The confinement of electrically charged particles to tiny regions of space is pertinent to many areas of physics research. By localizing atoms and molecules to regions with small dimensions relative to wavelengths of energy-level transitions, electromagnetic traps can be used to place particle dynamics in what is known as the Lambe-Dicke regime. Because first and second-order Doppler effects are negligible in the Lambe-Dicke regime, atomic and molecular spectroscopy of unprecedented resolution can be conducted.[5,11] Electromagnetic traps have also raised the prospect of a frequency standard with superior precision to that of cesium atomic clocks.
As one might suspect, the confinement of elementary particles to small spatial regions for long periods of time has led to a cascade of breakthroughs in quantum research. Investigation of the energy levels of the ``pseudoatom'' geonium, which consists of an electron in orbit inside a Penning electromagnetic trap, enables measurement of the electron g-factor to a precision 30000 times greater than was previously possible. Experimentally measured g-factors agree with Dirac's theory to within 6 parts per . Geonium investigation of the anomalous magneton moment of suggests a structure to the electron (electron radius m) which defies the theoretical notion of a ``point particle.''[9,15] Frequency shifts of electrons in Penning traps provide a mechanism for continuous monitoring of a single particle's quantum state and observation of the aptly named ``continuous'' Stern-Gerlach effect.[10,9]
The theory of E.P. Wigner predicts crystallization for ion configurations
with a large amount of potential energy of repulsive Coulomb interactions relative to the amount kinetic energy.
First reported by Wuerker, et al., Wigner crystallization in the Paul trap enables study of few-body phase transitions. The phenomenon of Wigner crystallization within ion traps also raises the possibility of creating ordered ion beams in high-energy storage rings. The resultant compression of ion velocity spread
could facilitate the investigation of nuclear reactions with tiny cross-sections.[5,3,35]