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Zeitschrift für Physik D Atoms Molecules and Clusters

Quantum mechanics of a single ion in a paul trap: motion influenced by a time dependent linear force

Albrecht Lindner

Published Mar 1, 1995• 1 citation
Publisher
DOI
10.1007/bf01437091

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The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle which cannot be further shortened. A promising strategy is the utilization of multiple trapped ions. The ions of the same kind then repulse each other with the Coulomb force, which is countered by the ponderomotive force of the time depended field in the trap. A few ions form a chain along the axis of a linear Paul trap. Adding more ions (a few tens or hundreds) gives rise to Coulomb crystals. We created an efficient simulation code which calculates the motion of such collections of ions in quasi-static radiofrequency fields of real linear quadrupole traps (including the micromotion). We include a model for laser cooling of the ions. The simulation tool can be used to study the formation and the dynamics of Coulomb crystals under conditions corresponding to various experimental setups.

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Summary form only given. The recent experimental generation of nonclassical states of the motion of an ion in a Paul trap has propelled the field of quantum state preparation into a new era. But how to prove that the ion is indeed in a Fock, a squeezed, or a Schrodinger cat state? How can we measure a motional state which, due to the explicit time dependence of the binding force of the Paul trap, displays a complicated time dependence? In this paper we present the first method that measures a vibratory state of an ion taking into account the complete time dependence of the Paul trap. Moreover our technique operates outside the Lamb-Dicke regime and is not limited to pure states only.

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The anharmonicity of the trap potential influences the motion of trapped and laser-cooled ions. The magnitudes of higher-order components of the trap potential depend on the electrode geometry. In this paper we provide a numerical study of the anharmonicity of linear Paul trap potentials with different electorode geometies. We have also experimentally observed nonlinear resonances of laser-cooled ions, and have studied the effect of anharmonicity in three types of liner Paul trap that have different distances between electrodes.

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The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle which cannot be further shortened. A promising strategy is the utilization of multiple trapped ions. The ions of the same kind then repulse each other with the Coulomb force, which is countered by the ponderomotive force of the time depended field in the trap. A few ions form a chain along the axis of a linear Paul trap. Adding more ions (a few tens or hundreds) gives rise to Coulomb crystals. We created an efficient simulation code which calculates the motion of such collections of ions in quasi-static radiofrequency fields of real linear quadrupole traps (including the micromotion). We include a model for laser cooling of the ions. The simulation tool can be used to study the formation and the dynamics of Coulomb crystals under conditions corresponding to various experimental setups.
Summary form only given. The recent experimental generation of nonclassical states of the motion of an ion in a Paul trap has propelled the field of quantum state preparation into a new era. But how to prove that the ion is indeed in a Fock, a squeezed, or a Schrodinger cat state? How can we measure a motional state which, due to the explicit time dependence of the binding force of the Paul trap, displays a complicated time dependence? In this paper we present the first method that measures a vibratory state of an ion taking into account the complete time dependence of the Paul trap. Moreover our technique operates outside the Lamb-Dicke regime and is not limited to pure states only.
The anharmonicity of the trap potential influences the motion of trapped and laser-cooled ions. The magnitudes of higher-order components of the trap potential depend on the electrode geometry. In this paper we provide a numerical study of the anharmonicity of linear Paul trap potentials with different electorode geometies. We have also experimentally observed nonlinear resonances of laser-cooled ions, and have studied the effect of anharmonicity in three types of liner Paul trap that have different distances between electrodes.