Cooling below the recoil limit

To date, two specific phase-space optical-pumping schemes have been demonstrated. One uses a two-photon Raman transition and the other is based on the velocity-selective coherent population-trapping (VSCPT) effect. 

Raman cooling uses a two-photon transition between two h q)erfine-structure levels in the ground state of the atom and provides coherent displacement of parts of the velocity distribution toward zero velocity. Such cooling was successfully demonstrated in an experiment by Kasevich and Chu (1992). Consider a three-level A-atom in which 1) and 2) are the lower energy levels and e) is the upper level, placed in the field 

2 Velocity-selective coherent population trapping of ultracold atoms 

The coherent population-trapping effect is manifested in various domains of atomic and laser physics (see Section 4.4.2). Let a quantum mechanical system described by a nonperturbed operator Hq be placed in an external field. Its interaction with the field is described by an operator V. In this case, the temporal evolution of the state t) of the system in the interaction representation is described by the Schrodinger equation as 

In some special cases, the Schrodinger equation may have a solution j Z nc) satisfying the equation 

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