  Non-classical states of light, such as number-squeezed light, with
fluctuations below the classical shot noise level, have important uses in
metrology, communication, quantum information processing, and quantum
simulation. However, generating these non-classical states of light, especially
with high intensity and high degree of squeezing, is challenging. To address
this problem, we introduce a new concept which uses gain to generate intense
sub-Poissonian light at optical frequencies. It exploits a strongly nonlinear
gain for photons which arises from a combination of frequency-dependent gain
and Kerr nonlinearity. In this laser architecture, the interaction between the
gain medium and Kerr nonlinearity suppresses the spontaneous emission at high
photon number states, leading to a strong "negative feedback" that suppresses
photon-number fluctuations. We discuss realistic implementations of this
concept based on the use of solid-state gain media in laser cavities with Kerr
nonlinear materials, showing how 90% squeezing of photon number fluctuations
below the shot noise level can be realized.
