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Squeezed Light: Time for a Coincidence?

Jasper Kranias, Christian Drago, Colin Vendromin, John E. Sipe

Published Jan 1, 2025• 0 citations
Publisher

Abstract

The Whittaker-Shannon decomposition provides a temporally localized description of squeezed light. We show an exmaple of its usefulness by calculating coincidence detection probabilities in the continuous-wave limit.
DOI
10.1364/cleo_at.2025.jps200_30

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The birth, life, and death of squeezed light

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In this thesis we study three aspects of squeezed light. First, we investigate the generation of pulsed, near‑pure, degenerate, single‑temporal‑mode squeezed light produced by dual‑pump spontaneous four wave mixing in integrated silicon‑nitride coupled‑ring resonators. We show that parasitic spontaneous four wave mixing processes inherent to the dual‑pump configuration can substantially degrade the amount of generated squeezing and state purity. To mitigate these effects we explore pump detuning, engineered dispersion, and an auxiliary‑ring structure as suppression strategies. We then optimize the incident pump amplitude and phase, demonstrating that longer pump pulses can yield highly squeezed, temporally separable states and that an appropriate pre‑chirp tracks the effects of self‑ and cross‑phase modulation, increasing intracavity pump amplitudes and the amount of generated squeezing. Next, we analyze the spectral–temporal structure and photon statistics of strongly correlated squeezed light. We develop a general formalism based on the Whittaker–Shannon interpolation of the joint‑temporal amplitude that is particularly useful in the long‑pulse and continuous‑wave limits, where the instantaneous photon density is low but the total photon number may be large. This packet‑based description provides a local, physically transparent account of the state and its photon statistics that complements the Schmidt decomposition, and extends to nonclassical states for which a Schmidt decomposition is not available. Finally, we examine whether or not squeezed illumination can enhance two‑photon excitation relative to classical light, and whether any enhancement is experimentally detectable. We construct a model including radiative and nonradiative broadening to compute scattered and absorbed energy, and apply it to fluorescence from cesium atoms in a magneto‑optical trap driven by classical and squeezed light in both continuous‑wave and pulsed regimes. Under ideal conditions squeezed light can produce a measurable enhancement in both limits, but the gains are moderate and smaller than some recent molecular reports; additional broadening or loss would further reduce detectability.

•Jun 1, 2026•0 citations
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.
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.
In this thesis we study three aspects of squeezed light. First, we investigate the generation of pulsed, near‑pure, degenerate, single‑temporal‑mode squeezed light produced by dual‑pump spontaneous four wave mixing in integrated silicon‑nitride coupled‑ring resonators. We show that parasitic spontaneous four wave mixing processes inherent to the dual‑pump configuration can substantially degrade the amount of generated squeezing and state purity. To mitigate these effects we explore pump detuning, engineered dispersion, and an auxiliary‑ring structure as suppression strategies. We then optimize the incident pump amplitude and phase, demonstrating that longer pump pulses can yield highly squeezed, temporally separable states and that an appropriate pre‑chirp tracks the effects of self‑ and cross‑phase modulation, increasing intracavity pump amplitudes and the amount of generated squeezing. Next, we analyze the spectral–temporal structure and photon statistics of strongly correlated squeezed light. We develop a general formalism based on the Whittaker–Shannon interpolation of the joint‑temporal amplitude that is particularly useful in the long‑pulse and continuous‑wave limits, where the instantaneous photon density is low but the total photon number may be large. This packet‑based description provides a local, physically transparent account of the state and its photon statistics that complements the Schmidt decomposition, and extends to nonclassical states for which a Schmidt decomposition is not available. Finally, we examine whether or not squeezed illumination can enhance two‑photon excitation relative to classical light, and whether any enhancement is experimentally detectable. We construct a model including radiative and nonradiative broadening to compute scattered and absorbed energy, and apply it to fluorescence from cesium atoms in a magneto‑optical trap driven by classical and squeezed light in both continuous‑wave and pulsed regimes. Under ideal conditions squeezed light can produce a measurable enhancement in both limits, but the gains are moderate and smaller than some recent molecular reports; additional broadening or loss would further reduce detectability.