A series of pulsed electric fields can be arranged such that it creates a t
raveling potential well in which neutral dipolar molecules can be confined.
This provides a method to transport, to decelerate, and to cool a sample o
f neutral molecules while maintaining the initial phase-space density. This
method is described using the concept of phase stability. The oscillating
motion of molecules in the traveling potential well, reaching a minimum vel
ocity spread corresponding to a translational temperature of 4 mK, is exper
imentally observed.