Time-ordering effects in a one-atom laser based on electromagnetically induced transparency

The one-atom laser based on electromagnetically induced transparency, suggested recently [Phys. Rev Lett. 124, 093603 (2020)], is capable of generating Schrodinger cat states in the regime of strong ground-state coupling. In this regime, we find the exact solution for the Schrodinger equation with a time-dependent effective Hamiltonian by considering the Magnus expansion of the time-ordered exponential and calculating analytically the time-ordering terms, omitted in the previous study. We show that the time-ordering term affects the relative phase of two coherent components of the generated Schrodinger cat state. We show this influence by calculating various nonclassicality indicators for the cavity field, such as total noise, average parity, and relative total noise. We find that time-ordering becomes important at the average photon number in the cavity below 1, in striking contrast to the case of single-pass parametric downconversion, where it becomes important at average photon number in one optical mode above 4. (C) 2021 Optical Society of America