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 or 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 2nd red sideband transition and to compare it with the one-phonon amplitude (1st red sideband).