Broadband pseudothermal states with tunable spectral coherence generated via nonlinear optics

It is well known that the reduced state of a two-mode squeezed vacuum state is a thermal state---i.e. a state whose photon-number statistics obey a geometric distribution. More exotic \emph{broadband} states can be realized as the reduced state of two spectrally-entangled beams generated using nonlinear optics. We show that these broadband "pseudothermal" states are tensor products of states in spectral Schmidt modes, whose photon-number statistics obey a geometric distribution. We study the spectral and temporal coherence properties of these states and show that their spectral coherence can be tuned---from perfect coherence to complete incoherence---by adjusting the pump spectral width. In the limit of a cw pump, these states are tensor products of true thermal states, but with different temperatures at each frequency. This could be an interesting state of light for investigating the interplay between spectral, temporal, and photon-number coherences.