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Journal of Atomic and Molecular Physics

A dimension energy eigenstates's character of two Bi~+ in Paul trap

Wu Yun-Wen

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We exact calculate wave function,energy and average of relatively distance in Paul trap with two Bi~+.Our computation result is a value for actual experiments of trap ion.Theoretical analysis a dimension eigenstates's character of two Bi~+.

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We develop models for the motion of two trapped ions in one dimension, including both harmonic trapping forces and the Coulomb interaction between the ions. Mathematical and physical consistency dictates that the divergence of the Coulomb interaction at small distances be tempered with a soft core. A split-operator method is used to analyze numerically the energies and eigenstates of the motion of the two ions. Classification and closed-form expressions are also presented 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 zero-point motion of the ions. Implications of the results for the properties of two identical ions with Bose-Einstein or Fermi-Dirac statistics are discussed.
The stability regions of an ion in a two-dimensional Paul trap are studied by a quantum-mechanical treatment, which is very important for the experiment when the temperature is fairly low. The result is compared with a classical one published before by Paul [Rev. Mod. Phys. 62, 531 (1990)]. It is shown that their properties are quite similar and their differences are related to the quantum effect, which cannot be included within a classical description. All of these properties are discussed in detail.
By use of the well-known truncating series method, A program for calculating the Schrodinger exact solutions of quantum gate by two ions confined in a linear Paul trap is presented. The lower energy's state function for center of mass is analyzed. Probability distributing grawing is given. We calculate quantum state of variance in relatively position△r2 h/2 and quantum state of variance in relatively momentum△p2 h/2, the variance in position and momentum given by the Heisenberg uncertainty principle△r·△p h/2. It is a condition for squeezed states. We conclude that with center of mass in ground state, the quantum states of two ions in relatively position are squeezed states, and the quantum state of two ions is an entanglement state. Uncertainty of quantum measurement and entanglement must be consider in experiment.