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arXiv:0710.4401 · Physical Review A

Dynamics of axialized laser-cooled ions in a Penning trap

E. S. Phillips, Richard Hendricks, A M Abdulla, Hamid Ohadi, D. R. Crick, Kyo-Woog Koo, D. M. Segal, Richard Claude Thompson

Published Sep 3, 2008• 16 citations
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Abstract

We report the experimental characterization of axialization---a method of reducing the magnetron motion of a small number of ions stored in a Penning trap. This is an important step in the investigation of the suitability of Penning traps for quantum-information processing. The magnetron motion was coupled to the laser-cooled modified cyclotron motion by the application of a near-resonant oscillating quadrupole potential (the ``axialization drive''). Measurement of cooling rates of the radial motions of the ions showed an order-of-magnitude increase in the damping rate of the magnetron motion with the axialization drive applied. The experimental results are in good qualitative agreement with a recent theoretical study. In particular, a classical avoided crossing was observed in the motional frequencies as the axialization drive frequency was swept through the optimum value, proving that axialization is indeed a resonant effect.

DOI
10.1103/physreva.78.032307

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We report the experimental characterization of axialization---a method of reducing the magnetron motion of a small number of ions stored in a Penning trap. This is an important step in the investigation of the suitability of Penning traps for quantum-information processing. The magnetron motion was coupled to the laser-cooled modified cyclotron motion by the application of a near-resonant oscillating quadrupole potential (the ``axialization drive''). Measurement of cooling rates of the radial motions of the ions showed an order-of-magnitude increase in the damping rate of the magnetron motion with the axialization drive applied. The experimental results are in good qualitative agreement with a recent theoretical study. In particular, a classical avoided crossing was observed in the motional frequencies as the axialization drive frequency was swept through the optimum value, proving that axialization is indeed a resonant effect.
We report the first demonstration of the axialization of laser cooled ions in a Penning trap. Axialization involves the application of a small radial quadrupole drive which couples the cyclotron and magnetron motions. This enhances the laser cooling, allowing tighter confinement of the ions to the central axis of the trap than is otherwise possible. Using an intensified charge-coupled device (ICCD) camera we have imaged the axialization process for the first time. For a single ion, we recorded a large decrease of the magnetron amplitude corresponding to a reduction in ion temperature of approximately 2 orders of magnitude to an upper limit of order 10 mK. We have discovered dynamics specific to the laser cooled system which depend critically on the axial drive frequency and amplitude.
Ions stored in Penning traps may have useful applications in the field of quantum information processing. There are, however, difficulties associated with the laser cooling of one of the radial motions of ions in these traps, namely the magnetron motion. The application of a small radio-frequency quadrupolar electric potential resonant with the sum of the two radial motional frequencies has been shown to couple these motions and to lead to more efficient laser cooling. We present an analytical model that enables us to determine laser cooling rates in the presence of such an ‘axializing’ field. It is found that this field leads to an averaging of the laser cooling rates for the two motions and hence improves the overall laser cooling efficiency. The model also predicts shifts in the motional frequencies due to the axializing field that are in qualitative agreement with those measured in recent experiments. It is possible to determine laser cooling rates experimentally by studying the phase response of the cooled ions to a near resonant excitation field. Using the model developed in this paper, we study the expected phase response when an axializing field is present.
We report a study of the axialization and laser cooling of single ions and small clouds of ions in a Penning trap. A weak radiofrequency (rf) signal applied to a segmented ring electrode couples the magnetron motion to the cyclotron motion, which results in improved laser cooling of the magnetron motion. This allows us to approach the trapping conditions of a Paul trap, but without any micromotion. Using an ICCD camera we show that the motion of a single ion can be confined to dimensions of the order of 20 µm or less. We have measured increased magnetron cooling rates for clouds of a few ions, using an rf-photon correlation technique. For certain laser cooling conditions, the magnetron motion of the centre of mass of the cloud grows and stabilizes at a large value. This results in the ions orbiting the centre of the trap together in a small cloud, as confirmed by photon–photon correlation measurements.
We use the results of a Lagrangian formulation of the dynamics of ions in a Penning trap to calculate the motional frequencies of the ions as a function of the trapping parameters. We then add realistic perturbations to the ideal trapping fields in the formalism and deduce the effects of these perturbations on the ion motion. For an ideal trap there exist values of the applied trapping fields that result in a degeneracy in the ion oscillation frequencies associated with different types of motion. We show that this motional frequency degeneracy is lifted by the inclusion of the effect of a tilt of the trap axis with respect to the axis of the applied magnetic field, leading to an ``avoided crossing'' between the oscillation frequencies. We calculate typical ion orbits for trap parameters that give oscillation frequencies near the avoided crossing between the axial and modified cyclotron frequencies. We generalize the analysis to include the motion of ions in a combined (Penning-Paul) trap and perform an experiment to test the predictions of the theory for a degeneracy between the modified cyclotron frequency and the axial frequency for Mg+{\mathrm{Mg}}^{+}Mg+ ions held in a tilted combined trap. The oscillation frequencies are measured for a range of tilt angles using a photon-photon correlation technique. There is good agreement between the experimental results and the theoretical predictions. The method we describe may prove to be a useful means by which trap imperfections can be identified and subsequently removed.
We report a study of the axialisation and laser cooling of single ions and small clouds of ions in a Penning trap. A weak radiofrequency signal applied to a segmented ring electrode couples the magnetron motion to the cyclotron motion, which results in improved laser cooling of the magnetron motion. This allows us to approach the trapping conditions of a Paul trap, but without any micromotion. Using an ICCD camera we show that the motion of a single ion can be confined to dimensions of the order of 10 μμμm. We have measured increased magnetron cooling rates using an rf-photon correlation technique. For certain laser cooling conditions, the magnetron motion of the centre of mass of the cloud grows and stabilises at a large value. This results in the ions orbiting the centre of the trap together in a small cloud, as confirmed by photon-photon correlation measurements.
We present a phase-space picture of laser cooling of the radial motion of ions in a Penning trap. This picture enables a particularly simple derivation of the condition for simultaneous cooling of all degrees of freedom of a single ion to be obtained. It also allows a physically intuitive approach to be taken to the cooling process. Using this approach, we discuss different aspects of the cooling of a single ion in a Penning trap, including the formation of ``trapped'' states where the steady-state motion amplitude is nonzero for either the magnetron or modified cyclotron motion. We use an analytical approach where the approximation of small-amplitude motions can be made, and we use numerical calculations for larger-amplitude motions. The best procedure to use for effective laser cooling is derived. A similar approach is then used to treat the laser cooling of two ions in the Penning trap. We show that the use of the phase-space approach allows new insights into many aspects of the laser-cooling process to be gained, and we indicate how these insights may be applied in experimental investigations.