Structure of the Harmonic Oscillator Hilbert space
Eduardo Zubizarreta Casalengua, Juan Camilo López Carreño, Elena del Valle, Fabrice P. Laussy · arXiv (Cornell University) · 2016
We map Hilbert space of quantum Harmonic oscillator to space of Glauber's $n$th-order intensity correlators, in effect showing the correlations between correlators for a random sampling of quantum states. In particular, we show how popular $g^{(2)}$ function is correlated to mean population and how a recurrent criterion to identify single-particle states or emitters, namely $g^{(2)}<1/2$, is incorrect as states exist that satisfy this condition with average population larger than one. Our charting of Hilbert space allows 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.