Radiative cascade from quantum dot metastable spin-blockaded biexciton

We detect a radiative cascade which initiates from a metastable biexciton state in a neutral semiconductor quantum dot. In this biexciton, the heavy holes form a spin-triplet configuration, Pauli blockaded from relaxation to the spin-singlet ground state. The triplet biexciton has two photon-phonon-photon decay paths. Unlike in the singlet-ground-state biexciton radiative cascade, in which the two photons are colinearly polarized, in the triplet-biexciton cascade they are cross-linearly polarized. We measured the two-photon polarization density matrix and show that the phonon emitted when the intermediate exciton relaxes from excited to ground state, preserves the exciton’s spin. The phonon, thus, does not carry with it any which-path information other than its energy. Nevertheless, entanglement distillation by spectral filtering was found to be rather ineffective for this cascade. This deficiency results from the opposite sign of the anisotropic electron-hole exchange interaction in the excited exciton relative to that in the ground exciton.

Figure 1

(Color online) (a) Energy levels diagram for excitons and biexcitons in a neutral QD. Single-carrier level occupations are given along side each many-carrier level. The spin wave functions are depicted above each level. The symbol $\uparrow$ $(\Downarrow )$ represents spin-up (spin-down) electron (hole). Short blue (long red) symbols represent charge carriers in the first (second) energy level. S $\left({\text{S}}^{\ast }\right)$ indicates ground (excited) biexciton hole-singlet state. ${\text{T}}_0$ $\left({\text{T}}_{\pm 3}\right)$ indicates the metastable spin-triplet-biexciton state with $z$-axis spin projection of 0 $\left(\pm 3\right)$. The solid (curly) vertical arrows indicate spin preserving (non)radiative transitions. Green (dark-gray) [orange (light-gray)] arrows represent photon emission in horizontal—H (vertical—V) polarization. (b) Polarized PL spectra. H (V) in green (orange). Spectral lines which are relevant to this work are marked and linked to the transitions in (a) by dashed lines. (c) Linear polarization spectrum. The value 1 $\left(-1\right)$ means full H (V) polarization.

Figure 2

(Color online) [(a) and (c)] Measured intensity correlation functions for the spin-blockaded and ground-state biexciton cascades, respectively. Blue (dark-gray) [red (light-gray)] line represents the correlation in co-[cross-]linear polarizations. The coincidence rates are indicated by the scale bars in units of coincidences per time bin (80 ps) per minute. [(b) and (d)] Real parts of the two-photon polarization density matrices measured for the spin-blockaded and ground-state biexciton cascades, respectively.

Figure 3

(Color online) [(a) and (b)] Measured two-photon polarization density matrices for the ground-state (S) and spin-blockaded $\left({\text{T}}_0\right)$ biexciton cascades, respectively, as obtained with spectral filtering. Real (imaginary) parts are shown in the top (bottom) panels. The Peres criterion (negativity of the partially transposed matrix) for the matrix in (a) [(b)] is $0.15\pm 0.03$ $\left[0.05\pm 0.1\right]$.

Figure 4

(a) Ideal direct cascade. The widths of the levels represent their decay rate. (b) Ground-state biexciton cascade in an anisotropic QD. (c) Schematic two-photon probability distribution. Dark gray—high probability areas. Cross hatched—spectral filter. Light gray—inhomogeneous broadening due to spectral diffusion. [(d)–(f)] Same as (a)–(c) (respectively), for an indirect cascade. In (e) and (f) only the case of splittings in opposite directions is shown. The dotted rectangle in (f) is an example for a filter not penetrated by the high-probability areas for any amount of spectral diffusion.