Quantum optomechanical system in a Mach-Zehnder interferometer

We consider an oscillating micromirror replacing one of the two fixed mirrors of a Mach-Zehnder interferometer. In this ideal optical set-up the quantum oscillator is subjected to the radiation pressure interaction of travelling light waves, no cavity is involved. This configuration shows that squeezed light can be generated by pure scattering on a quantum system, without involving a cavity. The squeezing can be detected at the output ports of the interferometer either by direct detection or by measuring the spectrum of the difference current. We use the Hudson-Parthasarathy equation to model the global evolution. It can describe the scattering of photons and the resulting radiation pressure interaction on the quantum oscillator. It allows to consider also the interaction with a thermal bath. In this way we have a unitary dynamics giving the evolution of oscillator and fields. The Bose fields of quantum stochastic calculus and the related generalized Weyl operators allow to describe the whole optical circuit. By working in the Heisenberg picture, the quantum Langevin equations for position and momentum and the output fields arise, which are used to describe the monitoring in continuous time of the light at the output ports. In the case of strong laser and weak radiation pressure interaction highly non-classical light is produced, and this can be revealed either by direct detection (a negative Mandel Q-parameter is found), either by the intensity spectrum of the difference current of two photodetector; in the second case a nearly complete cancellation of the shot noise can be reached. In this last case it appears that the Mach-Zehnder configuration together with the detection of the difference current corresponds to an homodyne detection scheme, so that we can say that the apparatus is measuring the spectrum of squeezing.