Structure of the harmonic oscillator in the space of <i>n</i>-particle Glauber correlators

Abstract

We map the Hilbert space of the quantum harmonic oscillator to the space of Glauber’s nth-order intensity correlators, in effect showing “the correlations between the correlators” for a random sampling of the quantum states. In particular, we show how the popular g(2) function is correlated to the mean population and how a recurrent criterion to identify single-particle states or emitters, namely, g(2)&amp;lt;1/2, actually identifies states with at most two particles on average. Our charting of the Hilbert space allows us to capture its structure in a simpler and physically more intuitive way that can be used to classify quantum sources by surveying which territory they can access.