We present two-loop calculations on the axial-vector form factors F A of semileptonic radiative kaon and pion decays in chiral perturbation theory. The relevant dimension-6 terms of the lagrangian are evaluated from the resonance contribution and the results of the irreducible two-loop graphs of the sunset topology are given in detail. We also explicitly show that the divergent parts in F A are cancelled exactly as required.

The generation of a register of highly coherent, but independent, qubits is a prerequisite to performing universal quantum computation. Here we introduce a qubit encoded in two nuclear spin states of a single 87Sr atom and demonstrate coherence approaching the minute-scale within an assembled register of individually-controlled qubits. While other systems have shown impressive coherence times through some combination of shielding, careful trapping, global operations, and dynamical decoupling, we achieve comparable coherence times while individually driving multiple qubits in parallel. We highlight that even with simultaneous manipulation of multiple qubits within the register, we observe coherence in excess of 105 times the current length of the operations, with $${T}_{2}^{{{{{\mathrm{echo}}}}}}=\left(40\pm 7\right)$$ T 2 echo = 40 ± 7 seconds. We anticipate that nuclear spin qubits will combine readily with the technical advances that have led to larger arrays of individually trapped neutral atoms and high-fidelity entangling operations, thus accelerating the realization of intermediate-scale quantum information processors.

We discuss π 0-η mixing and its implication for ε ′ /ε to next-to-leading order in the low-energy expansion. The big effect due to η-η ′ mixing is shown to be largely cancelled by other contributions occurring at the same order in the chiral expansion.

Single photons of subnatural linewidth and high spectral brightness are necessary for efficient lightmatter interaction at the single photon level, which lies at the heart of many quantum photonic technologies. Here we demonstrate a bright source of single photons with subnatural linewidth, controllable waveforms, and a high spectral brightness of 3.67 × 10 5 s −1 mW −1 MHz −1 . The interaction between the single photons and atoms is demonstrated by the controlled absorption of the single photons in an atomic vapor. Our work has potential applications in quantum information technologies.