  The key challenge to scalable optical quantum computing, boson sampling, and
quantum metrology is sources of single photons with near-unity system
efficiency and simultaneously near-perfect indistinguishability in all degrees
of freedom (including spectral, temporal, spatial, and polarization). However,
previous high-indistinguishability solid-state single-photon sources had to
rely on polarization filtering that reduced the system efficiency by at least
50%. Here, we overcome this challenge by developing a new single-photon source
based on a coherently driven quantum dot embedded in an elliptical micropillar.
The asymmetric cavity lifts the polarization degeneracy into two orthogonal
linearly polarized modes with a suitable energy separation. We design an
excitation-collection scheme that allows the creation and collection of single
photons with an indistinguishability of 0.976(1) and a degree of polarization
of 91%. Our method provides a solution of combining near-unity system
efficiency and indistinguishability compatible with background-free resonant
excitation, and opens the way to truly optimal single-photon sources for
scalable photonic quantum technologies.
