  We investigate the interaction between a moving detector and a quantum field,
especially about how the trajectory of the detector would affect the vacuum
fluctuations when the detector is moves in a quantum field (the Unruh effect).
We focus on two moving detectors system for future application in quantum
teleportation. We find that the rajectory of a uniformly accelerated detector
in Rindler space cannot be extended to a trajectory in which a detector moves
at constant velocity. Based on our previous work, we redo the calculations and
find that a term is missing from the past calculations, and we also find that
there are some restrictions on the values for the parameters in the solutions.
In addition, without inclusion of the missing term, the variance from the
quantum field for the inertial detector will be zero and is unlikely in such a
system. When all these points are combined, there is a difference in the
two-point correlation function between the inertial detector and the
accelerated detector in the early-time region. The influence of proper
acceleration can be seen in the two-point correlation functions. This might
play a role in the quantum teleportation process and be worth studying
thoroughly.
