Quantum simulation of the Dirac equation
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 setups, in which parameter tunability allows access to different physical regimes. Here we perform a proofofprinciple quantum simulation of the onedimensional 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 negativeenergy spinor states, as well as the crossover from relativistic to nonrelativistic dynamics. The high level of control of trappedion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics.
 Publication:

Nature
 Pub Date:
 January 2010
 DOI:
 10.1038/nature08688
 arXiv:
 arXiv:0909.0674
 Bibcode:
 2010Natur.463...68G
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 5 pages