Quantum simulation of the Klein paradox with trapped ions

Abstract

We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a frame-by-frame visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.© 2011 American Physical Society. ; We gratefully acknowledge support by the Austrian Science Fund (FWF), by the European Commission (Marie-Curie program), by the Institut fu¨r Quanteninformation GmbH and IARPA. E. S. thanks for support from the Spanish MICINN project FIS2009- 12773-C02-01, Basque Government Grant IT472-10, ITN CCQED and SOLID European projects. J. C. acknowledges the Basque Government BFI08.211.J. J. G.-R. acknowledges the Spanish projects MICINN FIS2009-10061 and QUITEMAD. ; Peer Reviewed