Onset of Quantum Magnetism

“Onset of a Quantum Phase Transition with a Trapped Ion Quantum Simulator,” R. Islam, E.E. Edwards, K. Kim, S. Korenblit, C. Noh, H. J. Carmichael, G.-D. Lin, L.-M. Duan, C.-C. Joseph Wang, J.K. Freericks & C. Monroe, Nature Comm. 2, 377 (2011)

Quantum spin models are powerful because they can describe many types of physical phenomena such as phase transitions in magnets. Simulations of these models can provide insights when the actual system of interest is difficult to understand theoretically or challenging to experimentally probe. Recently, PFC-supported researchers at the JQI have used a small crystal of ion spins to experimentally simulate quantum magnetism. Quantum simulations of this type, that push the limits of current computations have applications in quantum information science.

To mimic a model that describes quantum magnetism, known as the transverse field Ising model, the researchers shine different colors of laser light onto an ion crystal. They choose specific colors to create spin-spin interactions that are analogous to that of a quantum ferromagnet. The scientists build up the simulator, one spin at a time, allowing them to explore finite-size effects, such as how the transition to ferromagnetism sharpens with each additional particle.

Each ion represents a spin and can be thought of as a bar magnet that can be oriented up or down. The spins interact such that they prefer to orient themselves along the same direction. At the beginning of the experiment, a large effective magnetic field overpowers the spin system’s tendency to order. Thus, the spins are in a disordered state (eachspin depicted as blue arrows pointed randomly along up or down). A crossover to ferromagnetism (FM)occurs when this magnetic field is weakened comparedto the spin-spin interaction, and all spins are oriented in the same direction. In the quantum regime, the ferromagnet can be preparedsuperposition of all spins simultaneouslyin the up and down state (shown in red).

As ion spins are added to the system, the magnetization, is measured. This parameter quantifies the number of spins pointed up or down and equals one for a ferromagnet. The scientists observe a sharpening in the transition as the size of the system is increased.

Increase in ‘steepness’

spin-spin FM interaction strength