton cluster states consisting of indistinguishable entangled photons. A promising method for creating such cluster states on demand is spin-photon entanglement using the spin of a resident charge carrier in a quantum dot, precessing in a weak external magnetic field. In this work, we show theoretically and experimentally that spin-photon entanglement is strongly affected by the hidden anisotropy of quantum dots, which can arise from mechanical stress, shape anisotropy and even specific crystal structure. In the measurements of time-resolved photoluminescence and cross-polarized second-order photon correlation function in a magnetic field, the anisotropy manifests itself in the spin dynamics and, as a consequence, in the spin-photon concurrence. The measured time-filtered spin-photon Bell state fidelity depends strongly on the excitation polarization and reaches an extremely high value of 94% at maximum. We specify the magnetic field and excitation polarization directions that maximize spin-photon entanglement and thereby enhance the fidelity of multiphoton entangled states.

Figures (11)

• Figure 1: (a) Energy levels and optical transitions in a negatively charged QD. (b)---(e) Spin evolution during spin-photon entanglement. (b) Electron spin precession from $\bm{S}_0$ to $\bm{S}_\perp + \bm{S}_z$ with frequency $\bm{\Omega}_e$ in an external magnetic field $\bm{B}$ [Eq. \ref{['eq_e_spin_before_exc_simple']}]. (c) Excitation of a trion by linearly polarized light ($\bm{E}$), which initializes the trion pseudospin $\bm{J}_0 = \bm{J}_{0\perp} + \bm{J}_{0z}$ with the $\bm{J}_{0\perp}$ component rotated relative to $\bm{S}_\perp$ [Eq. \ref{['eq_h_spin_after_exc_simple']}]. (d) Precession of the hole spin from $\bm{J}_0$ to $\bm{J}$ with frequency $\bm{\Omega}_h$ [Eq. \ref{['eq_h_spin_before_emission_simple']}]. (e) Emission of a photon entangled with the remaining electron according to Eq. \ref{['eq_concurrence_main']}.
• Figure 2: (a) Scanning electron microscope image of a typical micropillar structure in which an InAs/GaAs QD is placed in a $\lambda$-cavity between two Bragg reflectors (BR). (b) PL decay curves after pulsed $\sigma^-$ LA phonon-assisted trion excitation in co- and cross-polarizations in a transverse magnetic field of 195 mT. The black dots show the sum of the experimental signals, and the lines show the theoretical fit. (c) The degree of circular polarization of the PL, determined from the dependences shown in figure (b). d) The hole spin precession frequency as a function of the transverse magnetic field in the [110] direction for $\sigma^+$ and $\sigma^-$ excitations, used to determine the effective $g$-factor. (e) Anisotropy of the effective $g$-factor over the direction of the magnetic field. (f) Same as in (c), but in a tilted magnetic field of 183 mT, making an angle $\theta_B=63^\circ$ with the $z$ axis. The inset shows the corresponding hole spin ($\bm J$) precession, taking into account the anisotropic hole $g$-factor.
• Figure 3: (a) Cross-correlation $g^{(2)}$ functions of $\sigma^+$ and $\sigma^-$ photons (blue dots) or V and H photons (black dots) under continuous linearly polarized excitation in the absence of a magnetic field. (b) Electron spin $S_z(t)$ (black dots) determined from the dependence shown in panel (a), and its fit after Eq. \ref{['eq:MER']} (red line). The inset illustrates the process of electron spin initialization by projective spin measurement. (c,d) Cross-correlation function in a magnetic field of 195 mT applied along the $\langle110\rangle$ direction, measured for excitation polarizations along $\langle1\bar{1}0\rangle$ (c) and $\langle110\rangle$ (d), and their modelling. (e) Start-stop measurement scheme in the circular polarization basis with the application of an external magnetic field. (f) Dependence of the electron spin precession frequency on the magnetic field applied along the $\langle110\rangle$ axis. (g) Anisotropy of the transverse electron $g$-factor.
• Figure 4: (a) Cross-correlation function of $\sigma^+$ and $\sigma^-$ photons in a transverse magnetic field $B=195$ mT of different directions specified by the angle $\alpha$ measured relative to the $\langle110\rangle$ axis. The excitation polarization is along $\langle1\bar{1}0\rangle$. (b) Spin-photon concurrence for photons emitted at a certain time $t$ after spin initialization via projective measurement. Black dots are obtained from experimental values of $g^{(2)}$ measured at $B = 95$ mT using Eq. \ref{['eq_zero_lifetime_concurrence_and_g2']}. The red line shows the exact theoretical simulation with experimental parameters. (c) Maximum spin-photon concurrence at $B = 195$ mT as a function of excitation polarization.
• Figure 5: Fidelity anisotropy of a 5-photon cluster state generation in a positively charged InAs/GaAs QD for the three values of magnetic field given in the legend.