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arXiv:quant-ph/0211016

Improvement of Laser Cooling of Ions in a Penning Trap by use of the Axialisation Technique

Powell, H. F., S.R. de Echaniz, E. S. Phillips, D. M. Segal, Richard Claude Thompson

Published Nov 5, 2002• 1 citation
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Abstract

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 $μ$m. 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.

DOI
10.48550/arxiv.quant-ph/0211016

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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 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 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.
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 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.
The limitations to the achievement of low kinetic energies for laser cooling of single ions confined in electromagnetic traps are discussed. Sideband cooling of an ion in an rf (Paul) trap is reexamined including the effects of finite laser bandwidth and the energy of the rf micromotion. The micromotion is the oscillatory motion of the ion at the same frequency as the rf voltage applied to the trap electrodes. Sideband cooling of ions in a Penning trap is examined for the first time. In both cases, cooling to the zero-point energy of the ion in the trap should be possible and a method for verifying this condition is suggested. The implications for high-resolution, high-accuracy spectroscopy are investigated. Under certain conditions, the uncertainty in the second-order Doppler shift may be significantly less than 1 part in 1018{10}^{18}1018. .AE
We present a model for laser cooling of a single ion in the Penning trap. The model solves the equations of motion in the presence of the damping caused by the interaction with the laser beam, and predicts for the first time the dependence of the cooling rates for the two radial degrees of freedom in the trap as a function of the laser detuning, laser beam offset and saturation parameter. The conditions derived for both radial degrees of freedom to be cooled simultaneously agree with those found in earlier studies. The results indicate that under conditions where both motions are cooled simultaneously, the cooling rates are both significantly smaller than the maximum rate for either motion considered in isolation. Furthermore, the magnetron cooling rate is typically much lower than the cyclotron cooling rate, as has been found in experiments. The model indicates how the cooling rate for a single ion may be optimized.