Communications of the ACM
Turning on Frustration
Camera images of different magnetic states in an ion trap.
Credit: C. Monroe / Joint Quantum Institute, University of Maryland
Frustration crops up throughout nature when conflicting constraints on a physical system compete with one another. The way nature resolves these conflicts often leads to exotic phases of matter that are poorly understood. The research group of Christopher Monroe at the Joint Quantum Institute, University of Maryland, explored how to frustrate a quantum magnet comprised of sixteen atomic ions — to date the largest ensemble of qubits to perform a simulation of quantum matter.
The results of their research are published as "Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quantum Simulator" in the latest issue of Science Magazine. The paper is also published on arXiv at http://arxiv.org/pdf/1210.0142v1.pdf.
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 the behaviors of complex material. Says Monroe, "With just 30 or so qubits, we should be able to study ordering and dynamics of this many-body system that cannot be predicted using conventional computers. In the future, make that a few hundred qubits and there's simply not enough room in the universe for all the memory required to do the calculation."
In this experiment, JQI physicists engineer a quantum magnet using lasers and ion qubits. The ion trap platform has long been a leader in the field of quantum information and is an ideal playground for quantum simulations. Ions are charged particles that interact strongly via the Coulomb force, which is an attraction/repulsion that decreases as particles separate. When a handful of positively charged ytterbium ions are thrown together, they repel each other, and, for this oblong ion trap, form a linear crystal. Each ion has two internal energy states that make up a qubit.
Laser beams can manipulate the Coulomb force to create tunable, long range magnetic-like interactions, where each ion qubit represents a tiny magnet*. Imagine that invisible springs connect the ions together. Vibrations occurring on one side of the crystal affect the entire crystal. This is called collective motion and is harnessed to generate a force that depends on how a magnet is oriented (which state the qubit is in). The team can program this state-dependent force by simultaneously applying multiple laser beams, whose colors (frequencies) are specially chosen with respect to the internal vibrations of the ion crystal. The amount of influence each magnet has on the rest of the chain primarily depends on the choice of laser frequencies. The crystal geometry has little to do with the interactions. In fact, for some laser configurations the ions that are farthest apart in space interact most strongly.
Phenomena due to this type of magnet-magnet interaction alone can be explained without quantum physics. An additional uniform magnetic field (here created with yet another laser beam) is necessary for introducing quantum phase transitions and entanglement. This added magnetic field (oriented perpendicular to the direction of the interactions) induces quantum fluctuations that can drive the system into different energy levels.
In the experiment, the long-range ion-ion interaction and a large effective magnetic field are turned on simultaneously. In the beginning of the simulation the ion magnets are oriented along the direction of the effective magnetic field. In the quantum world, if a magnet is pointing along some direction with certainty, its magnetic state along any perpendicular direction is totally random. Hence the system is in a disordered state along the perpendicular direction of magnetic [spin] interactions.
During the quantum simulation the magnetic field is reduced and the ion crystal goes from being in this disordered state, with each ion magnet pointing along a random direction, to being determined by the form of the magnetic interactions. For some cases of antiferromagnetic (AFM) interactions, the spins will end in a simple up-down-up-down-etc. configuration. With the turn of some knobs, the team can cause the AFM interactions to instead frustrate the crystal. For example, nearest neighbor AFM interactions can compete strongly with the next-nearest neighbor interactions and even the next-next-nearest neighbor constraints. The crystal can easily form various antiferromagnetic combinations, instead of the simple nearest neighbor antiferromagnet (up down up down). In fact, with a few technical upgrades, the researchers can potentially engineer situations where the magnets can reside in an exponentially large number of antiferromagnetic states, generating massive quantum entanglement that accompanies this frustration.
Previously, this same group of researchers performed quantum simulations of a ferromagnet (all magnets oriented same direction) and of the smallest system exhibiting frustration. Their ability to utilize the collective motion allows them to explore different facets of quantum magnetism. The team can 'at will' modify how the different collective modes contribute to magnetic order by merely changing the laser colors and/or the ion separation. This new work demonstrates the versatility of their system, even as particles are added. As lead author Rajibul Islam explains "We have a knob that adjusts the range of the interaction, something that is unavailable in real materials. This type of simulation could therefore help in the design of new types of materials that possess exotic properties, with potential applications to electrical transport, sensors, or transducers."
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*Physicists use mathematical spin models, such as the Ising model studied here, to understand quantum magnets, thus in this news article, for clarity the ions are called "magnets." In the language of the Science Magazine article, they are called "spins".
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