Optimal squeezing, pure states, and amplification of squeezing in resonance fluorescence

It is shown that 100% squeezed output can be produced in the resonance fluorescence from a coherently driven two-level atom interacting with a squeezed vacuum. This is only possible for $N=1/8$ squeezed input, and is associated with a pure atomic state, i.e., a completely polarized state. The quadrature for which optimal squeezing occurs depends on the squeezing phase $\Phi ,$ the Rabi frequency $\Omega ,$ and the atomic detuning $\Delta$. Pure states are described for arbitrary $\Phi ,$ not just $\Phi =0$ or $\pi$ as in previous work. For small values of $N,$ there may be a greater degree of squeezing in the output field than the input - i.e., we have squeezing amplification.