  The change in the relative phase between two light fields serves as a basic
principle for the measurement of the physical quantity that guides this change.
It would therefore be highly advantageous if the relative phase could be
amplified to enhance the measurement resolution. One well-known method for
phase amplification involves the use of the multi-photon number and path
entangled state known as the NOON state; however, a high-number NOON state is
very difficult to prepare and is highly sensitive to optical losses. Here we
propose and experimentally demonstrate in principle a phase amplifier scheme
with the assistance of a harmonic generation process. The relative phase
difference between two polarization modes in a polarized interferometer is
amplified coherently four times with cascaded second-harmonic generation
processes. We demonstrate that these amplification processes can be recycled
and therefore have the potential to realize much higher numbers of multiple
amplification steps. The phase amplification method presented here shows
considerable advantages over the method based on NOON states and will be highly
promising for use in precision optical measurements.
