9.7 The Sisyphus cooling technique 205Linear Linear Linear ...Energy(b)(c)(d)(a)Light
shiftLight
shiftLight
shiftLight
shiftDistance along standing wave,Distance along standing wave,Excited state:Ground state:Fig. 9.18Details of the Sisyphus cooling mechanism. (a) The electric dipole transitions between two levels with angular
momentaJ=1/2andJ′=3/2. The relative strength of each transition is indicated—this gives the relative intensity when the
states in the upper level are equally populated (each state has the same radiative lifetime). (b) The polarization in a standing
wave formed by two laser beams that propagate alonĝezand−̂ez, and have orthogonal linear polarizations alonĝexand̂ey,
respectively. The resultant electric field is circularly polarized (̂ex±îey)/
√
2 at positions where the two counter-propagating
beams have a phase difference of±π/2. The polarization changes fromσ+toσ−over a distance of ∆z=λ/4, and between
these positions the light has elliptical or linear polarization. (c) The energies of the states at positions ofσ−andσ+polarization
(the unperturbed energy of the lower level is shown as a dotted line). Absorption of the circularly-polarized light followed by
spontaneous emission transfers the population into the state with lowest energy (largest light shift). (d) The light shift varies
with position and the optical pumping process, outlined in (c), transfers atoms from the top of a hill to the bottom of a valley
(as shown in Fig. 9.17); or at least this process in which atoms lose energy happens more often than the other way around.