3 research outputs found
Modes of Oscillation in Radiofrequency Paul Traps
We examine the time-dependent dynamics of ion crystals in radiofrequency
traps. The problem of stable trapping of general three-dimensional crystals is
considered and the validity of the pseudopotential approximation is discussed.
We derive analytically the micromotion amplitude of the ions, rigorously
proving well-known experimental observations. We use a method of infinite
determinants to find the modes which diagonalize the linearized time-dependent
dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov')
transformation to coordinates of decoupled linear oscillators. We demonstrate
the utility of the method by analyzing the modes of a small `peculiar' crystal
in a linear Paul trap. The calculations can be readily generalized to
multispecies ion crystals in general multipole traps, and time-dependent
quantum wavefunctions of ion oscillations in such traps can be obtained.Comment: 24 pages, 3 figures, v2 adds citations and small correction
Quantum Magnetism of Spin-Ladder Compounds with Trapped-Ion Crystals
The quest for experimental platforms that allow for the exploration, and even
control, of the interplay of low dimensionality and frustration is a
fundamental challenge in several fields of quantum many-body physics, such as
quantum magnetism. Here, we propose the use of cold crystals of trapped ions to
study a variety of frustrated quantum spin ladders. By optimizing the trap
geometry, we show how to tailor the low dimensionality of the models by
changing the number of legs of the ladders. Combined with a method for
selectively hiding of ions provided by laser addressing, it becomes possible to
synthesize stripes of both triangular and Kagome lattices. Besides, the degree
of frustration of the phonon-mediated spin interactions can be controlled by
shaping the trap frequencies. We support our theoretical considerations by
initial experiments with planar ion crystals, where a high and tunable
anisotropy of the radial trap frequencies is demonstrated. We take into account
an extensive list of possible error sources under typical experimental
conditions, and describe explicit regimes that guarantee the validity of our
scheme