  The "trilobite" type of molecule, predicted in 2000 and observed
experimentally in 2015, arises when a Rydberg electron exerts a weak attractive
force on a neutral ground state atom. Such molecules have bond lengths
exceeding 100 nm. The ultra-long-range chemical bond between the two atoms is a
nonperturbative linear combination of the many degenerate electronic states
associated with high principal quantum numbers, and the resulting electron
probability distribution closely resembles a fossil trilobite from antiquity.
We show how to coherently engineer this same long-range orbital through a
sequence of electric and magnetic field pulses even when the ground state atom
is not present, and propose several methods to observe the resulting orbital.
The existence of such a ghost chemical bond in which an electron reaches out
from one atom to a nonexistent second atom is a consequence of the high level
degeneracy.
