Structure of the harmonic oscillator in the space of n-particle Glauber correlators

Abstract

We map the Hilbert space of the quantum Harmonic oscillator to the space of Glauber's nthorder 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) < 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.

Single Photon Emission from a Plasmonic Light Source Driven by a Local Field-Induced Coulomb Blockade

“…Based on a 2-particle Hilbert space argument, its dip intensity of 58% (i.e. g (2) (0) = 0.42) is consistent with imperfect single photon emission of at most [1-(1-2g (2) ) 1/2 ]/g (2) = 1.42 photons on average 24 . The antibunching lifetime is τ = 132 ps and reflects the tunneling of electrons from Ag(111) to the top C 60 layer.…”

Effective second-order correlation function and single-photon detection

“…These vacuum contributions entered our derivation quite naturally, and its physical origin was only explained afterwards. As indicated by the chosen examples the average photon number is an often determined quantity that may also provide further results on the SP character, compare also [26]. Other figures of merit for SP sources include indistinguishability [33] and coalescence [34] of different SPs, which require more emphasis on the decohering processes and thus the Hamiltonian and dissipative structure of the system at hand.…”

“…[28,29]. At this point, it is worth comparing with the results from [26]. In that work it was shown that g (2) 1/2 implies that the average photon number á ñ n has to be smaller or equal to 2, the equality given for the Fock state and thus  -[ ( )] q n n 2 1 n .…”

“…In other words, if in the experiments the vacuum contribution is not determined, equation (20) yields all that can be concluded from g (2) <1/2. This does not exclude further conclusions like an upper bound on q (see section 6) or on the average photon number [26]. It does provide one way to formulate this limited information quantitatively.…”

“…It should also be noted that g (2) (0)=0 is only a necessary criterion for SPs, not a sufficient one. Recently, a somewhat different interpretation of g (2) <1/2 was given in [26], where it was shown to imply that the average photon number of the quantum state is in that case limited by 2. This means that even states, which on average have more than one photon, may fall under this category.…”