Abstract
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 . 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 . 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 40Ca+, is used to reveal also the spin state of the simulator spin-3 ions, 50Mn+, which does not possess suitable levels for optical excitation and detection.
Highlights
Current ion trapping technology has led to rapid progress toward the realization of elementary quantum processors [1, 2]
We propose an efficient method for the creation of effective spin-spin interactions in ion crystals of spin
The paper is organized as follows: In sec. 2 we describe the theoretical background for the implementation of the effective spin-spin interactions in a (S, s) mixed spin system by using an oscillating magnetic field gradient
Summary
Current ion trapping technology has led to rapid progress toward the realization of elementary quantum processors [1, 2]. The internal states of laser-cooled and trapped ions represent effective spins, which can be made to interact with each other for performing magnetic quantum phase simulations These interactions may be realized by applying magnetic field gradients [5,6,7,8,9,10] or by laser light fields [11–. The ability to trap ions with large spins at a fixed position [31] and to tune the range and strength of the interactions makes the impurity doped ion crystal an analogue quantum simulator for quantum magnetism and frustration effects in a mixed spin system [32, 33]. In sec. 5 we give a summary of the results and discuss further and even more complex possibilities of quantum simulation with mixed ion crystals
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