Quantum fluctuations around bistable solitons in the cubic-quintic nonlinear Schrödinger equation

Small quantum fluctuations in solitons described by the cubic-quintic nonlinear Schrödinger equation (CQNLSE) are studied within the linear approximation. The cases of both self-defocusing and self-focusing quintic terms are considered (in the latter case, the solitons may be effectively stable, despite the possibility of collapse). The numerically implemented back-propagation method is used to calculate the optimal squeezing ratio for the quantum fluctuations versus the propagation distance. In the case of self-defocusing quintic nonlinearity, opposite signs in front of the cubic and quintic terms make the fluctuations around bistable pairs of solitons (which have different energies for the same width) totally different. The fluctuations of nonstationary Gaussian pulses in the CQNLSE model are also studied.