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Physical Review A

Addendum to “Quantum theory of the stability region of an ion in a Paul trap”

L.-L. Yan, Mang Feng, K. Wang

Published Mar 10, 2014• 3 citations
Publisher

Abstract

The authors call attention to a previous work [Kelin Wang, Mang Feng, and Juhao Wu, Phys. Rev. A 52, 1419 (1995)] for quantum-mechanically studying the stability region of the Paul trap, where the calculation does not work for the case of zero dc voltage. But the ions can be confined experimentally at zero dc voltage which is understandable via the Mathieu equation. We present a quantum-mechanical study for such a case as a supplement.

DOI
10.1103/physreva.89.035401

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The authors call attention to a previous work [Kelin Wang, Mang Feng, and Juhao Wu, Phys. Rev. A 52, 1419 (1995)] for quantum-mechanically studying the stability region of the Paul trap, where the calculation does not work for the case of zero dc voltage. But the ions can be confined experimentally at zero dc voltage which is understandable via the Mathieu equation. We present a quantum-mechanical study for such a case as a supplement.
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.
Abstract As a result of the current increase in interest in quantum computing and the unrelenting attempt to develop and establish a quantum computer, Many researchers in this field have turned to designing appropriate algorithms or investigating the possibilities of controlling and manipulating the quantum state. One of the most promising techniques involves using single ionized atoms kept in Paul traps. Each ion's internal state represents the lowest quantum informational unit (a qubit). That research used the trapped ions 40Ca + to illustrate a quantum qubit. According to the Paul linear trap, one of the essential traps for confining ions in one dimension, they may be easily handled and controlled in the quantum state. We used MATLAB programs to simulate the factors affecting the confined state and their impact on it after resolving Mathieu's equation and determining the vibrational state of the ion. That consists of superposition cases between the secular monition and the Micromotion. The a and q values in Mathieu's equation are necessary for three-dimensional confinement for the solutions to be simultaneously stable in both directions. The parameter a depends on the Dc voltage, the ion's mass, the Radio frequencies, and the distance between the trap center and the electrodes. The control by a variable voltage provided it. In addition, it illustrates its effect in a specific chain of trapped ions. This study opens the door to understanding the ideal condition through which it ensures the best state of confinement and selecting what is necessary to reach the resonance state for ions transport from the state (4S1/2) to the state (4P1/2). After that, the manipulation of the quantum state begins.
This work is devoted to the investigation of the possibility of controlling of ion motion inside the Paul trap. It has been shown that by proper selection of the parameters controlling the electric fields, stable localization of ions inside the Paul trap is possible. Quantum consideration of this problem is reduced to the investigation of the Mathieu–Schrodinger equation. It has been shown that quantum consideration is appreciably different from the classical one that leads to stronger limitations of the values of the parameters of stable motion. Connection between the problem under study and the possibility of experimental observation of quantum chaos has been shown.
This work is devoted to the investigation of possibility of controlling of ions motion inside Paul trap. It has been shown that by proper selection of the parameters of controlling electric fields, stable localization of ions inside Paul trap is possible. Quantum consideration of this problem is reduced to the investigation of the Mathieu-Schrodinger equation. It has been shown that quantum consideration is appreciably different from classical one that leads to stronger limitations of the values of the parameters of stable motion. Connection between the problem under study and the possibility of experimental observation of quantum chaos has been shown.