  In a quantum-noise limited system, weak-value amplification using
post-selection normally does not produce more sensitive measurements than
standard methods for ideal detectors: the increased weak value is compensated
by the reduced power due to the small post-selection probability. Here we
experimentally demonstrate recycled weak-value measurements using a pulsed
light source and optical switch to enable nearly deterministic weak-value
amplification of a mirror tilt. Using photon counting detectors, we demonstrate
a signal improvement by a factor of $4.4 \pm 0.2$ and a signal-to-noise ratio
improvement of $2.10 \pm 0.06$, compared to a single-pass weak-value
experiment, and also compared to a conventional direct measurement of the tilt.
The signal-to-noise ratio improvement could reach around 6 for the parameters
of this experiment, assuming lower loss elements.
