Ion trap analogue of particle creation in black holes and cosmology

We consider the transversal modes of ions in a linear radio frequency (rf) trap where we control the time dependent axial confinement to show that we can excite quanta of motion via a two-mode squeezing process. This effect is analogous to phenomena predicted to occur during the evaporation of black holes and cosmological particle creation, in general out of reach for experimental investigation. As substantial advantage of this proposal in comparison to previous ones we propose to exploit radial and axial modes simultaneously to permit experimental access of these effects based on state-of-the-art technology. In addition, we propose to create and explore entanglement, starting with two ions, and relate the results to fundamental aspects of the entropy of black holes.