Abstract
We study the quasiclassical dynamics of the cross-Kerr effect. In this approximation, the typical periodical revivals of the decorrelation between the two polarization modes disappear and remain entangled. By mapping the dynamics onto the Poincaré space, we find simple conditions for polarization squeezing. When dissipation is taken into account, the shape of the states in such a space is not considerably modified, but their size is reduced.
Highlights
We study the quasiclassical dynamics of the cross-Kerr effect
By mapping the dynamics onto the Poincarespace, we find simple conditions for polarization squeezing
The optical Kerr effect refers to the intensity-dependent phase shift that a light field experiences during its propagation through a third-order nonlinear medium
Summary
The optical Kerr effect refers to the intensity-dependent phase shift that a light field experiences during its propagation through a third-order nonlinear medium. The transition between both can be best scrutinized by exploiting phase-space methods [58,59,60] This opens up the possibility of gaining some information about the nonclassical behavior with a quasiclassical description that employs essentially classical trajectories, while the correct quantum initial state is taken into account via, e.g., the Wigner function [61,62,63]. We capitalize on the quasiclassical approach to re-analyze the light propagation in this case in a very concise way: after neglecting higher-order fluctuations, we get an evolution equation for the Wigner function that can be integrated to an analytical form This allows us to study the dynamics of mode correlations. The resulting evolution reveals that the shape of the Wigner functions is not considerably modified, but their size is shrunk
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