Abstract
The mechanism responsible for transitions of laser-cooled trapped ions from an ordered “crystal” state to an irregular “cloud” state has been discussed controversially. A numeric and analytic study of the relative motion of two trapped ions without laser cooling is performed and compared with the results of previous simulations involving the laser. It turns out that the system without laser, in spite of its simplicity, already exhibits a non-monotonic dependence of crystal stability on trap parameters, which is linked to the presence of low-order nonlinear resonances.
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Coefficients in (15) vanish for odd values ofk 2. This is due to symmetry with respect to thex−y-plane of the crystal under consideration, which implies that there are no odd powers of ε2 inH 2. Therefore, the (k 0,k 1,k 2) = (−1,1,3) resonance should be called more appropriately a (−2,2,6) resonance here
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Vogt, A.W. Nonlinear resonances and phase transitions of two-ion Coulomb clusters in a Paul trap: Calculations without laser cooling. Appl. Phys. B 58, 57–62 (1994). https://doi.org/10.1007/BF01081714
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DOI: https://doi.org/10.1007/BF01081714