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Springer eBooks

The Semiclassical Tool in Complex Physical Systems: Mesoscopics and Decoherence

Rodolfo A. Jalabert, Horacio M. Pastawski

Published Oct 12, 2007• 5 citations
Publisher
DOI
10.1007/3-540-44946-9_39

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A mesoscopic evolution equation for an ensemble of mesoparticles follows from the elimination of internal degrees of freedom. If the system is composed of a hierarchy of scales then the reduction procedure could be worked repeatedly and the characterization of this iterating method is carried out. Namely, a prescription describing a discrete hierarchy of master equations for the density operator is obtained. Decoherence follows from the irreversible coupling between the system, defined by mesoscopic variables, and internal degrees of freedom. We briefly discuss the existence of systems with the same dynamics laws at different scales. We made an explicit calculation for an ensemble of particles with internal harmonic interaction in an external anharmonic field. New conditions related to the semiclassical limit for mesoscopic systems (Wigner-function) are conjectured.
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.