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Quantum simulation

Toy model

To understand the physics of complicated systems, physicists choose to work with simplified models that can be easily manipulated and observed: from eighteenth-century orreries to the twentieth-century Feynman quantum simulator, the toy models may have grown in complexity, but the principle remains the same. Now, using cold trapped ions — as though in a game of marbles on a lattice board — Joseph Britton and colleagues demonstrate such a toy model for quantum magnetism (Nature 484, 489–492; 2012).

Credit: © ISTOCKPHOTO/ADELINE LIM

Spin frustration is one of the tricky problems in quantum magnetism that cannot be efficiently tackled using computer simulation. The challenge is to find the minimum-energy configurations for spins on a triangular lattice — however, the lattice geometry forbids the simultaneous minimization of the interaction energies at a given site. In analogy with marbles on a board, the problem corresponds to trying to fill the board with blue and red marbles such that no marble has two neighbours of the same colour.

An alternative to this difficult computation is to actually construct a triangular lattice of interacting spins and have them evolve into various configurations. This can be done by trapping neutral atoms in periodic optical potentials; but, although the method is elegant, inducing the required type of interactions between the atoms is not straightforward. Ion interactions, on the other hand, are stronger and easier to control.

Britton et al. trapped hundreds of beryllium ions using electric and magnetic fields. The laser-cooled ions crystallized into a two-dimensional triangular lattice structure — an ion 'marble' at each site, with its electronic ground and excited states representing the 'colour': spin up or spin down. Using a pair of off-resonance laser beams, the researchers excited the collective motion of the ions. Then, through the entanglement of the ions' motion and their electronic states, this excitation could be translated into an effective ion–ion Ising-type interaction.

Several proof-of-concept experiments on spin interactions and quantum phase transitions have already been performed by other researchers, using few ions. But Britton and colleagues' work using hundreds of ions has created a new playground in which to explore quantum magnetism, far beyond simple computable scenarios.

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Georgescu, I. Toy model. Nature Phys 8, 444 (2012). https://doi.org/10.1038/nphys2340

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