Squeezing in resonance fluorescence and Schrödingerʹs uncertainty relation

Resonance fluorescence can exhibit squeezing in its quadrature components. Historically, this squeezing is defined with respect to Heisenbergʹs uncertainty relation, but when the lower limit on the uncertainty product becomes state dependent, this concept becomes rather artificial. Schrödingerʹs uncertainty relation sets a higher lower bound on the uncertainty product when the two observables are correlated. In the steady state both limits are nearly equal, but for pulsed excitation they can differ considerably. It is shown that after excitation with a π/2 or π pulse, the fluorescence is never squeezed. The squeezing is optimum for a π/3 or 2π/3 pulse, and is a factor of two better than for the best case in the steady state. If the inversion is zero after the pulse, then the fluctuations in the quadrature field are considerably below the Schrödinger limit, but the field is never squeezed below the Heisenberg limit.