Control of Squeezed Phonon and Spin States

In this paper we analyze the quantum control of squeezed states of harmonic oscillators as well as spin squeezing and its relationship to quadrature squeezed states of other bosonic fields. Squeezing provides a method for reducing noise below the quantum limit and provides an example of the control of under-actuated control systems in the stochastic and quantum context. We consider also the interaction of a squeezed quantum oscillator with an external heat bath and the problem of cancellation of squeezed states. Our controls consist of single or multiple pulses.