Quantum simulation of the Dirac equation

Quantum simulation of the Dirac equation The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation—relativistic quantum mechanics—is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein’s paradox and ‘Zitterbewegung’, an unexpected quivering motion of a free relativistic quantum particle . These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups , in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nature Nature Publishing Group (NPG)

Quantum simulation of the Dirac equation

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Publisher
Nature Publishing Group (NPG)
Copyright
Copyright © 2010 Macmillan Publishers Limited. All rights reserved
ISSN
0028-0836
eISSN
1476-4687
D.O.I.
10.1038/nature08688
Publisher site
See Article on Publisher Site

Abstract

The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation—relativistic quantum mechanics—is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein’s paradox and ‘Zitterbewegung’, an unexpected quivering motion of a free relativistic quantum particle . These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups , in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental

Journal

NatureNature Publishing Group (NPG)

Published: Jan 7, 2010

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