  We study the full entanglement dynamics of two uniformly accelerated
Unruh-DeWitt detectors with no direct interaction in between but each coupled
to a common quantum field and moving back-to-back in the field vacuum. For two
detectors initially prepared in a separable state our exact results show that
quantum entanglement between the detectors can be created by the quantum field
under some specific circumstances, though each detector never enters the
other's light cone in this setup. In the weak coupling limit, this entanglement
creation can occur only if the initial moment is placed early enough and the
proper acceleration of the detectors is not too large or too small compared to
the natural frequency of the detectors. Once entanglement is created it lasts
only a finite duration, and always disappears at late times. Prior result by
Reznik derived using the time-dependent perturbation theory with extended
integration domain is shown to be a limiting case of our exact solutions at
some specific moment. In the strong coupling and high acceleration regime,
vacuum fluctuations experienced by each detector locally always dominate over
the cross correlations between the detectors, so entanglement between the
detectors will never be generated.
