Using master equation and quantum Monte Carlo wavefunction approaches, we study the circumstances surrounding the emergence and degradation of the elusive squeezing of fluctuations in two-level atom resonance fluorescence. For its measurement we suggest conditional homodyne detection (CHD) [G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, H.J. Carmichael, Phys. Rev. Lett. 85, pp. 3149-3152, 2000], which is nearly independent of detector efficiencies, which have harmed previous attemps. Squeezing in resonance fluorescence requires a weak laser, so the average interval between emitted photons is much longer than the regression time to the steady state; here, the spectrum of the out-of-phase quadrature is a negative peak. In CHD, moderate fields generate a non-zero third-order correlation in the dipole fluctuations that contaminates squeezing, making the noise non-Gaussian. If the probability to emit two and even three close photons is still small the additional contribution is also negative, helping to make the full spectrum a bit larger and easier to measure. Strong driving spreads the photoemission distribution, which destroys squeezing, and the third order fluctuations become responsible for the non-classicality of the fluorescence.
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