  It is known that quantum interference can disappear with the mere possibility
of distinguishability without actually performing the act. We create such
distinguishability in an unbalanced SU(1,1) interferometer and indeed observe
no interference in the direct photodetection of the outputs. On the other hand,
such distinguishability can be erased with a projective measurement. Here, we
report a method of homodyne detection that can also recover interference
effect. We find that it is the indistinguishability in amplitude measurement
that leads to the recovery of interference, and the quantum nature of homodyne
detection and the detector's slow response time both play an essential role.
This is different from the quantum eraser schemes mentioned above. It
demonstrates that quantum interference occurs in the measurement processes.
With no need for path compensation, the unbalanced interferometers studied here
should have practical applications in quantum metrology and sensing.
