Prepare non-classical collective spin state by designing control fields

Abstract

We propose a control method inspired by Lyapunov control to prepare non-classical state for a collective spin model. The spin squeezed states with entanglement can be prepared effectively. Meanwhile, the spin squeezed direction is fixed and the coherence can be maintained largely. It costs less time to obtain the non-classical state for larger systems and the control method performs effectively in a range of amplitudes of the control fields. The control method not only can be optimized by reducing the fast oscillations in the control fields but also behaves robustly for a range of deviation in the initial state and imperfections in the control fields during evolution. The non-classical states can be prepared in the presence of decoherence due to interaction with the environment in a range. We confirm that this closed-loop method can be applied to open-loop procedure in order to avoid quantum collapse resulting from measurement. This method can be applied in precision metrology by atom interferometry with a Bose-Einstein condensate.