Design of a biased Stark trap of molecules that move adiabatically in an electric field

A suitable arrangement of biased conductors @1# leads to an electrostatic field of zero magnitude at a central location that grows to tens of kV/cm away from the center. Such a field has allowed polar molecules to be confined in far deeper potential wells than may be realized with magnetic traps @2,3#. The neutral particles we consider do not move in a potential proportional to the electrostatic potential V, but instead, the motion is dictated by the spatial dependence of the shift quantum energy due to the local magnitude of the electric field. For this reason, the electrostatic trapping we consider does not contradict the fact that a charged particle cannot be held in stable equilibrium by electrostatic forces alone ~as first pointed out by Earnshaw @4#!. In the limit of adiabatic motion, the effective potential is dependent only on the particle quantum state and the local magnitude of the electric field E5uEW u. Although Maxwell’s equations do not allow a local minimum in V, no such constraint forbids a local minimum in E. The purpose of this work is to show that it is possible to build an electrostatic trap that has a nonzero bias field at the center. Our device may serve the same purpose as the Ioffe@5# Pritchard @6# magnetostatic trap; namely, the suppression of nonadiabatic motion that occurs in regions where the field ~and hence the energy splitting between quantum states! goes to zero or the gradient of the trap potential diverges. We speculate that this problem of nonadiabatic motion will be especially severe for those cases in which the Stark energy U of the molecules grows quadratically rather than linearly with electric field. Throughout this work we consider a hypothetical particle traveling in the quadratic Stark potential