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arXiv:1602.05144 · Physical Review A

Perpendicular laser cooling with a rotating-wall potential in a Penning trap

Steven B. Torrisi, J. Britton, Justin Bohnet, J. J. Bollinger

Published Apr 26, 2016• 17 citations
arXivHTMLPDF

Abstract

We investigate the impact of a rotating-wall potential on perpendicular laser cooling in a Penning ion trap. By including energy exchange with the rotating wall, we extend previous Doppler laser-cooling theory and show that low perpendicular temperatures are more readily achieved with a rotating wall than without. Detailed numerical studies determine optimal operating parameters for producing low-temperature, stable two-dimensional crystals, important for quantum information processing experiments employing Penning traps.

DOI
10.1103/physreva.93.043421

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We investigate the impact of a rotating-wall potential on perpendicular laser cooling in a Penning ion trap. By including energy exchange with the rotating wall, we extend previous Doppler laser-cooling theory and show that low perpendicular temperatures are more readily achieved with a rotating wall than without. Detailed numerical studies determine optimal operating parameters for producing low-temperature, stable two-dimensional crystals, important for quantum information processing experiments employing Penning traps.
A direct numerical simulation of many interacting ions in a Penning trap with a rotating wall is presented. The ion dynamics is modeled classically. Both axial and planar Doppler laser cooling processes are modeled using stochastic momentum impulses based on two-level atomic scattering rates. The plasmas being modeled are ultracold two-dimensional crystals made up of hundreds of ions. We compare Doppler cooled results directly to a previous linear eigenmodes analysis. Agreement in both frequency and mode structure is obtained. Additionally, when Doppler laser cooling is applied, the laser cooled steady state plasma axial temperature agrees with the Doppler cooling limit. Numerical simulations using the approach described and benchmarked here will provide insights into the dynamics of large trapped-ion crystals, improving their performance as a platform for quantum simulation and sensing.
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Two-dimensional planar ion crystals in a Penning trap are a platform for quantum information science experiments. However, the low-frequency planar modes of these crystals are not efficiently cooled by laser cooling, which can limit the utility of the drumhead modes for quantum information processing. Recently, it has been shown that nonlinear mode coupling can enhance the cooling of the low-frequency planar modes. Here, we demonstrate in numerical simulations that this coupling can be dynamically tuned by adiabatically changing the rotation frequency of the ion crystal during experiments. Furthermore, we show that this technique can, in addition, produce lower temperatures for the low-frequency planar modes via an adiabatic cooling process. This result allows cooling of the planar modes to sub-millikelvin temperatures, resulting in improved spectral resolution of the drumhead modes at experimentally relevant rotation frequencies, which is crucial for quantum information processing applications.
The steady-state temperature of an ion plasma in a Penning trap, cooled by a laser beam perpendicular to the trap axis, has been calculated and measured. The rotation of the plasma, due to crossed E and B fields, strongly affects the minimum attainable temperature. This is because the velocity distribution of the ions, as seen by a laser beam intersecting the plasma at some distance from the axis of rotation, is skewed, and this leads to a change in the velocity distribution (and hence temperature) at which a steady state is attained. The calculated temperature is a function of the intensity, frequency, and position of the laser beam, and of the rotation frequency of the plasma. Temperatures of 9Be+^{9}\mathrm{Be}^{+}9Be+ plasmas were measured for a wide range of experimental parameters. The lowest and highest temperatures were approximately 40 mK and 2 K. The measured and calculated temperatures are in agreement.
Efficient Three-Dimensional Sub-Doppler Cooling of 40^{40}40Ca+^++ in a Penning Trap
We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a 40^{40}40Ca+^++ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8) μμμs, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 μμμs as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $ω_z = 2π~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.