Quantum spin models with electrons in Penning traps

We propose a scheme to engineer an effective spin Hamiltonian starting from a system of electrons confined in micro-Penning-traps. By means of appropriate sequences of electromagnetic pulses, alternated with periods of free evolution, we control the shape and strength of the spin-spin interaction. Moreover, we can modify the effective magnetic field experienced by the particle spin. This procedure enables us to reproduce notable quantum spin systems, such as Ising and $XY$ models. Thanks to its scalability, our scheme can be applied to a fairly large number of trapped particles within the reach of near future technology.