Quantum fluctuations in a continuous vectorial Kerr medium model

Abstract

We consider a model for a Kerr medium in a planar resonator, which takes into account the vectorial character of the radiation field. We analyze the spatial behavior of quantum fluctuations around a steady state, with a roll-pattern configuration in the beam cross section, using a Langevin treatment based on the Wigner representation. The spatial distribution of the quantum fluctuations around the roll pattern is dominated by the neutral ͑or Goldstone͒ mode, corresponding to rigid spatial displacements of the pattern. The spatial configuration of the field immediately outside the cavity input-output mirror depends on the time window over which fluctuations are averaged: only when the time window is on the order of the cavity lifetime the output field fluctuations are qualitatively similar to that of the intracavity field. The quantum correlations among the fields in play, as described by the full multimode model, turn out to be in good agreement with those predicted by a simple three-mode model.

Transverse Patterns in Nonlinear Optical Resonators

“…Second, owing to noise, the precursors of patterns can be seen below the pattern formation threshold [160][161][162]. While a noiseless pattern-forming system below the pattern formation thresh- old shows no pattern at all, since all perturbations decay, one observes in the presence of noise a particular form of spatially filtered noise, which in the field of nonlinear optics has been called "quantum patterns" when the noise is of quantum origin [163][164][165]. Above the pattern formation threshold, noise can also result in defects (dislocations or disclinations) of the patterns [166,167].…”

Macroscopic quantum fluctuations in noise-sustained optical patterns

“…Such Fokker-Planck equations can be represented in terms of stochastic Langevin equations for the c-number field α 1 ( x) [6]. The same type of approximation, linearizing around a pattern solution [8], is generally possible in the absolutely unstable regime above threshold. A common feature of these two regimes (absolutely stable and unstable) is that quantum noise does not change drastically the solution with respect to the stable deterministic solution.…”

“…These distributions are functionals of the c-number fields α i ( x) associated with the operators i ( x). This evolution equation is obtained by substituting products of field operators and the density operator, depending on the ordering, by suitable operations on the distribution functionals [6,8]. The evolution equations obtained in this way for the distributions are functional partial differential equations.…”

“…The Heisenberg picture produces a hierarchy of coupled nonlinear operator equations that usually defies analysis. The preferred method to date has been to linearize the quantum fluctuations about a classical field amplitude that usually takes a constant value below threshold [6,7], but may be associated with a stable pattern above threshold [8].…”

Quadrature and polarization squeezing in a dispersive optical bistability model

“…Also quantum fluctuations have been studied in this system but, as far as we know, only from the perspective of pattern formation [21], i.e., by considering a continuum of transverse modes. Here we consider the single transverse mode model and study quadrature and polarization squeezing in the field exiting the nonlinear cavity.…”