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Physics Letters A

On the phase space description of quantum nonlinear dynamics

Natig M. Atakishiyev, S. M. Chumakov, Ana Leonor Rivera, Kurt Bernardo Wolf

Published Jun 1, 1996• 18 citations
Publisher
DOI
10.1016/0375-9601(96)00188-0

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We establish that permutation-invariant emitter ensembles with local dissipation admit a semiclassical description on the four-dimensional phase space of a variable-length collective spin, within a perturbative truncated Wigner approximation (TWA). The TWA captures nonlinear dynamics and nonclassical signatures without prescribing closures of correlations. We cast a class of spatially extended emitter systems as interacting ensembles tractable in the TWA to show how quantum fluctuations reshape directional cooperative emission beyond mean-field predictions in a pumped chain containing tens of thousands of emitters, using hundreds of phase-space variables. Our results offer a unified description of collective dynamics beyond the classical limit in emitter ensembles.
Constrained Hamiltonian dynamics is exploited to provide the mathematical framework of a coarse-grained description of the quantum system of nonlinear interacting oscillators. The coarse graining is treated as an equivalence relation on the set of quantum states resulting in the emergence of classical phase space. The equivalence relation imposes constraints on the Hamiltonian dynamics of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of the corresponding classical system on a sufficiently large scale.