Quantum states of multiple entangled photons constitute an important resource
for measurement-based quantum computing and all-photonic quantum repeaters.
However, the generation of such states is challenging, and the probabilistic schemes
pursued until now are difficult to scale. Here, we investigate deterministic entanglement
generation using a spin-photon interface which, through repeated optical
manipulation, can emit longs strings of entangled photons. Specifically, we employ
a solid-state InAs quantum dot charged with a single hole spin. Additionally, we
embed the quantum dot in a photonic crystal waveguide, thereby strongly coupling
the emitter to a single optical mode and modifying the light-matter interaction.
A common limitation encountered with quantum dots is the incompatibility of
coherent spin control and optical cycling transitions. By applying an in-plane magnetic
field and by selectively coupling the linear optical dipoles to the waveguide
mode, we measure a broadband increase in optical cyclicity up to X14:7 while retaining
the ability to drive optical Raman transitions. The waveguide geometry also
allows selective pumping of the optical transitions leading to 98% spin initialisation
fidelity. We demonstrate a T2 = 23:2 ns spin dephasing time, which exceeds most
experiments employing comparable nanostructures.
These capabilities allow the realisation of a time-bin entanglement protocol,
which we analyse in great detail. By combining resonant optical pulses and Raman
pulses, the protocol can generate GHZ states and linear cluster states containing
the QD spin and N photons, where each photon is emitted in a superposition of two
temporal modes. This protocol is insensitive to T2 , thanks to a built-in spin-echo
process, and is compatible with high magnetic fields and waveguides. We calculate
error rates of 2:1% pr. photon while considering realistic parameters and optimal
use of the waveguide. The protocol is implemented experimentally, and we realize a
spin-photon Bell state with a 66.6% fidelity and 124 Hz detection rate. By using a
self-stabilising double-pass interferometer, we are able to construct exact GHZ and
Bell state delity estimates. Extending to three qubits, we observe clear signatures
of coherence which, however, lack the amplitude for certiffiable entanglement. By
constructing an exhaustive Monte Carlo simulation, we are able to include nearly all
relevant errors and identify our modest 88.5% spin rotation fidelity as the leading
error mechanism. Other experiments have demonstrated better spin control, and
we discuss several possible paths towards achieving higher fidelity and scaling up
to more qubits.