Efficient wave function simulations in nonlinear quantum optics using an adaptive coherent state basis

Full text: We show that a suitable set of coherent basis states placed on a discrete hexagonal grid can be used to numerically very accurately represent general quantum states in a memory efficient way. Adding an algorithm for dynamic basis adaptation allows highly accurate Quantum Monte Carlo wave function simulations with small basis sets. At the example of the intricate nonlinear dynamics of an optical parametric oscillator around threshold, we demonstrate that this approach yields accurate time dependent solutions with a substantially smaller basis sets than required for a photon number basis. Above threshold the adaptive basis splits into localized subsets allowing efficient representation of bimodal or even more complex phase space distributions and directly yields an intuitive physical picture of the ongoing dynamics. (author)