  We investigate the quantum dynamics of ultra-long-range trilobite molecules
exposed to homogeneous electric fields. A trilobite molecule consists of a
Rydberg atom and a ground-state atom, which is trapped at large internuclear
distances in an oscillatory potential due to scattering of the Rydberg electron
off the ground-state atom. Within the Born-Oppenheimer approximation, we derive
an analytic expression for the two-dimensional adiabatic electronic potential
energy surface in weak electric fields valid up to 500 V/m. This is used to
unravel the molecular quantum dynamics employing the Multi-Configurational
Time-Dependent Hartree method. Quenches of the electric field are performed to
trigger the wave packet dynamics including the case of field inversion.
Depending on the initial wave packet, we observe radial intra-well and
inter-well oscillations as well as angular oscillations and rotations of the
respective one-body probability densities. Opportunities to control the
molecular configuration are identified, a specific example being the
possibility to superimpose different molecular bond lengths by a series of
periodic quenches of the electric field.
