  We investigate the dynamics of a three-dimensional Bose-Einstein condensate
of ultracold atomic gases with a soft-core shape long-range interaction, which
is induced by laser dressing the atoms to a highly excited Rydberg state. For a
homogeneous condensate, the long-range interaction drastically alters the
dispersion relation of the excitation, supporting both roton and maxon modes.
Rotons are typically responsible for the creation of supersolids, while maxons
are normally dynamically unstable in BECs with dipolar interactions. We show
that maxon modes in the Rydberg-dressed condensate, on the contrary, are
dynamically stable. We find that the maxon modes can be excited through an
interaction quench, i.e. turning on the soft-core interaction instantaneously.
The emergence of the maxon modes is accompanied by oscillations at high
frequencies in the quantum depletion, while rotons lead to much slower
oscillations. The dynamically stable excitation of the roton and maxon modes
leads to persistent oscillations in the quantum depletion. Through a
self-consistent Bogoliubov approach, we identify the dependence of the maxon
mode on the soft-core interaction. Our study shows that maxon and roton modes
can be excited dynamically and simultaneously by quenching Rydberg-dressed
long-range interactions. This is relevant to current studies in creating and
probing exotic states of matter with ultracold atomic gases.
