Using Algebra to Dissect Quantum Optical Evolution for Quantum Control

Quantum control is the ability to affect quantum systems through judicious selection of dynamical parameters and their time dependence. Wei-Norman factorization [Wei and Norman, Proc. Amer. Math.Soc.15, 327 (1964)] is a powerful method to parametrize the quantum mechanical evolution operator before applying it to specific states. We first illustrate this method on the dynamics of optomechanical oscillators. We then extend the method to the pseudo-dynamics associated with the squeeze operator and characterize its action on a variety of optical states. This leads to improved insight into quantum control at a level accessible to undergraduates.