Dynamical excitation of the Bogoliubov vacuum in a two-component Bose-Einstein condensates.

We investigate the parametric amplification of the zero-point fluctuations in the spin modes of a two-component Bose-Einstein condensate, that is triggered by the dynamical evolution of the background density. By working in the Thomas-Fermi limit, we first develop a theoretical model for the free dynamics of the Bogoliubov excitations, in a system that is trapped by a time-dependent harmonic potential. Furthermore, we perform an ab-initio numerical study of the two-body (density-density) correlations in the more general inhomogeneous configuration. We consider both the cases of the expanding and oscillating systems. In the former case, we find that the signal due to the particle creation in the spin modes, driven by the dynamical evolution of the overall density of the system, is weak and does not show any particular feature. In the oscillating case instead, because of the onset of resonance between the density oscillations and certain spin modes, the density correlations show a strong signature of the parametric amplification, displaying a clear imprint of the structure of the resonant mode.