Quantum Control of the Squeezing Operator with Dynamics using Wei-Norman Factorization and the Time Evolution Operator

Control of quantum phenomena would allow for expanding control theory from classical systems to microscopic ones whose behavior is dictated by quantum mechanics. A current goal of quantum control is to develop a systematic methodology for the manipulation of systems. The approach typically used to solve dynamic quantum systems is useful to analyze characteristics of a system represented by a defined operator. The squeeze operator's actions are characterized by finding the time evolution operator using the Wei-Norman method on the associated Hamiltonian and applying this to number (Fock) states, coherent states, and Schrodinger cat states. This specific case analyzing the Squeeze operator shows that the Wei-Norman method to find time-evolution operator can reveal the dynamics of any system with an associated Lie Algebra basis. Documenting a variety of initial states and initial parameters in a library of cases provides a foundation to achieving greater control in experimental applications as well.