Engineering Photons for Quantum Networks: Temporal-Mode Control, Optimization and Post-Selection Demonstrated in Trapped Ions

Abstract

Control of the temporal waveform and Fock basis statistics of photons produced during spontaneous emission provides a crucial tool in the establishment of hybrid systems, optimal state transfer, interferometric stability and optimization of entanglement generation protocols for quantum networks. We describe novel methods to generate photons of any temporal waveform from emitters of any lifetime. Our broadly applicable approach has only two requirements for a candidate qudit: (1) control of the phase-parity and (2) modulation of the amplitude of a field coupling a ground state to an excited manifold which produces a photon during relaxation. We describe an approach to find optimal excitation pulse shapes, both numerically and experimentally, by employing variational algorithms to feedback on atomic populations. Additionally, we develop a quantum trajectory theoretical approach to determine emission statistics and establish tools for optimal post-selection to ensure maximum fidelity of photon generation protocols. We situate our work in the context of other prior research on bespoke single photon sources and networking including post-emission pulse shaping, temporal gating and cavity-based methods. In comparison, our free-space process has greater flexibility in producing any waveform, requires less infrastructure and can be readily applied across a wide domain of emitters of any frequency or lifetime. We validate our approach in a singly trapped $^{174}$Yb+ ion and provide experimental results demonstrating photon temporal waveform control.