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

TL;DR

This paper analytically investigates the impact of time-ordering effects on Schr"odinger cat states generated by a one-atom laser based on electromagnetically-induced transparency, revealing significant effects at low photon numbers.

Contribution

It provides an exact solution incorporating time-ordering effects in the dynamics of a one-atom laser, highlighting their influence on nonclassical state properties.

Findings

Time-ordering affects the phase of Schr"odinger cat states.

Time-ordering becomes significant at photon numbers below 1.

Contrasts with single-pass parametric downconversion results.

Abstract

One-atom laser based on electromagnetically-induced transparency, suggested recently [Phys. Rev. Lett. 124, 093603 (2020)], is capable of generating Schr\"odinger cat states in the regime of strong ground-state coupling. In this regime, we find the exact solution for the Schr\"odinger 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 Schr\"odinger 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.