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Characterizing squeezed light: Schmidt decomposition vs. Whittaker-Shannon interpolation

Christian Drago, John E. Sipe

Published Jan 1, 2023• 0 citations
Publisher

Abstract

For squeezed light with a large spectro-temporal correlation, we construct an approximate Schmidt decomposition, which is equivalent to the Whittaker-Shannon interpolation formula. Our decomposition leads to an intuitive description of the squeezed light photon statistics.
DOI
10.1364/cleo_fs.2023.ftu4a.6

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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.
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 "take apart" 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.
The Whittaker-Shannon decomposition provides a temporally localized description of squeezed light, making it applicable in the CW limit and leading to a definition of squeezing strength based on the number of photon pairs at a time. We show examples of its usefulness by calculating quadrature variance in a homodyne detection scheme, coincidence detection probabilities in the continuous-wave limit, and analyzing the Hong-Ou-Mandel effect for strongly squeezed light. Quadrature uncertainty falls farther below the shot noise limit when squeezing is strong, but effects due to correlations between photon pairs are most significant with weak squeezing. Our analysis extends previous results to more general scenarios, and we leverage the Whittaker-Shannon formalism to interpret them based on the temporal properties of photon pairs.
Quantum systems comprised of interacting subsystems become highly correlated and their individual identities become entangled. This entanglement can be described using the Schmidt decomposition, in which a pair of preferred orthonormal bases can be constructed to emphasize the tight correlations between two quantum subsystems. Examples are given of how the Schmidt basis can be exploited to shed new light on entangled subsystems in quantum optics, paying special attention to two-mode squeezed states and to atom–field interaction.