Magdalena Stobińska

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 existent in this kind of system. We present detailed calculations confirming its feasibility for typical experimental conditions. Additionally, this method permits the generation of complex non-Gaussian states with negative Wigner functions. Especially, superpositions of many coherent states are achieved at a fraction of the time necessary to produce the cat state.

The efficient interaction between single photons and single matter objects in free space is of key importance for quantum technologies. An experimental setup for testing this possibility involves single two-level ion trapped at the focus of a parabolic metallic mirror. We study the conditions for the setup, under which the assumption about the free-space mode structure of the radiation field in the vicinity of the atom is justified. In our analysis we apply vectorial properties of light by including polarization degree of freedom. We look for possible changes in the spontaneous emission rate of the atom resulting from the presence of the parabolic boundary conditions.

According to the Gottesmann-Knill theorem the non-Gaussian states are necessary component for a nontrivial quantum computation. We show two efficient and deterministic methods of $χ^{(3)}$ non-Gaussian state generation for a cavity mode using a single trapped ion. Both require ion motional state transfer to the cavity field. The methods are experimentally feasible. The first is based on the well-known protocol for an ion finite motional superposition state generation. It allows for an arbitrary good approximation of $χ^{(3)}$ non-Gaussian states. We give criteria based on the Wigner function which quantify the error resulting from the approximation. The second and novel method enables an exact non-Gaussian state generation using one laser pulse only.

We present an effective method of coherent state superposition (cat state) generation using single trapped ion in a Paul trap. The method is experimentally feasible for coherent states with amplitude $α\le 2$ using available technology. It works both in and beyond the Lamb-Dicke regime.