Generation of Kerr non-Gaussian motional states of trapped ions

¹ Institute for Theoretical Physics II, University of Erlangen-Nuremberg - 91058 Erlangen, Germany, EU
² Max Planck Institute for the Science of Light - 91058 Erlangen, Germany, EU
³ Institute of Optics, Information and Photonics, University of Erlangen-Nuremberg - 91058 Erlangen, Germany, EU

^a alessandro.villar@mpl.mpg.de

Received: 14 January 2011
Accepted: 20 April 2011

Abstract

Non-Gaussian states represent a powerful resource for quantum information protocols in the continuous variables regime. Cat states, in particular, have been produced in the motional degree of freedom of trapped ions by controlled displacements dependent on the ionic internal state. An alternative method harnesses the Kerr nonlinearity naturally present in this kind of system. We perform detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits generation of all other complex non-Gaussian states with negative Wigner functions resulting from Kerr nonlinear interaction. Especially, superpositions of several coherent states are achieved at a fraction of the time necessary to produce the cat state.