The phase state revisited: the Heisenberg limit in a quantum nondemolitionmeasurement and the nonclassical depth of the state

We consider a quantum nondemolition measurement, the apparatus consisting o f a Mach-Zehnder single-photon (signal) interferometer where in one arm the signal interacts (through a Kerr medium) with a probe beam. This interacti on affects the visibility of the interferometer and induces a phase shift i n the state of the probe beam. Here we investigate the effects of such inte raction when the probe state is in the truncated phase state, \Theta (m)> = (1 + N)(-1/2) Sigma (N)(n=0) e(in Thetam)\n >, analyze the Heisenberg limi t for the phase shift measurement, and its possible relation to the nonclas sical depth of the state. (C) 2001 Published by Elsevier Science B.V.