Published online 6 January 2010 | Nature | doi:10.1038/news.2010.2

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Quivering ions pass quantum test

Table-top experiments unlock quantum realm predicted by Dirac equation.

Paul DiracPaul Dirac: author of the equation which predicts quantum quivering.Bettmann/CORBIS

Trapped ions masquerading as high-speed particles have been used to confirm a bizarre 80-year-old prediction of quantum mechanics.

Quantum particles racing at close to the speed of light were first predicted to jitter violently as they moved — a phenomenon known as the Zitterbewegung — in 1930, by the father of quantum mechanics, Erwin Schrödinger. The prediction was based on the Dirac equation, developed by British physicist Paul Dirac in 1928, which merges quantum mechanics with special relativity to describe how particles such as electrons behave.

"The motion is particularly unexpected because there aren't any forces acting on the particle to make it quiver," says physicist Rene Gerritsma at the Institute for Quantum Optics and Quantum Information in Innsbruck, Austria.

Instead, the jitter is caused by a combination of two effects. The first is the quantum property of superposition, which allows quantum objects to be in two mutually exclusive states or positions at the same time. The second is the existence of antimatter.

“If the Dirac equation is a true description of reality, then Zitterbewegung exists.”

Rene Gerritsma
Institute for Quantum Optics and Quantum Information in Innsbruck, Austria

When a particle is in a superposition between its matter and antimatter states, these two contradictory sides of its personality should interfere, setting the particle quivering, explains Gerritsma. However, the phenomenon has never been observed experimentally because the motion is too small and too fast to detect in real quantum systems.

"For a long time, people have debated if Zitterbewegung is a real effect or something artificial that falls out of the equation that describes the situation, the Dirac equation," says Gerritsma, "and if it is real, whether it could ever be measured."

Shake it up

Gerritsma and his colleagues have now simulated Zitterbewegung by manipulating a trapped ion with lasers. "It turns out that the mathematical model that describes the interaction of the lasers with the ion mirrors the Dirac equation," says Gerristma. Crucially, changing the frequency and intensity of the laser allowed the researchers to tune two key properties of the simulation: the effective mass of the quantum particle being simulated by the ion, and the effective speed of light in the system. The latter could be dialled down to less than 1 millimetre per second, slow enough for Zitterbewegung to be detected in the lab.

To mimic the superposition between matter and antimatter, the team manipulated an electron within the ion so that it existed in a superposition of both an excited, high-energy state and a non-excited, low-energy state. Computer simulations of Zitterbewegung suggested that under these conditions the ion should tremble back and forth over a distance of about 10 nanometres. This jitter would be too small to see directly, so the team shone a second laser on the ion that stopped it in its tracks, making it emit fluorescent light. The amount of fluorescence marked how far it had moved from its central position, explains Gerritsma.

In this way, the team could obtain snapshots of the ion's position after repeated runs of the experiment — each time halting the Zitterbewegung after a slightly different length of time, and building up a statistical pattern of the quivering motion that matched the calculations. "Our results show that if the Dirac equation is a true description of reality, then Zitterbewegung exists," says Gerritsma. The team's results are published in Nature1.

The new alchemy

The technique used by Gerritsma's team was originally outlined in 2007 by Tobias Schätz of the Max Planck Institute for Quantum Optics in Garching, Germany, and his colleagues2. Such simulations are important because limitations on processing power mean that classical computers can only model the behaviour of a few tens of quantum particles before the task becomes too much for them, says Schätz. "Quantum simulations are emerging in a lot of fields as a shortcut to quantum computation to help us model the behaviour of complex systems that occur in reality."

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"If the team can upgrade this to a few tens of particles, then this will really challenge simulations on classical computers," says Alán Aspuru-Guzik, a quantum chemist at Harvard University in Cambridge, Massachusetts.

In 2008, Schätz and his colleagues used trapped ions to simulate the magnetic properties of a quantum system3. He hopes that quantum simulations such as this and those by Gerritsma's team will eventually help to explain why certain materials, such as metal-oxide ceramics, can act as superconductors at relatively high temperatures. "This understanding is essential if we ever hope to use superconductivity at room temperature," he says. "Without it, high-temperature superconductivity is just alchemy." 

  • References

    1. Gerritsma, R. et al. Nature 463, 68-71 (2010). | Article
    2. Lamatta, L., León, J., Schätz, T. & Solano, E. Phys. Rev. Lett. 98, 253005 (2007). | Article | PubMed | ChemPort |
    3. Friedenauer, H., Schmitz, H., Glueckert, J. T., Porras, D. & Schaetz, T. Nature Phys. 4, 757-761 (2008). | Article | ChemPort |

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  • #61491

    I think the Dirac Equation reduces to the Schrodinger Equation (with the Pauli spin-term) in the limits where the antiparticle probabilities are low, and when pc << mc2.

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