Optimal Control of Large Spin Systems

A quantum system is said to be controllable if the accessible Hamiltonians (as a Lie algebra) generate all unitary operators on Hilbert space. Optimal quantum state control seeks a time-dependent sequence of Hamiltonians that maximize the fidelity with an arbitrary target state given a fixed initial state. We consider optimal control of the spin of a cesium atom restricted to its F=3 ground state hyperfine manifold, with a Hilbert space of dimension 2F+1=7. Control is implemented through time varying magnetic fields in two orthogonal directions along with a quadratic AC-Stark shift created by an off-resonant laser probe. The optimization is performed under several constraints, most importantly a temporal limitation determined by dephasing due to photon scattering and parameter inhomogeneity. The fidelity of state preparation is verified through both a full density matrix simulation and reconstruction from experimental data.