Characterisation and feasibility study for superradiant lasing in ⁴⁰Ca atoms

Superradiant active clocks operating on narrow linewidth clock transitions are predicted to achieve precision orders of magnitude higher than any currently existing optical atomic clocks. We introduce a theory of superradiant lasing and implement it for the example of ⁴⁰Ca atoms. The presented model, however, is valid for any two- or three-level system in an optical lattice. We perform a feasibility analysis and suggest a set of parameters for the experimental fulfillment of superradiant lasing in Ca. Moreover, we present an overview of different magic wavelengths for the 4s^{2 1}S₀ ↔ 4s4p³P₁ (m_J = 0) transition in Ca for different polarizations and a robustness analysis of these magic conditions. We also report the magic-zero wavelengths for the 4s4p³P₁, m_J = 0 state.