Raman cooling of atoms below the gravitational limit

Raman cooling of non-zero spin atoms in the presence of gravitational and external magnetic fields is investigated. The magnetic field is to be adjusted to compensate the gravitational force for ground-state atoms. The dark state (DS) is created and supported in momentum space with additional velocity-selective two-photon transitions. The minimum allowed temperature is found to be determined only by the width of velocity selection and therefore can be much less than the gravitational limit. Complete set of analytical formulas describing cooling of dilute atomic sample is derived. On this basis numerical simulations in one-dimension (1D) case are carried out