Modeling an efficient singlet-triplet-spin-qubit-to-photon interface assisted by a photonic crystal cavity

Efficient interconnection between distant semiconductor spin qubits with the help of photonic qubits offers exciting new prospects for future quantum communication applications. In this paper, we optimize the extraction efficiency of a novel interface between a singlet-triplet-spin-qubit and a photonic-qubit. The interface is based on a 220-nm-thick $\mathrm{Ga}\mathrm{As}/(\mathrm{Al},\mathrm{Ga})\mathrm{As}$ heterostructure membrane and consists of a gate-defined double quantum dot (GDQD) supporting a singlet-triplet qubit, an optically active quantum dot (OAQD) consisting of a gate-defined exciton trap, a photonic crystal cavity providing in-plane optical confinement, efficient outcoupling to an ideal free-space Gaussian beam while accommodating the gate wiring of the GDQD and OAQD, and a bottom gold reflector to recycle photons and increase the optical extraction efficiency. All the essential components can be lithographically defined and deterministically fabricated on the $\mathrm{Ga}\mathrm{As}/(\mathrm{Al},\mathrm{Ga})\mathrm{As}$ heterostructure membrane, which greatly increases the scalability of on-chip integration. According to our simulations, the interface provides an overall coupling efficiency of 28.7% into a free-space Gaussian beam, assuming a ${\mathrm{Si}\mathrm{O}}_{2}$ interlayer fills the space between the reflector and the membrane. The performance can be further increased by undercutting this ${\mathrm{Si}\mathrm{O}}_{2}$ interlayer below the photonic crystal. In this case, the overall efficiency is calculated to be 48.5%.