  We study the finite time response of an Unruh-DeWitt particle detector
described by a qubit (two-level system) moving with uniform constant
acceleration in maximally symmetric spacetimes. The $D$ dimensional massless
fermionic response function in de Sitter (dS) background is found to be
identical to that of a detector linearly coupled to a massless scalar field in
$2D$ dimensional dS background. Furthermore, we visit the status of Huygen's
principle in the Unruh radiation observed by the detector.
