Abstract

We present experimental results that demonstrate a high degree of control over the spin state of an atom. The experiment is carried out on a sample of about 10⁷ laser-cooled ^l33Cs atoms in their F = 4 ground state hyperfine level released from a magneto-optical trap. Our method is to apply a static magnetic field B₀ a time- dependent transverse magnetic filed B_x(t), and a linearly polarized off-resonance laser field to the atoms. The Hamiltonian is where B(t) = B₀z + B_x(t)x. B₀ induces a precession of the spins at the Larmor frequency . The second term in H arises from the laser field light shift; together with the static field B₀ it yields a finite “anharmonic” ladder of quantum states, labeled by the spin projection quantum number F. Because of the anharmonicity, B_x(t) induces motions of the spin that are not simply rotations of the initial state. Rather, through the application of quantum control theory,¹ it is possible to find a pulse B_x(t) that produces time evolution connecting arbitrary spin states.

© 1999 Optical Society of America