Number-phase Wigner representation for scalable stochastic simulations of controlled quantum systems

Simulation of conditional master equations is important to describe systems under continuous measurement and for the design of control strategies in quantum systems. For large bosonic systems, such as Bose-Einstein condensates and atom lasers, full quantum-field simulations must rely on scalable stochastic methods. Currently, these methods have a convergence time that is restricted by the use of representations based on coherent states. Here, we show that typical measurements on atom-optical systems have a common form that allows for an efficient simulation using the number-phase Wigner (NPW) phase-space representation. We demonstrate that a stochastic method based on the NPW can converge orders of magnitude longer and more precisely than its coherent equivalent. We then examine how these methods can be used in multimode simulations, demonstrated by a simulation of a two-mode Bose-Hubbard model. Finally, we combine these techniques to demonstrate a full-field simulation of a realistic multimode quantum system controlled by active feedback.