Fig. 2: Application of Airy transform to analyse nonlinearity accumulation with physical bounded gates.
From: Nonlinear phase gates as Airy transforms of the Wigner function
Action of the quartic bound cubic gate \({({U}_{3,4})}^{k}\) (top) for k = 1, 2, 3 left to right. Iteration of the gate increases the cubic effects, as seen by the re-emergence of the suppressed negative position and momentum region. This occurs even though at all stages the system is bounded from below by the quartic gate. The pure cubic phase states (bottom) have diverging momentum for both positive and negative momentum symmetrically. Initial states and parameters are as in Fig. 1. The effective potentials corresponding to the applied gates are shown below the Wigner functions (left) where quartic-bounded cubic potentials are solid, cubic potentials are dashed. Increasing k (blue, orange, green) leads to quartic-bounded cubic potentials that more closely approximate the cubic potential around the inflection point. However the increasing significance of the quartic term more strongly attenuates the nonlinear squeezing in absolute value in comparison with a cubic phase state (bottom right).
