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arXiv:1507.03438 · Physical Review A

Influence of ion movement in a particle trap on the bound electron g factor

Niklas Michel, Jacek Zatorski, Christoph H. Keitel

Published Nov 6, 2015• 1 citation
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Abstract

In the relativistic description of atomic systems in external fields, the total momentum and the external electric field couple to the angular momentum of the individual particles. Therefore, the motional state of an ion in a particle trap influences measurements of internal observables such as energy levels or the $g$ factor. We calculate the resulting relativistic shift of the Larmor frequency and the corresponding $g$-factor correction for a bound electron in a hydrogenlike ion in the $1 S$ state due to the ion moving in a Penning trap and show that it is negligible at the current precision of measurements. We also show that the analogous energy shift for measurements with an ion in the ground state of a Paul trap vanishes in leading order.

DOI
10.1103/physreva.92.052509

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In the relativistic description of atomic systems in external fields, the total momentum and the external electric field couple to the angular momentum of the individual particles. Therefore, the motional state of an ion in a particle trap influences measurements of internal observables such as energy levels or the ggg factor. We calculate the resulting relativistic shift of the Larmor frequency and the corresponding ggg-factor correction for a bound electron in a hydrogenlike ion in the 1S1 S1S state due to the ion moving in a Penning trap and show that it is negligible at the current precision of measurements. We also show that the analogous energy shift for measurements with an ion in the ground state of a Paul trap vanishes in leading order.
We report on the first observation of the continuous Stern-Gerlach effect on an electron bound in an atomic ion. The measurement was performed on a single hydrogenlike ion ( 12C5+) in a Penning trap. The measured g factor of the bound electron, g = 2.001 042(2), is in excellent agreement with the theoretical value, confirming the relativistic correction at a level of 0.1%. This proves the possibility of g-factor determinations on atomic ions to high precision by using the continuous Stern-Gerlach effect. The result demonstrates the feasibility of conducting experiments on single heavy highly charged ions to test quantum electrodynamics in the strong electric field of the nucleus.
We calculate the energy levels of He+ ion placed in a uniform magnetic field directed perpendicular to the direction of its center of mass (CM) velocity vector, correct to relative order . Our calculations are within the frame work of an approximately relativistic theory, correct to relative order , of a two-particle composite system bound by electromagnetic forces, and written in terms of the position, momentum and spin operators of the constituent particles as proposed by Krajcik and Foldy, and also by Close and Osborn. Since the He+ ion has a net electric charge, the total or the CM momentum is not conserved and a neat separation of the CM and the internal motion is not possible. What is new in our approach is that, for the basis states in a first order degenerate perturbation theory to calculate the effects of the external magnetic field, we use the direct product of the coherent state of the Landau Hamiltonian of the He+ ion in a uniform magnetic field and of the simultaneous eigenstate of the internal Hamiltonian h, j2, l2, s2 and jz, where j, l and s are the internal total, orbital and spin angular moments of the He+ ion. The coherent state is an excellent approximation to the expected classical circular motion of the center of mass (CM) of the He+ ion. In addition to the Z2 a2 corrections to the usual nonrelativistic results, including the small corrections due to the nuclear motion, we also obtain corrections which depend on the kinetic energy (ECM ) of the CM circular motion of the He+ ion, in a nontrivial way. Even though these corrections are proportional to , where M is the mass of the He+ ion, and are small for nonrelativistic CM motion, the results should be verifiable in careful experiments. Our results may also have application in astrophysical observations of the spectral lines of He+ ions in magnetized astrophysical objects.
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We report on the measurement of the g-factor of the electron bound in an atomic ion. A single hydrogenic ion (12C5+) is stored in a Penning trap. The electronic spin state of the ion is monitored via the continuous Stern-Gerlach effect in a quantum non-demolition measurement. Quantum jumps between the two spin states (spin up and spin down) are induced by a microwave field at the spin precession frequency of the bound electron. The g-factor of the bound electron is obtained by varying the microwave frequency and counting the number of spin flips for a fixed time interval. Applications of the continuous Stern-Gerlach effect include high-accuracy tests of bound-state quantum electrodynamics (QED), the measurement of the atomic mass of the electron, the determination of the fine structure constant α, and the measurement of nuclear g-factors.
We have developed and applied a novel method for the precise determination of small frequency differences of particle motions inside a Penning trap. In the present case, the frequency differences on the order of 100 mHz at motional frequencies on the order of 1 MHz are used to determine the spin state of an electron bound in a hydrogen-like ion. This novel technique measures the integrated phase difference of the particles' motions relative to an excitation with a well-defined phase. Thereby, the Fourier-limit for frequency measurements based on Fourier-analyses of detection signals can be overcome.