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Journal of Physics B Atomic Molecular and Optical Physics

Cooling and heating of crystalline ion beams

Ulrich Schramm, T Sch tz, Michael Bußmann, D. Habs

Published Jan 23, 2003• 23 citations
Publisher

Abstract

The crystallization of ion beams has recently been established in the rf quadrupole storage ring PALLAS (PAul Laser CooLing Acceleration System) for laser-cooled 24 Mg + ion beams at an energy of about 1 eV. Yet, unexpectedly sharp constraints had to be met concerning the confinement strength and the longitudinal laser cooling rate. In this paper, related and up to now unseen heating mechanisms are pinpointed for crystalline beams. The weak but inevitable diffusive transverse heating associated with the laser cooling process itself is investigated, possibly allowing the future measurement of the latent heat of the ion crystal. As a function of the beam velocity, the influence of bending shear on the attainability of larger crystalline structures is presented. Finally, rf heating of crystalline beams of different structure is studied for discontinuous cooling.

DOI
10.1088/0953-4075/36/3/314

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The crystallization of ion beams has recently been established in the rf quadrupole storage ring PALLAS (PAul Laser CooLing Acceleration System) for laser-cooled 24 Mg + ion beams at an energy of about 1 eV. Yet, unexpectedly sharp constraints had to be met concerning the confinement strength and the longitudinal laser cooling rate. In this paper, related and up to now unseen heating mechanisms are pinpointed for crystalline beams. The weak but inevitable diffusive transverse heating associated with the laser cooling process itself is investigated, possibly allowing the future measurement of the latent heat of the ion crystal. As a function of the beam velocity, the influence of bending shear on the attainability of larger crystalline structures is presented. Finally, rf heating of crystalline beams of different structure is studied for discontinuous cooling.
Several groups have recently used laser cooling to produce ordered arrays of ions, ion crystals, in rf quadrupole ion traps (Paul traps). Laser cooling has been understood using previous theories which ignore ion micromotion and replace the oscillating rf trap potential with a static pseudopotential. We show that in recent experiments, ion micromotion can exceed one wavelength of the cooling radiation and that the resulting Doppler shifts can transform laser cooling into laser heating. Changes in trap voltage, ion position, and laser intensity can all reverse the sign of laser cooling. This, together with ideas of deterministic chaos, can lead to a reinterpretation of experiments on ion crystals. The recognition that effects previously attributed to an experimental artifact, rf heating, may actually be due to a failure of laser cooling opens the door, on the one hand, to precise theories of phase transitions and, on the other, to improved cooling techniques that can permit the creation of larger ion crystals.
A longitudinal laser cooling of ion beams at about 5% of the velocity of light has been performed at the Heidelberg Test Storage Ring with various cooling schemes employing the spontaneous force. For a 7.29-MeV 9Be+^{9}\mathrm{Be}^{+}9Be+ beam with an initial longitudinal temperature of 2700 K, the main characteristics of laser cooling in a storage ring are discussed. When undamped, the transverse betatron oscillations of the coasting ions limit the longitudinal temperature after laser cooling to typically 1 K. After damping the transverse motion by precooling the ions with an electron cooler, longitudinal temperatures of below 30 mK have been obtained in the subsequent laser cooling. In this case, the longitudinal ion-beam temperature can be understood as an equilibrium of the laser cooling rate with the heating rate due to intrabeam scattering. Moreover, single binary Coulomb collisions between the (still transversely hot) ions can cause such longitudinal velocity changes that ions are lost out of the critical capture range of the laser cooling force. In these two ways, intrabeam scattering imposes a substantial limit on the temperature or number of laser cooled ions in a storage ring. In our experiments, this process presently limits the ratio between the density-dependent Coulomb energy and the longitudinal thermal energy spread to a value on the order of 1, where liquid rather than gaseous behavior of the ion beam is expected to set in.
An investigation of the sympathetic cooling \nmethod for the studies of large ultra-cold molecular ions in a quadrupole ion trap has been conducted.Molecular dynamics simulations are performed to study the rf heating mechanisms in the ion trap. The dependence of \nrf heating rates on the ion temperature, trapping parameters, \nand the number of ions is obtained. New rf heating mechanism \naffecting ultra-cold ion clouds exposed to laser radiation is described.The saturation spectroscopy setup of the hyperfine spectra \nof the molecular iodine has been built to provide an accurate frequency reference for the laser wavelength. This reference is used to obtain the fluorescence lineshapes of \nthe laser cooled Mg+^++ ions under different trapping conditions.The ion temperatures are deduced from the measurements, and \nthe influence of the rf heating rates on the fluorescence lineshapes \nis also discussed. Cooling of the heavy (m=720m=720m=720a.u.) fullerene ions to under 10K by the means of the sympathetic cooling by the Mg+^++ ions(m=24m=24m=24a.u.) is demonstrated. The single-photon imaging system has been developed and used to obtain the images of the Mg+^++ ion crystal structures at mK temperatures.
S-LSR is a compact ion storage ring constructed at Kyoto University several years ago. The ring is equipped with a Doppler laser cooling system aimed at beam crystallization. Bearing in mind hardware limitations in S-LSR, we try to find an optimum set of primary experimental parameters for the production of an ultracold heavy ion beam. Systematic molecular dynamics simulations are carried out for this purpose. It is concluded that the detuning and spot size of the cooling laser should be chosen around |−-−|42 MHz and 1.5 mm, respectively, for the most efficient cooling of 40 keV |24^{24}24|Mg|+^++| beams in S-LSR. Under the optimum conditions, the use of the resonant coupling method followed by radio-frequency field ramping enables us to reach an extremely low beam temperature on the order of 0.1 K in the transverse degrees of freedom. The longitudinal degree of freedom can be cooled to close to the Doppler limit; i.e., to the mK range. We also numerically demonstrate that it is possible to establish a stable, long one-dimensionally ordered state of ions.
We observed phase transitions and ordered structures of laser-cooled Mg+{\mathrm{Mg}}^{+}Mg+ ions stored in a radio-frequency quadrupole storage ring with a diameter of 115 mm. The ions are confined two dimensionally by a quadrupole field and can move freely along the ring circumference. By cooling the ions with tangentially intersecting laser beams, we observed a linear string of ions aligned along the center line of the quadrupole field. For higher ion densities the linear structure changes into a helical structure. The dynamics of the stored ions was studied.
A new type of ultra-cold ion source is under development which employs transverse laser cooling and compression of a thermal atomic rubidium beam followed by photo-ionization. The resulting ultra-cold plasma is focused to a nanometer-sized spot using an existing Focused Ion Beam column and this spot can be used for the fabrication of nano-structures. Simulations of a 10 cm long laser-cooling stage and of disorder-induced heating of the resulting ion beam, predict an achievable brightness for87Rb+ of order 107 A/m2 sr eV at an longitudinal energy spread of less than 1 eV and a current of tens of pA, which is substantially better than conventional ion sources. Experimental realization of the compact ion source has recently started with the development of an efficient high-flux atom source and a 2D laser cooler. Progress on these items will be reported.