Laser cooling has advanced to the point where atomic motion can no longer be described in terms of discrete particles moving on classical trajectories. Instead, de Broglie wave fields occupy quantum states of a potential created by the interaction between atoms and the light field. Atomic transitions between these quantum states are mediated by optical pumping, in much the same way as transitions were made between internal angular momentum states in Prof. Series' time. Some examples are studied here, with special emphasis on dark states.
Laser cooling in a trap is investigated for laser and trapping configurations which allow the existence of approximate ``dark states'' of the combined atom-plus-trap system, i.e., states that are decoupled from the laser light by quantum interference. We show that a one-dimensional (1D) free-particle dark state in angular momentum
Jg=1 to
Je=1 transitions and in two counterpropagating laser fields survives as an approximate dark state in a ``flat-bottom'' trap of size much larger than the optical wavelength. Furthermore, we show the existence of approximate dark states in 1D harmonic-oscillator potentials. In the latter configuration we are able to provide analytical results.