Number-Phase Wigner Representation for Scalable Stochastic Simulations of Controlled Quantum Systems

Abstract

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 BEC and atom lasers, full quantum field simulations must rely on scalable stochastic methods whose convergence time 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 over an order of magnitude longer and more precisely than its coherent equivalent. This opens the possibility of realistic simulations of controlled multi-mode quantum systems.

5 pages, 1 figure

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• Controlling spontaneous-emission noise in measurement-based feedback cooling of a Bose-Einstein Condensate
• Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems
• Emergent classicality in continuous quantum measurements
• Non-Gaussian pure states and positive Wigner functions
• Quantum dynamics and entanglement in coherent transport of atomic population
• From the Weyl quantization of a particle on the circle to number-phase Wigner functions
• Generating Macroscopic Superpositions with Interacting Bose-Einstein Condensates: Multi-Mode Speed-Ups and Speed Limits
• Generalized Weyl quantization on the cylinder and quantum phase
• Coherent functional expansions in quantum field theory