Deconstructing squeezed light: Schmidt decomposition versus the Whittaker-Shannon interpolation

Abstract

We develop a formalism to describe squeezed light with large spectral-temporal correlations. This description is valid in all regimes, but is especially applicable in the long pulse to continuous-wave limit where the photon density at any particular time is small, although the total number of photons can be quite large. Our method relies on the Whittaker-Shannon interpolation formula applied to the joint temporal amplitude of squeezed light, which allows us to “deconstruct” the squeezed state. This provides a local description of the state and its photon statistics, making the underlying physics more transparent than does the use of the Schmidt decomposition. The formalism can easily be extended to more exotic nonclassical states where a Schmidt decomposition is not possible.