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International Journal of Modern Physics B

DISSIPATIVE DYNAMICS OF A SINGLE PARTICLE IN AN ION TRAP

Chi‐Fai Lo, David Kiang

Published Apr 10, 2000• 1 citation
Publisher

Abstract

In this paper we have investigated the time evolution of a dissipative quantum time-dependent oscillator which can be used to model particle trapping in an ion trap. Our analysis shows that the nonadiabatic changes in the oscillator mass and/or frequency as well as the dissipation constitute two competing forces on the squeezing properties of the system — the former helps generate the squeezing effect whereas the latter tries to destroy it.

DOI
10.1142/s021797920000090x

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•Jan 1, 2013•0 citations
In this paper we have investigated the time evolution of a dissipative quantum time-dependent oscillator which can be used to model particle trapping in an ion trap. Our analysis shows that the nonadiabatic changes in the oscillator mass and/or frequency as well as the dissipation constitute two competing forces on the squeezing properties of the system — the former helps generate the squeezing effect whereas the latter tries to destroy it.
With time and space transformation, we first solve the Schrödinger equation of the time-dependent harmonic oscillator (TDHO) system. The properties of the squeezing in the case of , i.e., the Paul trap and , namely a stable frequency interfered by a single-pulsing-type disturbance, are investigated by using function series expansion. Results in the former case are compared with the numerical calculations carried out before. It is found that the condition related to the most strong squeezing is the direct result of our method, not any approximation is needed. Solutions of the latter one are valuable for the study of the ion trap, where different cases are studied in detail. Finally we made a discussion for the measurement and observation of a trapped ion by using squeezing properties.
In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.
The main objective of this study is to investigate the quantum mechanical lifetime of a trapped ion in a Paul trap. The motivation for this research is that there are several applications of trapped ion devices such as mass spectrometers, atomic clocks, and quantum computers. Active research is presently ongoing in the subject of an ion trapping by electric and magnetic fields. There are many classical studies of the characteristics of trapped ions, however there have been relatively few done quantum mechanically. It might be expected that purely quantum effects could play an important role in describing the trapped ions. So, those are the main factors behind the research on this topic. Time-dependent perturbation theory was used in this study which is to find the quantum mechanical lifetime of trapped ion in a Paul trap because time-dependent perturbation theory allows describing the complex system with the help of a simple system that can be calculated easily. It is shown that the lifetime of a trapped ion depends on its transition frequency and the transition between two allowed quantum states of the ion. The transition frequency of an ion has to be very close to the applied frequency of alternating current (AC). The results show that the lifetime of a trapped ion can be adjusted as desired for experimentation.