  Achieving higher sensitivity is an earnest purpose for precision metrology.
As a response to this goal, the weak value amplification approach has been
developed for measuring ultra-small physical effects, realizing sensitivity
that had never been reached before. Encouraged by the successes, many efforts
have been devoted to obtain ultimate sensitivity of weak value amplification.
However, the benefit would be easily compromised in practice, because the cost
of significant reduction on signal intensity leads to an ultra-low
signal-to-noise ratio. In this work, we bridge this gap by proposing an
alternative weak value amplification approach, which provides sensitivity
several orders of magnitude higher than the standard approach while being
compatible with practical imperfections. In the proof-of-principle experiment
of measuring longitudinal phase change in time-domain, sensitivity up to
$5\times10^{-4}$ attosecond is exemplified. Our approach can be applied to
measure other small parameters with extremely high sensitivity, providing a new
method for future precision metrology.
