  Gravitational waves reaching a Michelson interferometer are expected to
induce a very small change in the length of its arms causing a phase shift
between them, but it is very difficult to observe the extremely small phase
shift signals produced. In the present letter we show that the gravitational
waves signal could be amplified by orders of magnitude by using very special
conditions for a coherent-squeezed Michelson interferometer in which the
coherent state enters one port of the interferometer and the squeezed vacuum
enters in the other port. We treat the case where without the gravitational
induced phase shift the very strong coherent state goes out of one output port
while the squeezed vacuum goes out the other output port (the ``dark'' port).
While the phase shift produced by the gravitation waves does not give any
significant change in the strong coherent output, the light intensity in the
``dark'' port is amplified with decreased fluctuations as the squeezing
increases.
