Photon liquefaction in time

Abstract

We provide a mechanism to imprint local temporal correlations in photon streams with a character similar to spatial correlations in liquids. Typical single-photon light, such as that from an incoherently pumped two-level system, corresponds, in this picture, to a (temporal) gas, while uncorrelated light is the ideal gas. We argue that single-photon sources with good antibunching are those that exhibit temporal liquid features, i.e., a plateau for their short-time correlations (as opposed to a linear dependence) and oscillations at later times. This is a manifestation of photon time ordering that provides direct access to the single-photon purity, or probability of each emitted photon being detected, which is not usually available in stationary sources. We obtain general, closed-form analytical expressions for the second-order coherence function of a broad family of “liquid light,” which can be arbitrarily correlated, though never completely crystallized. These results invite us to reconsider what is understood as single-photon sources and how to implement them, as well as to deepen the analogies between time correlations of light and spatial correlations of matter.