Nonclassical states of light with a smooth $P$ function

TL;DR

This paper introduces a new class of nonclassical light states with smooth, regular $P$ functions that include negative features, making them more accessible for experimental realization and analysis.

Contribution

It presents a method to construct nonclassical states with regular $P$ functions by puncturing positive functions with negative peaks, expanding the types of states that can be experimentally realized.

Findings

Identified parameter regimes for puncturing without losing positivity.

Demonstrated regimes where states exhibit antibunching.

Proposed experimental methods for generating these states.

Abstract

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-delta 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, as well as the regimes yielding antibunching of light. Finally, we propose some possible experimental realizations of such states.