  Efficient interconnection between distant semiconductor spin qubits with the
help of photonic qubits would offer 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 GaAs/AlGaAs
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 and efficient out-coupling 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 essential components can be lithographically defined
and deterministically fabricated on the GaAs/AlGaAs 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 an SiO2 interlayer filling the space
between the reflector and the membrane. The performance can be further
increased by undercutting this SiO2 interlayer below the photonic crystal. In
this case, the overall efficiency is calculated to be 48.5%.
