  The permanent electric dipole moment (EDM) of the $^{171}$Yb $(I=1/2)$ atom
is measured with atoms held in an optical dipole trap (ODT). By enabling a
cycling transition that is simultaneously spin-selective and spin-preserving, a
quantum non-demolition measurement with a spin-detection efficiency of 50$\%$
is realized. A systematic effect due to parity mixing induced by a static E
field is observed, and is suppressed by averaging between measurements with
ODTs in opposite directions. The coherent spin precession time is found to be
much longer than 300 s. The EDM is determined to be
$d({\rm^{171}Yb})={\color{black}(-6.8\pm5.1_{\rm stat}\pm1.2_{\rm
syst})\times10^{-27}\ e\ \rm cm}$, leading to an upper limit of
$|d({\rm^{171}Yb})|<{\color{black}1.5\times10^{-26}\ e\ \rm cm}$ ($95\%$ C.L.).
These measurement techniques can be adapted to search for the EDM of
$^{225}$Ra.
