Steady state macroscopic superpositions in a micromaser

The micromaser field master equation has been solved for atoms injected in a coherent superposition of their upper and lower states. The results show that at very low temperatures, steady-state macroscopic superpositions can be generated in a micromaser pumped by two-level atoms injected in a coherent superposition of their upper and lower states. In particular, the steady-state field entropy undergoes a sharp transition as a function of the ratio N_ex = R/γ between the atomic injection rate and cavity decay rate. A broad region of generally constant entropy is followed by a region where S decreases approximately as 1/N_ex. This is clear evidence that the steady state of the micromaser field approaches a pure state. The impact of this transition on the mean photon number and the normalized variance as a function of N_ex is examined. At the transition, the micromaser field changes its character from a near-vacuum state for low N_ex to a field with distinctly super-Poissonian photon statistics. This transition is distinct from the conventional laser threshold.