Letter

Nature 463, 68-71 (7 January 2010) | doi:10.1038/nature08688; Received 31 August 2009; Accepted 11 November 2009

Quantum simulation of the Dirac equation

R. Gerritsma1,2, G. Kirchmair1,2, F. Zähringer1,2, E. Solano3,4, R. Blatt1,2 & C. F. Roos1,2

  1. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria
  2. Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
  3. Departamento de Química Física, Universidad del País Vasco - Euskal Herriko Unibertsitatea, Apartado 644, 48080 Bilbao, Spain
  4. IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011 Bilbao, Spain

Correspondence to: C. F. Roos1,2 Correspondence and requests for materials should be addressed to C.F.R. (Email: christian.roos@uibk.ac.at).

The Dirac equation1 successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter2 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 paradox3 and ‘Zitterbewegung’, an unexpected quivering motion of a free relativistic quantum particle4. 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-ups5, 6, 7, 8, 9, 10, 11, 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 ion7 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 parameters makes it possible to simulate textbook examples of relativistic quantum physics.

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