This work was done as part of the MSc of Yoav Sagi. I have considered two apparently different questions; First, what is the correct treatment of the class of continuous measurements in quantum optics. Second, what is the the role of coherent states in quantum optics experiments. I have shown that the answers to both these questions are linked. The coherent basis in quantum optics is the stable basis for systems that are being measured continuously, in the sense that every initial state of the system will collapse into a specific coherent state as a result of a continuous measurement. I have shown that the instability of non coherent states is an outcome of a spontaneous symmetry breaking imposed by the measurement process. Moreover, losses in the optical components which cause uncertainty in the number of photons in the system, drive to such a symmetry breaking. Thus, the conclusion is that sooner or later all optical systems end in a coherent state, regardless of their initial states.

I start by considering the problem of two cavities, a 50%-50% beam splitter and detectors. Using the Monte-Carlo Wave Functions method, it is shown that even when the cavities are initially in Fock states, the detectors’ readings exhibit a 100% visibility interference in any single realization. This surprising result, which was first discussed by K. Molmer (PRA 55, 3195, 1997), would be expected for cavities which are initially in coherent states. I show that the ”phase collapse” is occurring in the first few ‘clicks’ of the detector.

I continue by analyzing the same setup using the orthodox (non-stochastic) Langevin method. The expectation values for the detectors’ readings are found to exhibit no interference in the case where the cavities are initially in Fock states. At first sight, this result contradicts the MCWF method result. Nevertheless, there is no contradiction because the trajectory phase distribution in the MCWF method is random. This results in average values exhibiting no interference. Nevertheless, by correlation function analysis it is possible to show that even in the Langevin method there are remnants of the interference observed in the MCWF method.

The intriguing question whether we will observe a 100% visibility interference in one experimental run requires an experimental investigation. The main difficulty in realizing this setup is the creation of Fock states in the cavities. Until today only Fock states with very small occupation numbers were successfully realized in the laboratory. I therefore propose a different path which conserves the interesting characteristics of the original setup, but avoids the difficulties discussed above. In the proposed experiment, I use the process of parametric down-conversion to create a non-classical initial state in the cavities. This experiment is still waiting to be performed, so if you are interested in a collaboration in this subject – leave me a note.

The two cavities setup is a typical two sources optical experiment, which clearly display a spontaneous symmetry breaking. The arguments regarding the continuous measurements are applicable to a broader range of quantum optics problems. In fact, the physical interpretation of the detection as a symmetry breaking field can be employed to other bosonic systems. In all these phase symmetric bosonic systems the continuous measurement chooses a phase to the system according to a quantum distribution function. In this respect, the coherent basis is the natural basis for describing many quantum optics systems.