Tangent and cotangent states of the electromagnetic field

We consider a lossless micromaser in which a monoenergetic, low-density beam of two-level atoms in a coherent superposition of their upper and lower states is injected inside a single-mode high-Q cavity. This is a realization of a harmonic oscillator driven by a quantum current. We find that under appropriate conditions the field may evolve to pure states, which we call tangent and cotangent states, even for mixed-state initial conditions. In various limits, they exhibit nonclassical properties such as sub-Poissonian photon statistics, or even more interestingly acquire the characteristics of ``macroscopic'' quantum superpositions. The conditions under which these states are reached, as well as the dynamical approach of the system to steady state, are discussed in detail.