Nonclassical states of light with a smooth P function

摘要

There is a common understanding in quantum optics that nonclassical states of light are states that do not have a positive semidefinite and sufficiently regular Glauber-Sudarshan P function. Almost all known nonclassical states have P functions that are highly irregular, which makes working with them difficult and direct experimental reconstruction impossible. Here we introduce classes of nonclassical states with regular, non-positive-definite P functions. They are constructed by “puncturing” regular smooth positive P functions with negative Dirac-δ peaks or other sufficiently narrow smooth negative functions.We determine the parameter ranges for which such punctures are possible without losing the positivity of the state, the regimes yielding antibunching of light, and the expressions of the Wigner functions for all investigated punctured states. Finally, we propose some possible experimental realizations of such states.