Understanding Quantum Magnetism, Atom by Atom

The onset of a quantum phase transition

Newswise — Joint Quantum Institute (JQI) researchers led by Christopher Monroe, with theoreticians from University of Michigan, University of Auckland, and Georgetown University have observed a quantum ferromagnet using a nine ion crystal, in an atom-by-atom approach to quantum simulations of magnetism. These new results appear in the July 5, 2011 issue of Nature Communications in a paper entitled “Onset of a quantum phase transition with a trapped ion quantum simulator*.” This benchmark experiment paves the way for reliable simulations of model systems where conventional calculations become inefficient or even impossible.

Originating in large part with Richard Feynman’s 1982 proposal, quantum simulation has evolved into a field where scientists use a controllable quantum system to study a second, less experimentally feasible quantum phenomenon. In short, a full-scale quantum computer does not yet exist and classical computers often cannot solve quantum problems, thus a “quantum simulator” presents an attractive alternative for gaining insight into complex material properties, for example.

Can a quantum simulator provide solutions to physics or computation problems that cannot be tackled using conventional computers? In this work researchers have built an apparatus that lays the groundwork necessary to undertake this challenging question. Ion-trapping experiments are at the forefront of quantum information technology and it is the same robust nature and control of otherwise fragile quantum states that makes this platform ideal for simulations.

They present results using a crystal made with anywhere from two to nine ions to simulate a quantum phase transition to an ordered ferromagnet, as described by the transverse field Ising model (see Figure for description). Phase transitions can be thought of in terms of orderliness. For example, at zero degrees Celsius, liquid water freezes, and the tiny water molecules organize into an orderly crystal to form ice. Phase transitions can still occur at absolute zero or -273 Celsius, but are not governed by thermal properties. Here, quantum effects dominate and the state of orderliness can change abruptly when varying parameters, such as a magnetic field.

Why did the researchers choose the transverse field Ising model? According to lead author and graduate student Rajibul Islam, “In physics, the Ising model is perhaps the most simple of the spin models, and yet is believed to represent a good description of physical phenomena ranging from ferromagnetism to frustration in spin glasses, and even neural networks. When we add an external magnetic field to this model, quantum properties come into play. Then the physics gets even more interesting.” From the viewpoint of the scientists, the ultimate goal is to engineer any spin (magnetic) model, such that they might probe different types of complex phenomena including their current pursuit of quantum magnetism.

This particular spin model has a computation angle: for some cases discovering the lowest energy configuration or ground state is classified as an “NP-complete” problem. This famous class of problems cannot be efficiently solved using conventional computers, with the most popular example being the “traveling salesman problem” of discovering the shortest route through a number of cities on a map. While properties of a nine ion spin system can be calculated, the group is fast approaching the number of spins wherein calculations of system properties will be impossible even with state-of-the-art computing technology.

In order to simulate a crystal, the first goal is to benchmark the simulator for small, simple interactions like ferromagnetism (the familiar type of magnetism found in bar magnets), where solutions to this special case are known. As Islam says, “In this manner we can have confidence in further simulations where theoretical predications are not possible.”

In the experiment, laser-cooled ions arrange in a stable crystal because they are charged particles that repel each other while the trap pushes from the outside. To create conditions for observing the transition to ferromagnetism, the researchers shine different colors of laser light onto an ion crystal.

Here, each ion represents a spin and can be thought of as a tiny bar magnet. The scientists first engineer two types of laser-atom interactions. The first laser is analogous to adding a magnetic field that will independently “tip” each tiny magnet (cause a spin flip).

The second interaction is called the Ising interaction and is the long-range spin-spin coupling that will ultimately give rise to an ordered ferromagnet. Imagine that invisible springs connect the ions together so that vibrations occurring on one side of the crystal affect other ions in the chain. This is called collective motion and is at the heart of controlling the magnetic spin-spin (ion-ion) interactions. To generate a spin-spin interaction, they need a force that depends on whether a particular bar magnet, or spin, has its north pole oriented up or down. This is accomplished by simultaneously applying different laser beams, whose colors are specially chosen with respect to the internal vibrations of the ion string.

The power of this design is that there is a ‘magnetic interaction control knob’ that the researchers can vary at will. This makes the protocol inherently versatile in that it can be extended to other types of spin models. As co-author and postdoctoral researcher Emily Edwards points out, “We can even tune the lasers so that the spins that are furthest apart in the ion crystal have the strongest magnetic interaction.” The scientists build up the simulator, one spin at a time, allowing them to explore system-size effects, such as how the transition to ferromagnetism sharpens with each additional particle (see Figure).

In pushing the limits of the simulator and extending studies beyond ground state phases, the team hopes to uncover new physics and in the process, understand the true potential of quantum simulators.

Edwards continues, “While the trapped ion approach deals with small numbers of particles, in the future we will be able to program arbitrary interactions between all pairs of spins. Such a fully-connected set of interacting spins will allow the simulation of systems that can never be understood using conventional computers.”

* “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)