Quantum Motion of Two Trapped Particles
Abstract
We develop models for the quantum motion of two trapped particles, taking into account both the trapping forces and a repulsive interaction between the particles. A splitoperator method is used to analyze the energies and eigenstates of the twoparticle motion numerically. For the twoion case, a full classification and closedform expressions are found for the energies and the eigenstates in the limits when the equilibrium distance due to the Coulomb repulsion is either much smaller or much larger than the amplitude of the zeropoint motion of the ions. Effects of quantum statistics of the ions on the motion are discussed. Since the current ion traps do not provide a strong enough trapping force to allow the observation of the effects of quantum statistics on the centerofmass motion, we consider a general case with a inverse power law interaction 1/r^{n} between the particles and find that for n > 2, the quantum statistical regime occurs in the limit of weak confinement. As an example, two atoms in a magnetic trap with magnetic dipole interaction (n = 3) between them are readily deep in the quantum statistical regime.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT........48Y
 Keywords:

 ION TRAPPING;
 Physics: Optics; Physics: Atomic