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Modern Physics Letters B

PAUL TRAP AND THE PROBLEM OF QUANTUM STABILITY

A. Ugulava, L. Chotorlishvili, G. MCHEDLISHVILI, K. Nickoladze

Published Aug 10, 2008• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984908016637

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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.
Paul traps are ion traps that are widely used in spectroscopic experiments to confine and stabilize a charged particle within a small region using oscillating electric fields. The dynamics of the particle inside a Paul trap is described by Mathieu equations. It has been proposed that such traps can be used to detect the effects produced by spontaneous collapse of the associated wavefunction, as described by the model of CSL (Continuous Spontaneous Localization). This model is a non-linear, stochastic and non-relativistic modification to the Schrödinger equation which predicts an additional random motion of particles other than environmental effects. In this paper, we discuss the possibility that such a random motion can throw a particle out of its stable configuration within the Paul trap. We study the changes in the stability diagram of a Paul trap in the presence of CSL. We also constrain the CSL parameter space by assuming the fact that the stability diagram is not significantly altered. The bounds thus obtained are weaker than those coming from X-ray emission from Ge slab.
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.
Using numerical simulations of the time-dependent Schrödinger equation, we study the full quantum dynamics of the motion of an atomic ion in a linear Paul trap. Such a trap is based on a time-varying, periodic electric field and hence corresponds to a time-dependent potential for the ion, which we model exactly. We compare the center-of-mass motion with that obtained from classical equations of motion, as well as to results based on a time-independent effective potential. We also study the oscillations of the width of the ion’s wave packet, including close to the border between stable (bounded) and unstable (unbounded) trajectories. Our results confirm that the center-of-mass motion always follows the classical trajectory, that the width of the wave packet is bounded for trapping within the stability region, and therefore that the classical trapping criterion is fully applicable to quantum motion.
We present recent experimental and theoretical results on the behavior of two-, three-, and four-ion crystals close to the Mathieu instability. In particular, we show that the crystals are stable until the Mathieu instability is reached, i.e., for the parameter space investigated, there is no ``melting'' of the crystals. Laser and rf heating are studied in detail. A simple model of chaotic rf heating as well as a classification of the ion dynamics into four characteristic regimes are presented.