Deterministic generation of many-photon GHZ states using quantum dots in a cavity

We propose a novel theoretical scheme based on the off-resonant interaction of $N$ photons with four InAs/GaAs semiconductor quantum dots (QDs) in an GaAs microdisk cavity to create many-photon GHZ states deterministically in the polarization degree of freedom at a wavelength of 1.3 $\mu$m with probability $p=1$ for $N$ up to 60, without the need of any projective measurement or local unitary operation. Taking advantage of off-resonant interaction, the time evolution of the $N$-photon state is robust against decoherence due to exciton-phonon and hyperfine interactions. However, decoherence due to leakage of the photons out of the cavity is not negligible and is therefore considered. Remarkably, by taking advantage of a cascaded multi-level Landau-Zener transition, we are able to reduce the GHZ state generation time to below 100 ps for $N$ up to 60, which allows for the creation of GHZ states with $N$ up to 60 in cavities with $Q=10^6$ with fidelity above 70\% including decoherence due to leakage. Our method paves the way to the miniaturization of many-photon GHZ state sources to the nanoscale regime, with the possibility to integrate them on a computer chip based on semiconductor materials.