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Physical Review A

Perpendicular laser cooling of a rotating ion plasma in a Penning trap

Wayne M. Itano, Laurence R. Brewer, D. J. Larson, D. J. Wineland

Published Dec 1, 1988• 38 citations

Abstract

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 $^{9}\mathrm{Be}^{+}$ 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.

DOI: 10.1103/physreva.38.5698

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Physical Review A•Jun 1, 1999•7 citations

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

^{9}\mathrm{Be}^{+}

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.

We have determined the temperature and heating rate of laser-cooled ions in a Penning trap using Doppler laser spectroscopy. Between and ions are trapped in a Penning trap and Doppler laser cooled to temperatures of a few millikelvin, where they form ion crystals. This system is an example of a strongly coupled one-component plasma. The ion temperature was measured as a function of time after turning off the laser-cooling. In the solid phase, we measured a heating rate of . Information about possible heating mechanisms was obtained directly from temperature measurements, and also from measurements of the rate of radial expansion of the ion plasma. We determined that the observed heating is due to collisions with the residual gas of our vacuum system.

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.

Between 104 and 106 9Be+ ions are trapped in a Penning trap. The ions are laser‐cooled to ∼millikelvin temperatures, where they form ion crystals. This system is an example of a strongly coupled one‐component plasma. By means of Doppler laser spectroscopy we have measured the temperature and heating rate of the plasma. Initially the heating rate is low, 60 ± 40 mK/s, but after about 100 ms the plasma heats up rapidly to a few kelvin. The onset of the rapid heating coincides with the solid‐liquid phase transition.

Sympathetic cooling of trapped ions has been demonstrated in an experiment where

^{198}\mathrm{Hg}^{+}

ions were confined in a Penning ion trap with laser-cooled

^{9}\mathrm{Be}^{+}

ions.

^{198}\mathrm{Hg}^{+}

temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the

^{9}\mathrm{Be}^{+}

plasma were observed when the

^{198}\mathrm{Hg}^{+}

ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.

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.