Simulation of quantum magnetism in mixed-spin systems with impurity-doped ion crystals

We propose the realization of linear crystals of cold ions that contain different atomic species for investigating quantum phase transitions and frustration effects in spin systems beyond the commonly considered case of s = 1/2. Mutual spin-spin interactions between ions can be tailored via the Zeeman effect by applying oscillating magnetic fields with strong gradients. Further, collective vibrational modes in the mixed ion crystal can be used to enhance and to vary the strength of spin-spin interactions and even to switch the nature of the interacting forces from a ferro-to an antiferromagnetic character. We consider the behavior of the effective spin-spin couplings in an ion crystal of spin-1/2 ions doped with high-magnetic-moment ions with spin S = 3. We analyze the ground state phase diagram and find regions with different spin orders including ferrimagnetic states. In the most simple nontrivial example, we deal with a linear {Ca(+), Mn(+), Ca+} crystal with spins of {1/2, 3, 1/2}. To demonstrate feasibility with current state-of-the-art experiments, we discuss how quantum phases might be detected using a collective Stern-Gerlach effect of the ion crystal and high-resolution spectroscopy. Here, the state-dependent laser-induced fluorescence of the indicator spin-1/2 ion, of species (40)Ca(+), is used to reveal also the spin state of the simulator spin-3 ions, (50)Mn(+), which does not possess suitable levels for optical excitation and detection.