text: In the lin⊥lin configuration cooling is achieved via a Sisyphus effect. Consider two counterpropagating electromagnetic waves with equal amplitude and orthogonal linear polarizations  and , where k is the wavenumber . The superposition of  and  is given as:
  Introducing a new pair of coordinates  and  the field can be written as:
  The polarization of the total field changes with z. For example: we see that at  the field is linearly polarized along , at  the field has left circular polarization, at  the field is linearly polarized along , at  the field has right circular polarization, and at  the field is again linearly polarized along .
  Consider an atom interacting with the field detuned below the transition from atomic states  and  (). The variation of the polarization along z results in a variation in the light shifts of the atomic Zeeman sublevels with z. The Clebsch-Gordan coefficient connecting the  state to the  state is 3 times larger than connecting the  state to the  state. Thus for  polarization the light shift is three times larger for the  state than for the  state. The situation is reversed for  polarization, with the light shift being three times larger for the  state than the  state. When the polarization is linear, there is no difference in the light shifts between the two states. Thus the energies of the states will oscillate in z with period .
  As an atom moves along z, it will be optically pumped to the state with the largest negative light shift. However, the optical pumping process takes some finite time . For field wavenumber k and atomic velocity v such that , the atom will travel mostly uphill as it moves along z before being pumped back down to the lowest state. In this velocity range, the atom travels more uphill than downhill and gradually loses kinetic energy, lowering its temperature. This is called the Sisyphus effect after the mythological Greek character. Note that this initial condition for velocity requires the atom to be cooled already, for example through Doppler cooling.