Cooling without Spontaneous Emission
One of the important features of optical forces derived from multi-frequency light is the coherent control associated with the use of stimulated transitions. In single frequency light, stimulated emission produces light at the same frequency as the incoming light, so no energy exchange is possible. However, with multiple frequencies its possible to produce light by stimulated emission at a different frequency than the exciting light, thereby changing the energy of the light field. This process necessarily changes the atomic kinetic energy.
Cooling in bichromatic light in the absence of stimulated emission is possible because the the bichromatic force force vanishes at atomic speeds outside the range of ±δ/2k, where ±δ is the detuning from atomic resonance. This "speed limit" is easily derived from momentum conservation by requiring that Δp = 2ℏk (up and down in counterpropagating beams) where k ≡ 2π/λ so that ΔKE = MvΔv = 2ℏkv. For the bichromatic force the dressed state energy separations are ℏδ, and this upper limit of available energy sets the speed limit at δ/2k.
Atoms with speeds between ±δ/2k thus accumulate in a narrow range of velocities near the speed limit, and are therefore cooled in a reference frame moving at one of these speeds. A Gallilean transformation results in cold, slow atoms. The energy and entropy of the atoms are transferred to the light, and dissipated when the light is absorbed by the walls or other barriers (see paper).