Analogue of cosmological particle creation in an ion trap

We study phonons in a dynamical chain of ions confined by a trap with a time-dependent (axial) potential strength and demonstrate that they behave in the same way as quantum fields in an expanding/contracting universe. Based on this analogy, we present a scheme for the detection of the analogue of cosmological particle creation which should be feasible with present-day technology. In order to test the quantum nature of the particle creation mechanism and to distinguish it from classical effects such as heating, we propose to measure the two-phonon amplitude via the $2^{\mathrm{n}\mathrm{d}}$ red side-band and to compare it with the one-phonon amplitude ($1^{\mathrm{s}\mathrm{t}}$ red side-band). PACS: 04.62.+v, 98.80.-k, 42.50.Vk, 32.80.Pj.