We show that the magnetoplasmon collective modes in quasi-two-dimensional
semiconductor quantum dots can be parametrically amplified by periodically
modulating the magnetic field perpendicular to the nanostructure. The two
magnetoplasmon modes are excited and amplified simultaneously, leading to an
exponential growth of the number of bosonic excitations in the system. We
further demonstrate that damping mechanisms as well as anharmonicities in the
confinement of the quantum dot lead to a saturation of the parametric
amplification. This work constitutes a first step towards parametric
amplification of collective modes in many-body fermionic systems beyond one
dimension.Comment: 12 pages, 5 figures; published versio