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We study the emergence of non-Gaussian quantum features in pulsed squeezed light generation with a mesoscopic number (i.e., dozens to hundreds) of pump photons. Due to the strong optical nonlinearities necessarily involved in this regime, squeezing occurs alongside significant pump depletion, compromising the predictions made by conventional semiclassical models for squeezing. Furthermore, nonlinear interactions among multiple frequency modes render the system dynamics exponentially intractable in naïve quantum models, requiring a more sophisticated modeling framework. To this end, we construct a nonlinear Gaussian approximation to the squeezing dynamics, defining a “Gaussian interaction frame” in which non-Gaussian quantum dynamics can be isolated and concisely described using a few dominant (i.e., principal) supermodes. Numerical simulations of our model reveal non-Gaussian distortions of squeezing in the mesoscopic regime, largely associated with signal-pump entanglement. We argue that state of the art in nonlinear nanophotonics is quickly approaching this regime, providing an all-optical platform for experimental studies of the semiclassical-to-quantum transition in a rich paradigm of coherent, multimode nonlinear dynamics. Mesoscopic pulsed squeezing, thus, provides an intriguing case study of the rapid rise in dynamic complexity associated with semiclassical-to-quantum crossover, which we view as a correlate of the emergence of new information processing capacities in the quantum regime.
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Semiclassical perturbations of single-degree–of–freedom Hamiltonian systems I: Separatrix splitting
We study semiclassical perturbations of single-degree-of-freedom Hamiltonian systems possessing hyperbolic saddles with homoclinic orbits, and provide a sufficient condition for the separatrices to split, using a Melnikov-type approach. The semiclassical systems give approximations of the expectation values of the positions and momenta to the semiclassical Schrödinger equations with Gaussian wave packets as the initial conditions. The occurrence of separatrix splitting explains a mechanism for the existence of trajectories to cross the separatrices on the classical phase plane in the expectation value dynamics. Such separatrix splitting does not occur in standard systems of Hagedorn and Heller for the semiclassical Gaussian wave packet dynamics as well as in the classical systems. We illustrate our theory for the potential of a simple pendulum and give numerical computations for the stable and unstable manifolds in the semiclassical system as well as solutions crossing the separatrices.
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- Award ID(s):
- 2006736
- PAR ID:
- 10648541
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Journal of Mathematical Physics
- Volume:
- 65
- Issue:
- 10
- ISSN:
- 0022-2488
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0198420
